Publications

Summary

1/2017

publications: 11 in journals with IF, 23 in conference proceedings (16 Web of Science/WoS, 25 Scopus/Sco, 30 Google Scholar/GS, 27 RIV)
citations: 362 (114 WoS, 162 Sco, 349 GS) − 25 co-citations (14 WoS, 11 Sco, 24 GS) + 39 selfcitations (9 WoS, 24 Sco, 39 GS)
H-index: 12 (7 WoS, 8 Sco, 12 GS), without selfcitations 11 (7 WoS, 8 Sco, 11 GS), without self and co-citations 11 (7 WoS, 8 Sco, 11 GS)

Citations

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Journal papers

  1. Outrata Jan: A lattice-free concept lattice update algorithm.
    Int. Journal of General Systems 45(2)(2016), pp. 211–231.
    [Taylor & Francis Group,
    DOI 10.1080/03081079.2015.1072928, ISSN 0308–1079 (paper), 1563–5104 (online)]
    IF: 1.637, DB: WoS (WOS:000372036100008), Sco, GS
    abstract | 1 selfcitation (1 Sco, 1 GS)

    Abstract Upon a change of input data, one usually wants an update of output computed from the data rather than recomputing the whole output over again. In Formal Concept Analysis, update of concept lattice of input data when introducing new objects to the data can be done by any of the so-called incremental algorithms for computing concept lattice. The algorithms use and update the lattice while introducing new objects to input data one by one. The present concept lattice of input data without the new objects is thus required by the computation. However, the lattice can be large and may not fit into memory. In this paper, we propose an efficient algorithm for updating the lattice from the present and new objects only, not requiring the possibly large concept lattice of present objects. The algorithm results as a modification of the Close-by-One algorithm for computing the set of all formal concepts, or its modifications like Fast Close-by-One, Parallel Close-by-One or Parallel Fast Close-by-One, to compute new and modified formal concepts and the changes of the lattice order relation only. The algorithm can be used not only for updating the lattice when new objects are introduced but also when some existing objects are removed from the input data or attributes of the objects are changed. We describe the algorithm, discuss efficiency issues and present an experimental evaluation of its performance and a comparison with the AddIntent incremental algorithm for computing concept lattice.

    Citations
    1. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
      In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376.
      GS
  2. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
    Annals of Mathematics and Artificial Intelligence 72(1–2)(2014), pp. 3–22.
    [Springer,
    DOI 10.1007/s10472-014-9414-x, ISSN 1012–2443 (paper), 1573–7470 (online)]
    IF: 0.691, DB: WoS (WOS:000342438500002), Sco, GS, RIV
    PDF | abstract | 4 citations (2 WoS, 2 Sco, 4 GS) − 1 co-citation (1 GS) + 1 selfcitation (1 Sco, 1 GS)

    Abstract We explore a utilization of Boolean matrix factorization for data preprocessing in classification of Boolean data. In our previous work, we demonstrated that preprocessing that consists in replacing the original Boolean attributes by factors, i.e. new Boolean attributes obtained from the original ones by Boolean matrix factorization, can improve classification quality. The aim of this paper is to explore the question of how the various Boolean factorization methods that were proposed in the literature impact the quality of classification. In particular, we compare five factorization methods, present experimental results, and outline issues for future research.

    Citations
    1. Trnečka Martin: Decompositions of matrices with relational data: foundations and algorithms.
      Dissertation Thesis, 2016
      GS
    2. Ignatov D. I.: Introduction to formal concept analysis and its applications in information retrieval and related fields.
      In: 8th Russian Summer School on Information Retrieval, RuSSIR 2014, Communications in Computer and Information Science 505, 2015, pp. 42–141.
      WoS, Sco, GS
    3. Ignatov Dmitry I., Gnatyshak Dmitry V., Kuznetsov Sergei O., Mirkin Boris G.: Triadic Formal Concept Analysis and triclustering: searching for optimal patterns.
      Machine Learning 101(1-3)(2015), pp. 271–302.
      WoS, Sco, GS
    4. Sun Yuan, Ye Shiwei, Shi Huiyang, Wang Haobo, Sun Yi: Maximum likelihood estimation based DINA model and Q-matrix learning.
      In: Proceedings of 2014 IEEE International Conference on Behavior, Economic and Social Computing (BESC 2014), 2014, pp. 1–6.
      GS
    5. Belohlavek Radim, Outrata Jan, Trnecka Martin: How to assess quality of BMF algorithms?.
      In: Yager R., Sgurev V., Hadjiski M., Jotsov V. (Eds.): Proceedings of the IEEE 8th International Conference on Intelligent Systems, IS 2016, 2016, pp. 227–233.
      Sco, GS
  3. Belohlavek Radim, Grissa Dhouha, Guillaume Silvie, Mephu Nguifo Engelbert, Outrata Jan: Boolean factors as a means of clustering of interestingness measures of association rules.
    Annals of Mathematics and Artificial Intelligence 70(1–2)(2014), pp. 151–184.
    [Springer,
    DOI 10.1007/s10472-013-9370-x, ISSN 1012–2443 (paper), 1573–7470 (online)]
    IF: 0.691, DB: WoS (WOS:000334510500008), Sco, GS, RIV
    PDF | abstract | 4 citations (1 Sco, 4 GS) − 1 co-citation (1 GS)

    Abstract Measures of interestingness play a crucial role in association rule mining. An important methodological problem, on which several papers appeared in the literature, is to provide a reasonable classification of the measures. In this paper, we explore Boolean factor analysis, which uses formal concepts corresponding to classes of measures as factors, for the purpose of clustering of the measures. Unlike the existing studies, our method reveals overlapping clusters of interestingness measures. We argue that the overlap between clusters is a desired feature of natural groupings of measures and that because formal concepts are used as factors in Boolean factor analysis, the resulting clusters have a clear meaning and are easy to interpret. We conduct three case studies on clustering of measures, provide interpretations of the resulting clusters and compare the results to those of the previous approaches reported in the literature.

    Citations
    1. de Carvalho V. O., de Padua R., Rezende S. O.: Solving the problem of selecting suitable objective measures by clustering association rules through the measures themselves.
      In: Freivalds R. M., Engels G., Catania B. (Eds.): 42nd International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2016), Lecture Notes in Computer Science 9587, 2016, pp. 505–517.
      Sco, GS
    2. Bong Kok Keong, Joest Matthias, Quix Christoph, Anwar Toni: Automated Interestingness Measure Selection for Exhibition Recommender Systems.
      In: Nguyen N. T., Attachoo B., Trawiński B., Somboonviwat K. (Eds.): Intelligent Information and Database Systems, 6th Asian Conference, ACIIDS 2014, Proceedings, Part I, Lecture Notes in Computer Science 8397, 2014, pp. 221–231.
      GS
    3. Grissa Dhouha: Etude comportementale des mesures d'intérêt d'extraction de connaissances.
      Dissertation Thesis, 2013, 223 pp.
      GS
    4. Kumar Ch. Aswani: Fuzzy clustering-based formal concept analysis for association rules mining.
      Applied Artificial Intelligence 26(3)(2012), pp. 274–301.
      GS
  4. Krajca Petr, Outrata Jan, Vychodil Vilém: Computing formal concepts by attribute sorting.
    Fundamenta Informaticae 115(4)(2012), pp. 395–417.
    [IOS Press,
    DOI 10.3233/FI-2012-661, ISSN 0169–2968 (paper), 1875–8681 (online)]
    IF: 0.399, DB: WoS (WOS:000304190500008), Sco, GS, RIV
    PDF | abstract | 3 citations (2 WoS, 3 Sco, 3 GS) + 1 selfcitation (1 Sco, 1 GS)

    Abstract We present a novel approach to compute formal concepts of formal context. In terms of operations with Boolean matrices, the presented algorithm computes all maximal rectangles of the input Boolean matrix which are full of 1s. The algorithm combines basic ideas of previous approaches with our recent observations on the influence of attribute permutations and attribute sorting on the number of formal concepts which are computed multiple times. As a result, we present algorithm which computes formal concepts by successive context reduction and attribute sorting. We prove its soundness, discuss its complexity and efficiency, and show that it outperforms other algorithms from the CbO family in terms of substantially lower numbers of formal concepts which are computed multiple times.

    Citations
    1. Adaricheva Kira V., Nation James B.: Discovery of the D-basis in binary tables based on hypergraph dualization.
      Theoretical Computer Science 658(2017), pp. 307–315.
      Sco, GS
    2. Poelmans Jonas, Kuznetsov Sergei O., Ignatov Dmitry I., Dedene Guido: Formal Concept Analysis in knowledge processing: A survey on models and techniques.
      Expert Systems with Applications 40(16)(2013), pp. 6601–6623.
      WoS, Sco, GS
    3. Kuznetsov Sergei O., Poelmans Jonas: Knowledge representation and processing with formal concept analysis.
      Wiley Interdisciplinary Reviews-Data Mining and Knowledge Discovery 3(3)(2013), pp. 200–215.
      WoS, Sco, GS
    4. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
      In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376.
      GS
  5. Outrata Jan, Vychodil Vilém: Fast Algorithm for Computing Fixpoints of Galois Connections Induced by Object-Attribute Relational Data.
    Information Sciences 185(1)(2012), pp. 114–127.
    [Elsevier,
    DOI 10.1016/j.ins.2011.09.023, ISSN 0020–0255]
    IF: 3.643, DB: WoS (WOS:000297611600008), Sco, GS, RIV
    PDF | abstract | 28 citations (13 WoS, 16 Sco, 26 GS) + 5 selfcitations (3 WoS, 5 Sco, 5 GS)

    Abstract Fixpoints of Galois connections induced by object-attribute data tables represent important patterns that can be found in relational data. Such patterns are used in several data mining disciplines including formal concept analysis, frequent itemset and association rule mining, and Boolean factor analysis. In this paper we propose efficient algorithm for listing all fixpoints of Galois connections induced by object-attribute data. The algorithm, called FCbO, results as a modification of Kuznetsov's CbO in which we use more efficient canonicity test. We describe the algorithm, prove its correctness, discuss efficiency issues, and present an experimental evaluation of its performance and comparison with other algorithms.

    Citations
    1. Zhi Huilai, Li Jinhai: Influence of dynamical changes on concept lattice and implication rules.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–11.
      GS
    2. Trnečka Martin: Decompositions of matrices with relational data: foundations and algorithms.
      Dissertation Thesis, 2016
      GS
    3. Qian Ting, Wei Ling, Qi Jianjun: Decomposition methods of formal contexts to construct concept lattices.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–14.
      GS
    4. Li Xin, Shao Ming-Wen, Zhao Xing-Min: Constructing lattice based on irreducible concepts.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–14.
      GS
    5. Kodagoda Nuwan, Pulasinghe Koliya: Comparision Between Features of CbO based Algorithms for Generating Formal Concepts.
      International Journal of Conceptual Structures and Smart Applications 4(1)(2016).
      GS
    6. Naidenova Xenia A., Parkhomenko Vladimir A., Shvetsov Konstantin Vladimirovich, Yusupov Vladislav, Kuzina Raisa: Modification of good tests in dynamic contexts: Application to modeling intellectual development of cadets.
      In: Ojeda-Aciego M., Lepskiy A., Ignatov D.I. (Eds.): 2nd International Workshop on Soft Computing Applications and Knowledge Discovery, SCAKD 2016, 2016, pp. 51–62.
      Sco, GS
    7. Ganter Bernhard, Obiedkov Sergei: Conceptual Exploration.
      2016.
      GS
    8. Andrews Simon, Polovina Simon, Akhgar Babak, Staniforth Andrew, Fortune Da, Stedmon Alex: Tackling Financial and Economic Crime through Strategic Intelligence Management.
      In: Hostile Intent and Counter-Terrorism: Human Factors Theory and Application, Human Factors in Defence, 2015, pp. 161–176.
      WoS
    9. Wei Ling, Qian Ting: The Three-way Object Oriented Concept Lattice and The Three-way Property Oriented Concept Lattice.
      In: Machine Learning and Cybernetics (ICMLC), 2013 International Conference on (Volume:02), 2015, pp. 854–859.
      WoS
    10. Singh Prem Kumar, Kumar Cherukuri Aswani, Gani Abdullah: A Comprehensive Survey on Formal Concept Analysis, its Research Trends and Applications.
      International Journal of Applied Mathematics and Computer Science 26(2)(2016), pp. 495–516.
      WoS, Sco, GS
    11. Tu Xudong, Wang Yuanliang, Zhang Maolan, Wu Jinchuan: Using Formal Concept Analysis to Identify Negative Correlations in Gene Expression Data.
      IEEE/ACM Transactions on Computational Biology and Bioinformatics 13(2)(2016), pp. 380–391.
      WoS, Sco, GS
    12. Wray Timothy Daniel: Pathways through online museum collections: designing serendipitous user experiences using formal concept analysis.
      Dissertation Thesis, 2015, 212 pp.
      GS
    13. Ol'shanskii D. L.: Selection of an algorithm for the parallel implementation of the similarity method in intelligent DSM systems.
      Automatic Documentation and Mathematical Linguistics 49(4)(2015), pp. 109–116.
      GS
    14. Butka Peter, Pocs Jozef, Pocsova Jana: Distributed Computation of Generalized One-sided Concept Lattices on Sparse Data Tables.
      Computing and Informatics 34(1)(2015), pp. 77–98.
      WoS, Sco, GS
    15. Zou Ligeng, Zhang Zuping, Long, Jun, Zhang, Hao: A fast incremental algorithm for deleting objects from a concept lattice.
      Knowledge-based Systems 89(2015), pp. 411–419.
      WoS, Sco, GS
    16. Zou Ligeng, Zhang Zuping, Long Jun: A fast incremental algorithm for constructing concept lattices.
      Expert Systems with Applications 42(9)(2015), pp. 4474–4481.
      WoS, Sco, GS
    17. Andrews Simon: A ‘Best-of-Breed’ approach for designing a fast algorithm for computing fixpoints of Galois Connections.
      Information Sciences 295(2015), pp. 633–649.
      WoS, Sco, GS
    18. Zhang Tao, Li Hui, Hong Wenxue, Yuan Xiamei, Wei Xinyu: Deep First Formal Concept Search.
      The Scientific World Journal 2014(2014).
      WoS, Sco, GS
    19. Andrews Simon: A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms.
      In: Hernandez N., Jäschke R., Croitoru M. (Eds.): Graph-Based Representation and Reasoning, 21st International Conference on Conceptual Structures, ICCS 2014. Proceedings, Lecture Notes in Artificial Intelligence 8577, 2014, pp. 37–50.
      WoS, Sco, GS
    20. Andrews Simon, Akhgar Babak, Yates Simeon, Stedmon Alex, Hirsch Laurence: Using Formal Concept Analysis to Detect and Monitor Organised Crime.
      In: Larsen H. L., Martin-Bautista M. J., Vila M. A., Andreasen T., Christiansen H. (Eds.): Flexible Query Answering Systems, 10th International Conference, FQAS 2013, Proceedings, Lecture Notes in Computer Science 8132, 2013, pp. 124–133.
      Sco, GS
    21. Coulet Adrien, Domenach Florent, Kaytoue Mehdi, Napoli Amedeo: Using Pattern Structures for Analyzing Ontology-Based Annotations of Biomedical Data.
      In: Cellier P., Distel F., Ganter B. (Eds.): Formal Concept Analysis, 11th International Conference, ICFCA 2013. Proceedings, Lecture Notes in Computer Science 7880, 2013, pp. 76–91.
      Sco, GS
    22. Ferreira Tiago: Redes Sociais e Classificação Conceptual: Abordagem Complementar para um sistema de Recomendação de Coautorias.
      Dissertation Thesis, 2013, 91 pp.
      GS
    23. Kang Xiangping, Li Deyu, Wang Suge, Qu Kaishe: Rough set model based on formal concept analysis.
      Information Sciences 222(2013), pp. 611–625.
      WoS, Sco, GS
    24. Pang Jinzhong, Zhang Xiaoyan, Xu Weihua: Attribute Reduction in Intuitionistic Fuzzy Concept Lattices.
      Abstract and Applied Analysis (2013).
      WoS, Sco, GS
    25. Kuznetsov Sergei O., Poelmans Jonas: Knowledge representation and processing with formal concept analysis.
      Wiley Interdisciplinary Reviews-Data Mining and Knowledge Discovery 3(3)(2013), pp. 200–215.
      WoS, Sco, GS
    26. Kanovsky Jan, Macko Juraj: ConSeQueL - SQL Preprocessor Using Formal Concept Analysis with Measures.
      In: Andrews S., Dau F. (Eds.): The 2nd CUBIST Workshop (CUBIST-WS-12), Proceedings, 2012, pp. 33–52.
      GS
    27. Qi Jian-Jun, Liu Wei, Wei Ling: Computing the set of concepts through the composition and decomposition of formal contexts.
      In: Machine Learning and Cybernetics (ICMLC), 2012 International Conference on (Volume:4), 2012, pp. 1326–1332.
      Sco, GS
    28. Borchmann Daniel: A Generalized Next-Closure Algorithm -- Enumerating Semilattice Elements from a Generating Set.
      In: Szathmary L., Priss U. (Eds.): Proc. CLA 2012, 2012, pp. 9–20.
      Sco, GS
    29. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
      In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376.
      GS
    30. Outrata Jan: A lattice-free concept lattice update algorithm.
      Int. Journal of General Systems 45(2)(2016), pp. 211–231.
      WoS, Sco, GS
    31. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
      Annals of Mathematics and Artificial Intelligence 72(1–2)(2014), pp. 3–22.
      WoS, Sco, GS
    32. Outrata Jan: A lattice-free concept lattice update algorithm based on *CbO.
      In: Ojeda-Aciego M., Outrata J. (Eds.): CLA 2013: Proceedings of the 10th International Conference on Concept Lattices and Their Applications, 2013, pp. 261–274.
      Sco, GS
    33. Krajca Petr, Outrata Jan, Vychodil Vilém: Computing formal concepts by attribute sorting.
      Fundamenta Informaticae 115(4)(2012), pp. 395–417.
      WoS, Sco, GS
  6. Krajca Petr, Outrata Jan, Vychodil Vilém: Parallel Algorithm for Computing Fixpoints of Galois Connections.
    Annals of Mathematics and Artificial Intelligence 59(2)(2010), pp. 257–272.
    [Springer,
    DOI 10.1007/s10472-010-9199-5, ISSN 1012–2443 (paper), 1573–7470 (online)]
    IF: 0.430, DB: WoS (WOS:000286599400008), Sco, GS, RIV
    PDF | abstract | 26 citations (10 WoS, 15 Sco, 24 GS) − 1 co-citation (1 GS) + 5 selfcitations (3 WoS, 5 Sco, 5 GS)

    Abstract This paper presents a parallel algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. The algorithm results as a parallelization of CbO in which we process disjoint sets of fixpoints simultaneously. One of the distinctive features of the algorithm compared to other parallel algorithms is that it avoids synchronization which has positive impacts on its speed and implementation. We describe the parallel algorithm, prove its correctness, and analyze its asymptotic complexity. Furthermore, we focus on implementation issues, scalability of the algorithm, and provide an evaluation of its efficiency on various data sets.

    Citations
    1. Shemis Ebtesam E., Gadallah Ahmed M.: Enhanced algorithms for fuzzy formal concepts analysis.
      In: Hassanien A. E., Shaalan K., Azar A. T., Gaber T.,Tolba M. F. (Eds.): 2nd International Conference on Advanced Intelligent Systems and Informatics, AISI 2016, 2017, pp. 781–792.
      Sco, GS
    2. Qian Ting, Wei Ling, Qi Jianjun: Decomposition methods of formal contexts to construct concept lattices.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–14.
      GS
    3. Li Xin, Shao Ming-Wen, Zhao Xing-Min: Constructing lattice based on irreducible concepts.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–14.
      GS
    4. Ma Li, Mi Ju-Sheng, Xie Bin: Multi-scaled concept lattices based on neighborhood systems.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–9.
      GS
    5. de Moraes Nilander R. M., Dias Sergio M., Freitas Henrique C., Zarate Luis E.: Parallelization of the next Closure algorithm for generating the minimum set of implication rules.
      Artificial Intelligence Research 5(2)(2016).
      GS
    6. Cintra Marcos E., Camargo Heloisa A., Monard Maria C.: Genetic generation of fuzzy systems with rule extraction using formal concept analysis.
      Information Sciences 349(2016), pp. 199–215.
      WoS, Sco, GS
    7. Li Caiping, Li Jinhai, He Miao: Concept lattice compression in incomplete contexts based on K-medoids clustering.
      International Journal of Machine Learning and Cybernetics 7(4)(2016), pp. 539–552.
      WoS, Sco, GS
    8. Wray Timothy Daniel: Pathways through online museum collections: designing serendipitous user experiences using formal concept analysis.
      Dissertation Thesis, 2015, 212 pp.
      GS
    9. Nagao Masahiro, Seki Hirohisa: Towards parallel mining of closed patterns from multi-relational data.
      In: 8th IEEE International Workshop on Computational Intelligence and Applications (IWCIA 2015), 2015, pp. 103–108.
      WoS, Sco, GS
    10. Cintra Marcos E., Monard Maria C., Camargo Heloisa A.: FCA-BASED RULE GENERATOR, a framework for the genetic generation of fuzzy classification systems using formal concept analysis.
      In: IEEE (Ed.): 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), IEEE International Conference on Fuzzy Systems, 2015.
      WoS, Sco, GS
    11. Kamiya Yohei, Seki Hirohisa: Distributed Mining of Closed Patterns from Multi-Relational Data.
      Journal of Advanced Computational Intelligence and Intelligent Informatics 19(6)(2015), pp. 804–809.
      WoS, Sco
    12. Butka Peter, Pocs Jozef, Pocsova Jana: Distributed Computation of Generalized One-sided Concept Lattices on Sparse Data Tables.
      Computing and Informatics 34(1)(2015), pp. 77–98.
      WoS, Sco, GS
    13. Kamiya Yohei, Seki Hirohisa: Towards efficient closed pattern mining from distributed multi-relational data.
      In: 2014 Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS 2014) and 15th International Symposium on Advanced Intelligent Systems (ISIS 2014), 2014, pp. 1138–1141.
      WoS, Sco, GS
    14. Seki Hirohisa, Kamiya Yohei: Merging Closed Pattern Sets in Distributed Multi-Relational Data.
      In: Bertet K., Rudolph S. (Eds.): Proc. CLA 2014, 2014, pp. 71–83.
      Sco, GS
    15. Gajdos Petr, Snasel Vaclav: A new FCA algorithm enabling analyzing of complex and dynamic data sets.
      Soft Computing 18(4)(2014), pp. 683–694.
      WoS, Sco, GS
    16. Котельников E.B., Котельникова А.В.: Анализ тональности текстов с применением ДСМ-метода.
      2013
      GS
    17. Martin Trevor, Majidian Andrei: Finding Fuzzy Concepts for Creative Knowledge Discovery.
      International Journal of Intelligent Systems 28(1)(2013), pp. 93–114.
      WoS, Sco, GS
    18. Seki Hirohisa, Tanimoto Shoich: Distributed closed pattern mining in multi-relational data based on iceberg query lattices: Some preliminary results.
      In: Szathmary L., Priss U. (Eds.): Proc. CLA 2012, 2012, pp. 115–126.
      Sco
    19. Qi Jian-Jun, Liu Wei, Wei Ling: Computing the set of concepts through the composition and decomposition of formal contexts.
      In: Machine Learning and Cybernetics (ICMLC), 2012 International Conference on (Volume:4), 2012, pp. 1326–1332.
      Sco, GS
    20. Osička Petr: Concept analysis of three-way ordinal matrices.
      Dissertation Thesis, 2012, 77 pp.
      GS
    21. Cintra Marcos E., Monard Maria C., Camargo Heloisa A.: Using Fuzzy Formal Concepts in the Genetic Generation of Fuzzy Systems.
      In: IEEE (Ed.): 2012 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), IEEE International Conference on Fuzzy Systems, 2012.
      WoS, Sco, GS
    22. Cintra Marcos Evandro, Monard Maria Carolina, Martin Trevor P., de Arruda Camargo Heloisa: An Approach for the Extraction of Classification Rules from Fuzzy Formal Contexts.
      Technical Report, 2011, 28 pp.
      GS
    23. Cintra Marcos E., Monard Maria C., Camargo Heloisa A., Martin Trevor P., Majidian Andrei: On Rule Generation Approaches for Genetic Fuzzy Systems.
      In: Prati C. R., Dimuro G. P., Cunha Campos A. M. (Eds.): VIII Encontro Nacional de Inteligência Artificial (ENIA 2011), XXXI Congresso da Sociedade Brasileira de Computação (CSBC 2011), Proceedings, 2011.
      GS
    24. Majidian Andrei, Martin Trevor, Cintra Marcos E.: Fuzzy formal concept analysis and algorithm.
      In: Proceedings of the 11th UK Workshop on Computational Intelligence, 2011, pp. 61–67.
      GS
    25. Langdon W. B., Yoo Shin, Harman Mark: Formal Concept Analysis on Graphics Hardware.
      In: Napoli A., Vychodil V. (Eds.): Proc. CLA 2011, 2011, pp. 413–416.
      Sco, GS
    26. Krajca Petr, Vychodil Vilem: Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework.
      In: Adams N. M., Robardet C., Siebes A., Boulicaut J.-F. (Eds.): Advances in Intelligent Data Analysis VIII, 8th International Symposium on Intelligent Data Analysis, IDA 2009, Lecture Notes in Computer Science 5772, 2009, pp. 333–344.
      GS
    27. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
      In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376.
      GS
    28. Outrata Jan: A lattice-free concept lattice update algorithm.
      Int. Journal of General Systems 45(2)(2016), pp. 211–231.
      WoS, Sco, GS
    29. Outrata Jan: A lattice-free concept lattice update algorithm based on *CbO.
      In: Ojeda-Aciego M., Outrata J. (Eds.): CLA 2013: Proceedings of the 10th International Conference on Concept Lattices and Their Applications, 2013, pp. 261–274.
      Sco, GS
    30. Krajca Petr, Outrata Jan, Vychodil Vilém: Computing formal concepts by attribute sorting.
      Fundamenta Informaticae 115(4)(2012), pp. 395–417.
      WoS, Sco, GS
    31. Outrata Jan, Vychodil Vilém: Fast Algorithm for Computing Fixpoints of Galois Connections Induced by Object-Attribute Relational Data.
      Information Sciences 185(1)(2012), pp. 114–127.
      WoS, Sco, GS
  7. Belohlavek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Computing the lattice of all fixpoints of a fuzzy closure operator.
    IEEE Transactions on Fuzzy Systems 18(3)(2010), pp. 546–557.
    [IEEE,
    DOI 10.1109/TFUZZ.2010.2041006, ISSN 1063–6706]
    IF: 2.695, DB: WoS (WOS:000278538000009), Sco, GS, RIV
    PDF | abstract | 47 citations (25 WoS, 36 Sco, 44 GS) − 4 co-citations (4 WoS, 3 Sco, 4 GS)

    Abstract We present a fast bottom-up algorithm for computing all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees, along with the partial order on the set of all fixpoints. Fuzzy closure operators appear in several areas of fuzzy logic and its applications, including formal concept analysis which we use as a reference area of application in this paper. Several problems in formal concept analysis, such as computing all formal concepts from data with graded attributes or computing non-redundant bases of all attribute dependencies, can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data. The development of a general algorithm applicable in particular to these problems is the ultimate purpose of this paper. We present the algorithm, its theoretical foundations, and experimental evaluation.

    Citations
    1. Shemis Ebtesam E., Gadallah Ahmed M.: Enhanced algorithms for fuzzy formal concepts analysis.
      In: Hassanien A. E., Shaalan K., Azar A. T., Gaber T.,Tolba M. F. (Eds.): 2nd International Conference on Advanced Intelligent Systems and Informatics, AISI 2016, 2017, pp. 781–792.
      Sco, GS
    2. Boffa Stefania, De Maio Carmen, Di Nola Antonio, Fenza Giuseppe, Ferraioli Anna Rita, Loia Vincenzo: Unifying fuzzy concept lattice construction methods.
      In: 2016 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2016, 2016, pp. 209–216.
      Sco, GS
    3. Li Kewen, Shao Ming-Wen, Wu Wei-Zhi: A data reduction method in formal fuzzy contexts.
      International Journal of Machine Learning and Cybernetics (2016), pp. 1–11.
      GS
    4. Li Jinhai, Huang Chenchen, Mei Changlin, Yin Yunqiang: An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices.
      Intelligent Automation & Soft Computing (2016), pp. 1–15.
      GS
    5. Semenova Valentina A., Smirnov Sergey V.: Intelligent analysis of incomplete data for building formal ontologies.
      In: N. L. Kazanskiy, D. V. Kudryashov, S. B. Popov, V. V. Sergeev, R. V. Skidanov, V. A. Fursov, V. A. Sobolev (Eds.): Proc. Information Technology and Nanotechnology (ITNT 2016), 2016, pp. 796–805.
      GS
    6. Vychodil Vilem: Parameterizing the Semantics of Fuzzy Attribute Implications by Systems of Isotone Galois Connections.
      IEEE Transactions On Fuzzy Systems 24(3)(2016), pp. 645–660.
      WoS, Sco, GS
    7. Cui Fang-ting, Wang Li-ming, Zhang Zhuo: Construction Algorithm of Fuzzy Concept Lattice Based on Constraints.
      Computer Science 42(8)(2015), pp. 288–318.
      GS
    8. Gong Yang, Shao Ming-Wen, Qiu Guofang: Concept granular computing systems and their approximation operators.
      International Journal of Machine Learning and Cybernetics (2015), pp. 1–14.
      GS
    9. Stamenković Aleksandar, Ćirić Miroslav, Bašić Milan: Ranks of fuzzy matrices. Applications in state reduction of fuzzy automata.
      ResearchGate, 2015
      GS
    10. Ghosh Partha, Kundu Krishna: Rules for Computing Fixpoints of a Fuzzy Closure Operator.
      Annals of Fuzzy Mathematics and Informatics (2015).
      GS
    11. Shao Ming-Wen, Yang Hong-Zhi, Wu Wei-Zhi: Knowledge reduction in formal fuzzy contexts.
      Knowledge-Based Systems 73(2015), pp. 265–275.
      WoS, Sco, GS
    12. Cornejo M. Eugenia, Medina Jesús, Ramírez-Poussa Eloisa: On the use of thresholds in multi-adjoint concept lattices.
      International Journal of Computer Mathematics 92(9)(2015), pp. 1855–1873.
      WoS, Sco, GS
    13. Kohli Shruti, Gupta Ankit: Fuzzy information retrieval in WWW: a survey.
      International Journal of Advanced Intelligence Paradigms 6(4)(2014), pp. 272–311.
      Sco, GS
    14. Zhang Zhuo, Du Juan, Wang Li-ming: Load balance-based algorithm for parallelly generating fuzzy formal concepts.
      Kongzhi yu Juece/Control and Decision 29(11)(2014), pp. 1935–1942.
      Sco, GS
    15. Cross V.V.: Fuzzy ontologies: The state of the art.
      In: Gibbs M. (Ed.): Norbert Wiener in the 21st Century (21CW), 2014 IEEE Conference on, 2014, pp. 1–8.
      WoS, Sco, GS
    16. Shao Ming-Wen, Leung Yee: Relations between granular reduct and dominance reduct in formal contexts.
      Knowledge-Based Systems 65(2014), pp. 1–11.
      WoS, Sco, GS
    17. Diaz-Moreno Juan Carlos, Medina Jesus: Using concept lattice theory to obtain the set of solutions of multi-adjoint relation equations.
      Information Sciences 266(2014), pp. 218–225.
      WoS, Sco, GS
    18. De Maio C., Fenza G., Gallo M., Loia V., Senatore S.: Formal and relational concept analysis for fuzzy-based automatic semantic annotation.
      Applied Intelligence 40(1)(2014), pp. 154–177.
      WoS, Sco, GS
    19. Poelmans Jonas, Ignatov Dmitry I., Kuznetsov Sergei O., Dedene Guido: Fuzzy and rough formal concept analysis: a survey.
      International Journal of General Systems 43(2)(2014), pp. 105–134.
      WoS, Sco, GS
    20. Zhang Z., Chai Y.-M., Wang L.-M., Fan M.: A parallel algorithm generating fuzzy formal concepts.
      Moshi Shibie yu Rengong Zhineng/Pattern Recognition and Artificial Intelligence 26(3)(2013), pp. 260–269.
      Sco
    21. Antoni Ľubomír, Krajči Stanislav, Krídlo Ondrej, Pisková Lenka: Heterogeneous environment on examples.
      In: Cellier P., Distel F., Ganter B. (Eds.): Contributions to the 11 th International Conference on Formal Concept Analysis (ICFCA 2013), 2013, pp. 5–18.
      GS
    22. Tsang E.C.C., Shao Ming-Wen: Attribute reduction and attribute characteristics of formal contexts.
      In: Machine Learning and Cybernetics (ICMLC), 2013 International Conference on (Volume:01), 2013, pp. 124–129.
      WoS, Sco, GS
    23. Antoni Ľubomir, Krajci Stanislav, Kridlo Ondrej: On Different Types of Heterogeneous Formal Contexts.
      In: Pasi G., Montero J., Ciucci D. (Eds.): Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13), Advances in Intelligent Systems Research 32, 2013, pp. 302–309.
      WoS, Sco, GS
    24. Shao Mingwen, Liu Min, Guo Li: Vector-based Attribute Reduction Method for Formal Contexts.
      Fundamenta Informaticae 126(4)(2013), pp. 397–414.
      WoS, Sco, GS
    25. Martin Trevor, Majidian Andrei: Finding Fuzzy Concepts for Creative Knowledge Discovery.
      International Journal of Intelligent Systems 28(1)(2013), pp. 93–114.
      WoS, Sco, GS
    26. Poelmans Jonas, Kuznetsov Sergei O., Ignatov Dmitry I., Dedene Guido: Formal Concept Analysis in knowledge processing: A survey on models and techniques.
      Expert Systems with Applications 40(16)(2013), pp. 6601–6623.
      WoS, Sco, GS
    27. Carlos Diaz Juan, Medina Jesus: Multi-adjoint relation equations: Definition, properties and solutions using concept lattices.
      Information Sciences 253(2013), pp. 100–109.
      WoS, Sco, GS
    28. Medina Jesus, Ojeda-Aciego Manuel: Dual multi-adjoint concept lattices.
      Information Sciences 225(2013), pp. 47–54.
      WoS, Sco, GS
    29. Carlos Diaz Juan, Medina Jesus: Solving systems of fuzzy relation equations by fuzzy property-oriented concepts.
      Information Sciences 222(2013), pp. 405–412.
      WoS, Sco, GS
    30. Carlos Diaz Juan, Garcia Bosco, Medina Jesus, Rodriguez, Rafael: Building multi-adjoint concept lattices.
      In: Pasi G., Montero J., Ciucci D. (Eds.): Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13), Advances in Intelligent Systems Research 32, 2013, pp. 340–346.
      WoS, Sco, GS
    31. Krídlová Burdová E., Vilčeková S., Krídlo O., Nagy, R., Híreš J.: A Slovak environmental rating tool for buildings.
      In: 12th International Multidisciplinary Scientific GeoConference and EXPO - Modern Management of Mine Producing, Geology and Environmental Protection, SGEM 2012 (Volume 5), Proceedings, 2012, pp. 13–20.
      Sco, GS
    32. Díaz Juan Carlos, Medina Jesús, Rodríguez Rafael: Solving General Fuzzy Relation Equations Using Property-Oriented Concept Lattices.
      In: Greco S., Bouchon-Meunier B., Coletti G., Fedrizzi M., Matarazzo B., Yager R. R. (Eds.): Advances in Computational Intelligence, 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Proceedings, Part II, Communications in Computer and Information Science 298, 2012, pp. 395–404.
      Sco, GS
    33. Osicka Petr: Algorithms for Computation of Concept Trilattice of Triadic Fuzzy Context.
      In: Greco S., Bouchon-Meunier B., Coletti G., Fedrizzi M., Matarazzo B., Yager R. R. (Eds.): Advances in Computational Intelligence, 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Proceedings, Part III, Communications in Computer and Information Science 299, 2012, pp. 221–230.
      Sco, GS
    34. Borchmann Daniel: A Generalized Next-Closure Algorithm -- Enumerating Semilattice Elements from a Generating Set.
      In: Szathmary L., Priss U. (Eds.): Proc. CLA 2012, 2012, pp. 9–20.
      Sco, GS
    35. Osička Petr: Concept analysis of three-way ordinal matrices.
      Dissertation Thesis, 2012, 77 pp.
      GS
    36. Belohlavek Radim: Optimal decompositions of matrices with entries from residuated lattices.
      Journal of Logic and Computation 22(6)(2012), pp. 1405–1425.
      WoS, Sco, GS
    37. Medina Jesus, Ojeda-Aciego Manuel: On multi-adjoint concept lattices based on heterogeneous conjunctors.
      Fuzzy Sets and Systems 208(2012), pp. 95–110.
      WoS, Sco, GS
    38. Cross V., Kandasamy M., Yi W.: Comparing two approaches to creating fuzzy concept lattices.
      In: 2011 Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS'2011, 2011.
      Sco
    39. Díaz Juan Carlos, Medina-Moreno Jesús: Concept lattices in fuzzy relation equations.
      In: Napoli A., Vychodil V. (Eds.): Proc. CLA 2011, 2011, pp. 75–86.
      Sco, GS
    40. Majidian Andrei, Martin Trevor, Cintra Marcos E.: Fuzzy formal concept analysis and algorithm.
      In: Proceedings of the 11th UK Workshop on Computational Intelligence, 2011, pp. 61–67.
      GS
    41. Djouadi Yassine, Prade, Henri: Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices.
      Fuzzy Optimization and Decision Making 10(4)(2011), pp. 287–309.
      WoS, Sco, GS
    42. Cross Valerie, Kandasamy Meenakshi: Fuzzy Concept Lattice Construction A Basis for Building Fuzzy Ontologies.
      In: IEEE (Ed.): IEEE International Conference on Fuzzy Systems (FUZZ 2011), IEEE International Conference on Fuzzy Systems, 2011, pp. 1743–1750.
      WoS, Sco, GS
    43. Shao Mingwen, Guo Li, Li Lan: A Novel Attribute Reduction Approach Based on the Object Oriented Concept Lattice.
      In: Yao J. T., Ramanna S., Wang G. Y., Suraj Z. (Eds.): Rough Sets and Knowledge Technology, Lecture Notes in Artificial Intelligence 6954, 2011, pp. 71–80.
      WoS, Sco, GS
    44. Cross Valerie, Kandasamy Meenakshi: Creating Fuzzy Concepts: The One-Sided Threshold, Fuzzy Closure and Factor Analysis Methods.
      In: Kuznetsov S. O., Slezak D., Hepting D. H., Mirkin B. G. (Eds.): Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGRC 2011, Lecture Notes in Artificial Intelligence 6743, 2011, pp. 127–134.
      WoS, Sco, GS
    45. Belohlavek Radim: Formal Concept Analysis: Classical and Fuzzy.
      In: Belohlavek R., Klir G. J. (Eds.): Concepts and Fuzzy Logic, 2011, pp. 177–207.
      WoS, GS
    46. Belohlavek Radim: What is a Fuzzy Concept Lattice? II.
      In: Kuznetsov S. O., Slezak D., Hepting D. H., Mirkin B. G. (Eds.): Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGRC 2011, Lecture Notes in Artificial Intelligence 6743, 2011, pp. 19–26.
      WoS, Sco, GS
    47. Cross V., Kandasamy M., Yi Wenting: Fuzzy concept lattices: Examples using the Gene Ontology.
      In: Wierman M. (Ed.): 2010 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), Proceedings, 2010, pp. 1–6.
      Sco
  8. Belohlavek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Inducing decision trees via concept lattices.
    Int. Journal of General Systems 38(4)(2009), pp. 455–467.
    [Taylor & Francis Group,
    DOI 10.1080/03081070902857563, ISSN 0308–1079 (paper), 1563–5104 (online)]
    IF: 0.611, DB: WoS (WOS:000265295900006), Sco, GS, RIV
    PDF | abstract | 26 citations (13 WoS, 20 Sco, 26 GS) − 1 co-citation (1 WoS, 1 Sco, 1 GS)

    Abstract We present a novel method for the construction of decision trees. The method utilises concept lattices in that certain formal concepts of the concept lattice associated to input data are used as nodes of the decision tree constructed from the data. The concept lattice provides global information about natural clusters in the input data, which we use for selection of splitting attributes. The usage of such global information is the main novelty of our approach. Experimental evaluation indicates good performance of ourmethod. We describe the method, experimental results, and a comparison with standard methods on benchmark datasets.

    Citations
    1. Gupta Shivani, Gupta Atul: A set of measures designed to identify overlapped instances in software defect prediction.
      Computing (2017), pp. 1–26.
      GS
    2. Kashnitsky Yury: Lazy Learning of Classification Rules for Complex Structure Data.
      In: Ignatov D. I., Khachay M. Y., Labunets V. G., Loukachevitch N., Nikolenko S., Panchenko A., Savchencko A. V., Vorontosov K. V. (Eds.): Supplementary Proceedings of the Fifth International Conference on Analysis of Images, Social Networks and Texts (AIST 2016), 2016, pp. 73–84.
      GS
    3. Kashnitsky Yury, Kuznetsov Sergei O.: Global Optimization in Learning with Important Data: an FCA-Based Approach.
      In: Huchard M., Kuznetsov S. O. (Eds.): Proc. CLA 2016, 2016, pp. 189–201.
      Sco, GS
    4. Andrews Simon, Hirsch Laurence: A Tool for Creating and Visualising Formal Concept Trees.
      In: Andrews S., Polovina S. (Eds.): Proc. Fifth Conceptual Structures Tools & Interoperability Workshop (CSTIW 2016), 22nd International Conference on Conceptual Structures (ICCS 2016), 2016, pp. 1–9.
      Sco, GS
    5. Ignatov D. I.: Introduction to formal concept analysis and its applications in information retrieval and related fields.
      In: 8th Russian Summer School on Information Retrieval, RuSSIR 2014, Communications in Computer and Information Science 505, 2015, pp. 42–141.
      WoS, Sco, GS
    6. El Bekri Nadia, Angele Susanne, Peinsipp-Byma Elisabeth: Classification of short-lived objects using an interactive adaptable assistance system.
      In: Broome B. D., Hanratty T. P., Hall D. L., Llinas J. (Eds.): Proc. SPIE 9499, Next-Generation Analyst III, 949908, 2015.
      WoS, Sco, GS
    7. Ignatov Dmitry I., Gnatyshak Dmitry V., Kuznetsov Sergei O., Mirkin Boris G.: Triadic Formal Concept Analysis and triclustering: searching for optimal patterns.
      Machine Learning 101(1-3)(2015), pp. 271–302.
      WoS, Sco, GS
    8. Li Jinhai, Mei Changlin, Wang Lidong, Wang Junhong: On inference rules in decision formal contexts.
      International Journal of Computational Intelligence Systems 8(1)(2015), pp. 175–186.
      WoS, Sco, GS
    9. Wan Qing, Wei Ling: Approximate concepts acquisition based on formal contexts.
      Knowledge-Based Systems 75(2015), pp. 78–86.
      WoS, Sco, GS
    10. Li Leijun, Mi Jusheng, Xie Bin: Attribute reduction based on maximal rules in decision formal context.
      International Journal of Computational Intelligence Systems 7(6)(2014), pp. 1044–1053.
      Sco, GS
    11. Abudawood Tarek: Improving Predictions of Multiple Binary Models in ILP.
      The Scientific World Journal (2014).
      WoS, Sco, GS
    12. Girard Nathalie: Vers une approche hybride mêlant arbre de classification et treillis de Galois pour de l'indexation d'images.
      Dissertation Thesis, 2013
      GS
    13. Ikeda Madori, Yamamoto Akihito: Classification by Selecting Plausible Formal Concepts in a Concept Lattice.
      In: Carpineto C., Kuznetsov S. O., Napoli A. (Eds.): FCAIR 2012 Formal Concept Analysis Meets Information Retrieval Workshop co-located with the 35th European Conference on Information Retrieval (ECIR 2013), 2013, pp. 22–35.
      Sco, GS
    14. Poelmans Jonas, Kuznetsov Sergei O., Ignatov Dmitry I., Dedene Guido: Formal Concept Analysis in knowledge processing: A survey on models and techniques.
      Expert Systems with Applications 40(16)(2013), pp. 6601–6623.
      WoS, Sco, GS
    15. Kuznetsov Sergei O., Poelmans Jonas: Knowledge representation and processing with formal concept analysis.
      Wiley Interdisciplinary Reviews-Data Mining and Knowledge Discovery 3(3)(2013), pp. 200–215.
      WoS, Sco, GS
    16. Li Jinhai, Mei Changlin, Lv Yuejin: Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction.
      International Journal of Approximate Reasoning 54(1)(2013), pp. 149–165.
      WoS, Sco, GS
    17. Игнатов Д. И.: Анализ формальных понятий: от теории к практике.
      In: Игнатов Д.И., Яворский Р.Э. (Eds.): Анализ Изображений Сетей и Текстов, 2012, pp. 1–12.
      GS
    18. Li Jinhai, Mei Changlin, Lv Yuejin: Knowledge reduction in formal decision contexts based on an order-preserving mapping.
      International Journal of General Systems 41(2)(2012), pp. 143–161.
      WoS, Sco, GS
    19. Li Tong-Jun, Wu Ying-Xue, Yang Xiaoping: Dependence and Algebraic Structure of Formal Contexts.
      In: Yao JT., Ramanna S., Wang G., Suraj Z. (Eds.): Rough Set and Knowledge Technology, 6th International Conference, RSKT 2011, Lecture Notes in Computer Science 6954, 2011, pp. 51–56.
      Sco, GS
    20. Issa Adel S.: Intrusion Detection System Based on Decision Tree and Clustered Continuous Inputs.
      Raf. J. of Comp. & Math's. 8(1)(2011), pp. 79–87.
      GS
    21. Xie Chunzhi, Du Yajun, Gao Zhisheng: Algorithm for Construction of Evolution-Based Concept Lattices with Application to Public Sentiment Prediction.
      Journal of Information and Computational Science 8(16)(2011), pp. 4201–4208.
      Sco, GS
    22. Li Jinhai, Mei Changlin, Lv Yuejin: Knowledge reduction in decision formal contexts.
      Knowledge-Based Systems 24(5)(2011), pp. 709–715.
      WoS, Sco, GS
    23. Mi Ju-Sheng, Leung Yee, Wu Wei-Zhi: Approaches to attribute reduction in concept lattices induced by axialities.
      Knowledge-Based Systems 23(6)(2010), pp. 504–511.
      Sco, GS
    24. Alcalde Cristina, Burusco Ana, Fuentes-Gonzalez Ramon: Interval-valued linguistic variables: an application to the L-fuzzy contexts with absent values.
      International Journal of General Systems 39(3)(2010), pp. 255–270.
      WoS, Sco, GS
    25. Bertet K., Visani M., Girard N.: Treillis dichotomiques et arbres de décision.
      Traitement du Signal 26(5)(2009), pp. 409–418.
      GS
    26. Krajca Petr, Vychodil Vilem: Comparison of Data Structures for Computing Formal Concepts.
      In: Torra V., Narukawa Y., Inuiguchi M. (Eds.): Modeling Decisions for Artificial Intelligence, Proceedings, Lecture Notes in Artificial Intelligence 5861, 2009, pp. 114–125.
      WoS, Sco, GS
  9. Belohlavek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Characterizing trees in concept lattices.
    Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16(1)(2008), pp. 1–15.
    [World Scientific,
    DOI 10.1142/S0218488508005212, ISSN 0218–4885 (paper), 1793–6411 (online)]
    IF: 1.000, DB: WoS (WOS:000256307600002), Sco, GS, RIV
    PDF | abstract | 6 citations (3 WoS, 1 Sco, 5 GS)

    Abstract Concept lattices are systems of conceptual clusters, called formal concepts,which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output conceptlattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.

    Citations
    1. Mao Hua: Representing attribute reduction and concepts in concept lattice using graphs.
      Soft Computing (2016), pp. 1–19.
      GS
    2. Mao H.: Characterizing trees in property-oriented concept lattices.
      Armenian Journal of Mathematics 8(2)(2016), pp. 86–95.
      WoS, GS
    3. Poelmans Jonas, Ignatov Dmitry I., Kuznetsov Sergei O., Dedene Guido: Fuzzy and rough formal concept analysis: a survey.
      International Journal of General Systems 43(2)(2014), pp. 105–134.
      WoS, Sco, GS
    4. Fukuda Takashi, Murofushi Toshiaki: Hierarchical clustering methods using Formal Concept Analysis - The algorithms for single-link and complete-link clustering.
      In: 26th Fuzzy System Symposium, 2010, pp. 1049–1054.
      GS
    5. Poelmans Jonas: Essays on using formal concept analysis in information engineering.
      Dissertation Thesis, 2010, 297 pp.
      GS
    6. Javois C., Tardieu C., Lebel B., Seil R, Hulet C.: Comparative anatomy of the knee joint: Effects on the lateral meniscus.
      Orthopaedics & Traumatology-Surgery & Research 95(8)(2009), pp. S49–S59.
      WoS
  10. Belohlavek Radim, Outrata Jan, Vychodil Vilém: Fast factorization by similarity of fuzzy concept lattices with hedges.
    Int. Journal of Foundations of Computer Science 19(2)(2008), pp. 255–269.
    [World Scientific,
    DOI 10.1142/S012905410800567X, ISSN 0129–0541]
    IF: 0.554, DB: WoS (WOS:000255611400002), Sco, GS, RIV
    PDF | abstract | 13 citations (6 WoS, 9 Sco, 13 GS)

    Abstract The paper presents results on factorization by similarity of fuzzy concept lattices with hedges. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concept lattice, its factor lattice. The factor lattice contains less clusters than the original concept lattice but, at the same time, represents a reasonable approximation of the original concept lattice and provides us with a granular view on the original concept lattice. The factor lattice results by factorization of the original fuzzy concept lattice by a similarity relation. The similarity relation is specified by a user by means of a single parameter, called a similarity threshold. Smaller similarity thresholds lead to smaller factor lattices, i.e. to more comprehensible but less accurate approximations of the original concept lattice. Therefore, factorization by similarity provides a trade-off between comprehensibility and precision. We first describe the notion of factorization. Second, we present a way to compute the factor lattice directly from input data, i.e. without the need to compute the possibly large original concept lattice. Third, we provide an illustrative example to demonstrate our method.

    Citations
    1. Kohli Shruti, Gupta Ankit: Information Retrieval: A Fuzzy Perspective.
      International Journal of Applied Research on Information Technology and Computing 5(1)(2014), pp. 14–24.
      GS
    2. Kohli Shruti, Gupta Ankit: Fuzzy information retrieval in WWW: a survey.
      International Journal of Advanced Intelligence Paradigms 6(4)(2014), pp. 272–311.
      Sco, GS
    3. Poelmans Jonas, Ignatov Dmitry I., Kuznetsov Sergei O., Dedene Guido: Fuzzy and rough formal concept analysis: a survey.
      International Journal of General Systems 43(2)(2014), pp. 105–134.
      WoS, Sco, GS
    4. Kohli Shruti, Gupta Ankit: A Survey on Web Information Retrieval Inside Fuzzy Framework.
      In: Pant M., Deep K., Nagar A., Bansal J. Ch. (Eds.): Proceedings of the Third International Conference on Soft Computing for Problem Solving, SocProS 2013, Volume 2, Advances in Intelligent Systems and Computing 259, 2013, pp. 433–445.
      Sco, GS
    5. Formica Anna: Similarity reasoning for the semantic web based on fuzzy concept lattices: An informal approach.
      Information Systems Frontiers 15(3)(2013), pp. 511–520.
      WoS, Sco, GS
    6. Formica Anna: Semantic Web search based on rough sets and Fuzzy Formal Concept Analysis.
      Knowledge-Based Systems 26(2012), pp. 40–47.
      WoS, Sco, GS
    7. Ayouni Sarra, Ben Yahia Sadok, Laurent Anne: Extracting compact and information lossless sets of fuzzy association rules.
      Fuzzy Sets and Systems 183(1)(2011), pp. 1–25.
      WoS, Sco, GS
    8. Poelmans Jonas: Essays on using formal concept analysis in information engineering.
      Dissertation Thesis, 2010, 297 pp.
      GS
    9. Formica Anna: Concept Similarity in Fuzzy Formal Concept Analysis for Semantic Web.
      International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 18(2)(2010), pp. 153–167.
      WoS, Sco, GS
    10. Krupka Michal: Factorization of fuzzy concept lattices with hedges by modification of input data.
      Annals of Mathematics and Artificial Intelligence 59(2)(2010), pp. 187–200.
      WoS, Sco, GS
    11. Formica Anna: Concept Similarity in Fuzzy Formal Concept Analysis for Semantic Web.
      2009, 17 pp.
      GS
    12. Formica Anna: Similarity of XML-schema Elements: A Structural and Information Content Approach.
      Computer Journal 51(2)(2008), pp. 240–254.
      GS
    13. Krupka Michal: Factorization of Concept Lattices with Hedges by Means of Factorization of Residuated Lattices.
      In: Belohlavek R., Kuznetsov S. O. (Eds.): Proc. CLA 2008, 2008, pp. 231–241.
      Sco, GS
  11. Bělohlávek Radim, Dvořák Jiří, Outrata Jan: Fast factorization by similarity in formal concept analysis of data with fuzzy attributes.
    Journal of Computer and System Sciences 73(6)(2007), pp. 1012–1022.
    [Elsevier,
    DOI 10.1016/j.jcss.2007.03.016, ISSN 0022–0000]
    IF: 1.185, DB: WoS (WOS:000248133700011), Sco, GS, RIV
    PDF | abstract | 39 citations (17 WoS, 23 Sco, 36 GS) − 11 co-citations (7 WoS, 6 Sco, 10 GS) + 2 selfcitations (1 WoS, 1 Sco, 2 GS)

    Abstract We present a method of fast factorization in formal concept analysis (FCA) of data with fuzzy attributes. The output of FCA consists of a partially ordered collection of clusters extracted from a data table describing objects and their attributes. The collection is called a concept lattice. Factorization by similarity enables us to obtain, instead of a possibly large concept lattice, its factor lattice. The elements of the factor lattice are maximal blocks of clusters which are pairwise similar to degree exceeding a user-specified threshold. The factor lattice thus represents an approximate version of the original concept lattice. We describe a fuzzy closure operator the fixed points of whichare just clusters which uniquely determine the blocks of clusters of the factor lattice. This enables us to compute the factor lattice directly from the data without the need to compute the whole concept lattice. We present theoretical solution and examples demonstrating the speed-up of our method.

    Citations
    1. Benítez M. José, Medina Jesús, Slezak Dominik: Attribute Reduction in Fuzzy Formal Concept Analysis from Rough Set Theory.
      In: Kóczy L., Medina J. (Eds.): ESCIM 2016, 2016, pp. 49–54.
      GS
    2. Ciobanu Gabriel, Văideanu Cristian: An efficient method to factorize fuzzy attribute-oriented concept lattices.
      Fuzzy Sets and Systems (2016).
      GS
    3. Ravanbakhsh Siamak, Barnabás Póczos, Greiner Russell: Boolean Matrix Factorization and Noisy Completion via Message Passing.
      In: Balcan M. F., Weinberger K. Q. (Eds.): 33rd International Conference on Machine Learning, ICML 2016, 2016, pp. 1486–1499.
      Sco, GS
    4. Belohlavek Radim, Konecny Jan: Bases of closure systems over residuated lattices.
      Journal of Computer and System Sciences 82(2)(2016), pp. 357–365.
      WoS, Sco, GS
    5. Singh Prem Kumar, Kumar C. Aswani, Li Jinhai: Knowledge representation using interval-valued fuzzy formal concept lattice.
      Soft Computing 20(4)(2016), pp. 1485–1502.
      WoS, Sco, GS
    6. Gardiner E. J., Gillet V. J.: Perspectives on Knowledge Discovery Algorithms Recently Introduced in Chemoinformatics: Rough Set Theory, Association Rule Mining, Emerging Patterns, and Formal Concept Analysis.
      Journal of Chemical Information and Modeling 55(9)(2015), pp. 1781–1803.
      Sco, GS
    7. Konecny Jan, Krupka Michal: Complete relations on fuzzy complete lattices.
      arXiv:1506.03930, 2015, 24 pp.
      GS
    8. Ciobanu Gabriel, Văideanu Cristian: Similarity relations in fuzzy attribute-oriented concept lattices.
      Fuzzy Sets and Systems 275(2015), pp. 88–109.
      WoS, Sco, GS
    9. Vaideanu Mihai Cristian: Metric and Topological Aspects in Distributed Systems.
      Dissertation Thesis, 2014, 25 pp.
      GS
    10. Poelmans Jonas, Ignatov Dmitry I., Kuznetsov Sergei O., Dedene Guido: Fuzzy and rough formal concept analysis: a survey.
      International Journal of General Systems 43(2)(2014), pp. 105–134.
      WoS, Sco, GS
    11. Akhgar B., Yates S.: Strategic intelligence management: National security imperatives and information and communications technologies.
      2013.
      Sco
    12. Safaeipour H., Zarandi M. H. F., Turksen I. B.: Developing type-2 fuzzy FCA for similarity reasoning in the semantic web.
      In: Pedrycz W., Reformat M. Z. (Eds.): Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, pp. 1477–1482.
      Sco, GS
    13. Navarro Emmanuel: Métrologie des graphes de terrain, application à la construction de ressources lexicales et à la recherche d'information.
      Dissertation Thesis, 2013, 234 pp.
      GS
    14. Song Xiao-Xue, Wang Xia, Zhang Wen-Xiu: Axiomatic approaches of fuzzy concept operators.
      In: Machine Learning and Cybernetics (ICMLC), 2012 International Conference on (Volume:1), 2012, pp. 249–254.
      Sco, GS
    15. Hou Lijuan, Li Shuyu: Semantic Web Service Matching Based on Fuzzy Concept Lattice.
      International Journal of Applied Mathematics and Computer Science 28(8)(2011), pp. 67–70.
      GS
    16. Guo M. M., Dou Jhua, Jiang W., Yang Bin: Entropy-based attributes significance measure and its application in concept approximation.
      American Journal of Engineering and ... (2011).
      GS
    17. Belohlavek Radim: Formal Concept Analysis: Classical and Fuzzy.
      In: Belohlavek R., Klir G. J. (Eds.): Concepts and Fuzzy Logic, 2011, pp. 177–207.
      WoS
    18. Li Sheng-Tun, Chen Chih-Chuan, Huang Fernando: Conceptual-driven classification for coding advise in health insurance reimbursement.
      Artificial Intelligence in Medicine 51(1)(2011), pp. 27–41.
      WoS, Sco, GS
    19. Belohlavek Radim: What is a Fuzzy Concept Lattice? II.
      In: Kuznetsov S. O., Slezak D., Hepting D. H., Mirkin B. G. (Eds.): Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGRC 2011, Lecture Notes in Artificial Intelligence 6743, 2011, pp. 19–26.
      WoS, Sco, GS
    20. Yang Ling-Yun, Xu Luo-Shan: Separations of Formal Contexts.
      2010
      GS
    21. Wang Lidong, Gong Dianxuan: A structural information method for evaluating concept similarity.
      In: Li M., Liang Q., Wang L., Song Y. (Eds.): Fuzzy Systems and Knowledge Discovery (FSKD), 2010 Seventh International Conference on (Volume:4 ), Proceedings, 2010, pp. 1966–1970.
      Sco, GS
    22. Cross V., Kandasamy M., Yi Wenting: Fuzzy concept lattices: Examples using the Gene Ontology.
      In: Wierman M. (Ed.): 2010 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), Proceedings, 2010, pp. 1–6.
      Sco, GS
    23. Poelmans Jonas: Essays on using formal concept analysis in information engineering.
      Dissertation Thesis, 2010, 297 pp.
      GS
    24. Li Sheng-Tun, Tsai Fu-Ching: Constructing tree-based knowledge structures from text corpus.
      Applied Intelligence 33(1)(2010), pp. 67–78.
      WoS, Sco, GS
    25. Belohlavek Radim, Vychodil Vilem: Discovery of optimal factors in binary data via a novel method of matrix decomposition.
      Journal of Computer and System Sciences 76(1)(2010), pp. 3–20.
      WoS, Sco, GS
    26. Song Xiao-Xue, Zhang Wen-Xiu, Zhao, Qiang: Conceptual Reduction of Fuzzy Dual Concept Lattices.
      In: Yu J., Greco S., Lingras P., Wang G., Skowron A. (Eds.): Rough Set and Knowledge Technology (RSKT), Lecture Notes in Artificial Intelligence 6401, 2010, pp. 187–194.
      WoS, Sco, GS
    27. Krupka Michal: Factorization of fuzzy concept lattices with hedges by modification of input data.
      Annals of Mathematics and Artificial Intelligence 59(2)(2010), pp. 187–200.
      WoS, Sco, GS
    28. Tsai Fu-Ching, Cheng Yi-Chung, Li Sheng-Tun, Chen Ciian-Yuan: Heuristic-Based Approach for Constructing Hierarchical Knowledge Structures.
      In: Chien B.-Ch., Hong T.-P., Chen S.-M., Ali M. (Eds.): Next-Generation Applied Intelligence, 22nd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2009, Proceedings, Lecture Notes in Computer Science 5579, 2009, pp. 439–448.
      Sco, GS
    29. Belohlavek Radim, Krupka Michal: Grouping fuzzy sets by similarity.
      Information Sciences 179(15)(2009), pp. 2656–2661.
      WoS, Sco, GS
    30. Hou Lijuan, Li Shuyu: Semantic Web Service Matching Based on Fuzzy Concept Lattice.
      In: Zhang S. (Ed.): International Symposium on Computer Science & Technology, Proceedings, 2009, pp. 85–89.
      WoS
    31. Krupka Michal: Factorization of residuated lattices.
      Logic Journal of the IGPL 17(2)(2009), pp. 205–223.
      WoS, Sco, GS
    32. Krupka Michal: Factorization of Concept Lattices with Hedges by Means of Factorization of Residuated Lattices.
      In: Belohlavek R., Kuznetsov S. O. (Eds.): Proc. CLA 2008, 2008, pp. 231–241.
      Sco, GS
    33. Belohlavek Radim: Relational Data, Formal Concept Analysis, and Graded Attributes.
      In: Galindo J. (Ed.): Handbook of Research on Fuzzy Information Processing in Databases, 2008, pp. 462–489.
      GS
    34. Belohlavek Radim, Krupka Michal: Factor structures and central points by similarity.
      In: IEEE (Ed.): 2008 4th International IEEE Conference Intelligent Systems, Vols 1 and 2, 2008, pp. 634–637.
      WoS, Sco, GS
    35. Belohlavek Radim: Optimal decompositions of matrices with grades.
      In: IEEE (Ed.): 2008 4th International IEEE Conference Intelligent Systems, Vols 1 and 2, 2008, pp. 628–633.
      WoS, Sco, GS
    36. Yang Li, Xu Yang: Linguistic truth-valued concept lattice based on lattice-valued logic.
      In: ATlantic PRess (Ed.): Proceedings of the International Conference on Intelligent Systems and Knowledge Engineering (ISKE 2007), Advances in Intelligent Systems Research, 2007.
      WoS, GS
    37. Bělohlávek Radim, Vychodil Vilém: Estimations of Similarity in Formal Concept Analysis of Data with Graded Attributes.
      In: Last M., Szczepaniak P. S., Volkovich Z., Kandel A. (Eds.): Advances in Web Intelligence and Data Mining, 2006, pp. 243–252.
      GS
    38. Belohlavek R., Vychodil V.: Similarity issues in attribute implications from data with fuzzy attributes.
      In: Zhang D., Khoshgoftaar T. M., Joshi J. B. D. (Eds.): Proceedings of the 2006 IEEE International Conference on Information Reuse and Integration (IRI - 2006), 2006, pp. 132–135.
      GS
    39. Belohlavek R., Vychodil V.: Geometry and heuristics for discovery of optimal factors in binary data.
      GS
    40. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: Direct factorization by similarity of fuzzy concept lattices by factorization of input data.
      In: Ben Yahia S., Mephu Nguifo E., Belohlavek R. (Eds.): Concept Lattices and their Applications, Lecture Notes in Artificial Intelligence 4923, 2008, pp. 68–79.
      WoS, Sco, GS
    41. Outrata Jan: Factorizing Fuzzy Concept Lattices by Similarity.
      Dissertation Thesis, 2006, 77 pp.
      GS
  12. Outrata Jan: Similarity clarification in formal concept analysis.
    Journal of Electrical Engineering 56(12/s)(2005), pp. 41–45.
    [Slovak University of Technology, ISSN 1335–3632]
    DB:
    RIV
    abstract | 1 selfcitation (1 GS)

    Abstract Formal concept analysis (FCA) is an algebraic method of data miningwhich aims at extracting a hierarchical structure (so-called conceptlattice) of clusters (so-called formal concepts) from object-attributedata tables. One of the hottest problems in application of FCA is alarge number of clusters extracted from data. We try to cope withthis problem by reducing the amount of input data by the well-knownmethod called clarification, extended to fuzzy setting. This reductionhas the effect of clustering of similar formal concepts and therebymakes the concept lattice smaller.

    Citations
    1. Outrata Jan: Factorizing Fuzzy Concept Lattices by Similarity.
      Dissertation Thesis, 2006, 77 pp.
      GS

Papers in conference proceedings

  1. Outrata Jan, Trnecka Martin: Evaluating Association Rules in Boolean Matrix Factorization.
    In: Brejová B. (Ed.): Proceedings of the 16th ITAT Conference Information Technologies - Applications and Theory, ITAT 2016, Workshop on Computational Intelligence and Data Mining, WCIDM 2016, 2016, pp. 147–154, Tatranské Matliare, Slovakia, 9/2016.
    [CreateSpace Independent Publishing Platform,
    CEUR WS, Vol. 1649, ISBN 978-1537016740]
    DB: GS
    PDF | abstract | 1 citation (1 GS) − 1 co-citation (1 GS)

    Abstract Association rules, or association rule mining, is a well-established and popular method of data mining and machine learning successfully applied in many different areas since mid-nineties. Association rules form a ground of the Asso algorithm for discovery of the first (presumably most important) factors in Boolean matrix factorization. In Asso, the confidence parameter of association rules heavily influences the quality of factorization. However, association rules, in a more general form, appear already in GUHA, a knowledge discovery method developed since mid-sixties. In the paper, we evaluate the use of various (other) types of association rules from GUHA in Asso and, from the other side, a possible utilization of (particular) association rules in other Boolean matrix factorization algorithms not based on the rules. We compare the quality of factorization produced by the modified algorithms with those produced by the original algorithms.

    Citations
    1. Trnečka Martin: Decompositions of matrices with relational data: foundations and algorithms.
      Dissertation Thesis, 2016
      GS
  2. Belohlavek Radim, Outrata Jan, Trnecka Martin: How to assess quality of BMF algorithms?.
    In: Yager R., Sgurev V., Hadjiski M., Jotsov V. (Eds.): Proceedings of the IEEE 8th International Conference on Intelligent Systems, IS 2016, 2016, pp. 227–233, Sofia, Bulgaria, 9/2016.
    [IEEE,
    DOI 10.1109/IS.2016.7737426, ISBN 978-1-5090-1353-8]
    DB: Sco, GS
    PDF | abstract | 1 citation (1 GS) − 1 co-citation (1 GS)

    Abstract We critically examine the problem of quality assessment of algorithms for Boolean matrix factorization. We argue that little attention is paid to this problem in the literature. We view this problem as a multifaceted one and identify key aspects with respect to which the quality of algorithms should be assessed. Because of its utmost importance, we focus on assessment of quality of sets of factors extracted from Boolean data, propose ways to assess such quality and provide experimental evaluation involving selected factorization algorithms. We argue that the views involved in our proposal, represent reasonable basic standpoints for further systematic approaches to quality assessment.

    Citations
    1. Trnečka Martin: Decompositions of matrices with relational data: foundations and algorithms.
      Dissertation Thesis, 2016
      GS
  3. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
    In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376, Moscow, Russia, 7/2016.
    [National Research University Higher School of Economics, Moscow, Russia,
    CEUR WS, Vol. 1624, ISBN 978-5-600-01454-1]
    DB: GS
    PDF | abstract

    Abstract Formal Concept Analysis – known as a technique for data analysis and visualisation – can also be applied as a means of creating interaction approaches that allow for knowledge discovery within collections of content. These interaction approaches rely on performant algorithms that can generate conceptual neighbourhoods based on a single formal concept, or incrementally compute and update a set of formal concepts given changes to a formal context. Using case studies based on content from museum collections, this paper describes the scalability limitations of existing interaction approaches and presents an implementation and evaluation of the FCbO update algorithm as a means of updating formal concepts from large and dynamically changing museum datasets.

  4. Outrata Jan: A lattice-free concept lattice update algorithm based on *CbO.
    In: Ojeda-Aciego M., Outrata J. (Eds.): CLA 2013: Proceedings of the 10th International Conference on Concept Lattices and Their Applications, 2013, pp. 261–274, La Rochelle, France, 10/2013.
    [Laboratory L3i, University of La Rochelle, La Rochelle, France,
    CEUR WS, Vol. 1062, ISBN 978–2–7466–6566–8]
    DB: Sco, GS, RIV
    PDF | abstract | 3 citations (3 Sco, 3 GS) + 1 selfcitation (1 GS)

    Abstract Updating a concept lattice when introducing new objects to input data can be done by any of the so-called incremental algorithms for computing concept lattice of the data. The algorithms use and update the lattice while introducing new objects one by one. The present concept lattice of input data without the new objects is thus required before the update. In this paper we propose an efficient algorithm for updating the lattice from the present and new objects only, not requiring the possibly large concept lattice of present objects. The algorithm results as a modification of the CbO algorithm for computing the set of all formal concepts, or its modifications like FCbO, PCbO or PFCbO, to compute new and modified formal concepts only and the changes of the lattice order relation when input data changes. We describe the algorithm and present an experimental evaluation of its performance and a comparison with AddIntent incremental algorithm for computing concept lattice.

    Citations
    1. Naidenova Xenia A., Parkhomenko Vladimir A., Shvetsov Konstantin Vladimirovich, Yusupov Vladislav, Kuzina Raisa: Modification of good tests in dynamic contexts: Application to modeling intellectual development of cadets.
      In: Ojeda-Aciego M., Lepskiy A., Ignatov D.I. (Eds.): 2nd International Workshop on Soft Computing Applications and Knowledge Discovery, SCAKD 2016, 2016, pp. 51–62.
      Sco, GS
    2. Zou Ligeng, Zhang Zuping, Long Jun: A fast incremental algorithm for constructing concept lattices.
      Expert Systems with Applications 42(9)(2015), pp. 4474–4481.
      WoS, Sco, GS
    3. Kauer Martin, Krupka Michal: Removing an incidence from a formal context.
      In: Bertet K., Rudolph S. (Eds.): Proc. CLA 2014, 2014, pp. 195–207.
      Sco, GS
    4. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
      In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376.
      GS
  5. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
    In: Szathmary L., Priss U. (Eds.): CLA 2012: Proceedings of the 9th International Conference on Concept Lattices and Their Applications, 2012, pp. 305–316, Fuengirola (Málaga), Spain, 10/2012.
    [Universidad de Málaga, Málaga, Spain,
    CEUR WS, Vol. 972, ISBN 978–84–695–5252–0]
    DB: Sco, RIV
    PDF | abstract | 1 citation (1 Sco, 1 GS)

    Abstract The paper explores a utilization of Boolean factorization as a method for data preprocessing in classification of Boolean data. In previous papers, we demonstrated that data preprocessing consisting in replacing the original Boolean attributes by factors, i.e. new Boolean attributes that are obtained from the original ones by Boolean factorization, improves the quality of classification. The aim of this paper is to explore the question of how the various Boolean factorization methods that were proposed in the literature impact the quality of classification. In particular, we compare three factorization methods, present experimental results, and outline issues for future research.

    Citations
    1. Sun Yuan, Ye Shiwei, Shi Huiyang, Wang Haobo, Sun Yi: Maximum likelihood estimation based DINA model and Q-matrix learning.
      In: Proceedings of 2014 IEEE International Conference on Behavior, Economic and Social Computing (BESC 2014), 2014, pp. 1–6.
      Sco, GS
  6. Krajca Petr, Outrata Jan, Vychodil Vilém: Using frequent closed itemsets for data dimensionality reduction.
    In: Cook D., Pei J., Wang W., Zaiane O., Wu X. (Eds.): Proceedings of the ICDM 2011, The 11th IEEE International Conference on Data Mining, 2011, pp. 1128–1133, Vancouver, Canada, 12/2011.
    [IEEE Computer Society, Conference Publishing Services, Los Alamitos, California, USA,
    DOI 10.1109/ICDM.2011.154, ISBN 978–0–7695–4408–3]
    DB: GS, RIV
    abstract | 6 citations (6 GS)

    Abstract We address important issues of dimensionality reduction of transactional data sets where the input data consists of lists of transactions, each of them being a finite set of items. The reduction consists in finding a small set of new items, so-called factor-items, which is considerably smaller than the original set of items while comprising full or nearly full information about the original items. Using this type of reduction, the original data set can be represented by a smaller transactional data set using factor-items instead of the original items, thus reducing its dimensionality. The procedure utilized in this paper is based on approximate Boolean matrix decomposition. In this paper, we focus on the role of frequent closed itemsets that can be used to determine factor-items. We present the factorization problem, its reduction to Boolean matrix decompositions, experiments with publicly available data sets, and an algorithm for computing decompositions.

    Citations
    1. Li Yun, Xu Jie, Yuan Yun-Hao, Chen Ling: A new closed frequent itemset mining algorithm based on GPU and improved vertical structure.
      Concurrency and Computation, Practice and Experience (2016).
      GS
    2. Mirisaee S. H., Gaussier E., Termier A.: Itemset approximation using Constrained Binary Matrix Factorization.
      In: Data Science and Advanced Analytics (DSAA), 2014 International Conference on, 2014, pp. 39–45.
      GS
    3. Sánchez Carlos A.: Timetabling in Higher Education: Considering the Combinations of Classes Taken by Students.
      In: Özcan E., Burke E. K., McCollum B. (Eds.): 10th International Conference of the Practice and Theory of Automated Timetabling (PATAT 2014), Proceedings, 2014, pp. 549–553.
      GS
    4. Li Taoshen, Luo Dan: A New Improved Apriori Algorithm Based on Compression Matrix.
      In: Luo X., Xu Yu J., Li Z. (Eds.): Advanced Data Mining and Applications, 10th International Conference, ADMA 2014, Proceedings, Lecture Notes in Computer Science 8933, 2014, pp. 1–15.
      GS
    5. Li Yun, Xu Jie, Zhang Xiaobing, Li Chen, Zhang Yingjuan: An Incremental Closed Frequent Itemsets Mining Algorithm Based on Shadow Prefix Tree.
      In: Web Information System and Application Conference (WISA), 2013 10th, Proceedings, 2013, pp. 440–445.
      GS
    6. Souza Alan: Implementing and analysing dataset dimensionality reduction through frequent closed itemsets.
      GS
  7. Belohlavek Radim, Grissa Dhouha, Guillaume Silvie, Mephu Nguifo Engelbert, Outrata Jan: Boolean factors as a means of clustering of interestingness measures of association rules.
    In: Napoli A., Vychodil V. (Eds.): CLA 2011: Proceedings of the 8th International Conference on Concept Lattices and Their Applications, 2011, pp. 207–222, Nancy, France, 10/2011.
    [INRIA Nancy - Grand Est and LORIA, Nancy, France,
    CEUR WS, Vol. 959, ISBN 978–2–905267–78–8]
    DB: Sco, RIV
    PDF | abstract

    Abstract Measures of interestingness play a crucial role in association rule mining. An important methodological problem is to provide a reasonable classification of the measures. Several papers appeared on this topic. In this paper, we explore Boolean factor analysis, which uses formal concepts corresponding to classes of measures as factors, for the purpose of classification and compare the results to the previous approaches.

  8. Outrata Jan: Boolean factor analysis for data preprocessing in machine learning.
    In: Draghici S., Khoshgoftaar T. M., Palade V., Pedrycz V., Wani M. A., Zhu X. (Eds.): Proceedings of The Ninth Int. Conf. on Machine Learning and Applications (ICMLA 2010), 2010, pp. 899–902, Washington, D.C., USA, 12/2010.
    [IEEE,
    DOI 10.1109/ICMLA.2010.141, ISBN 978–0–7695–4300–0]
    DB: Sco, GS, RIV
    abstract | 14 citations (2 WoS, 10 Sco, 14 GS) + 2 selfcitations (2 Sco, 2 GS)

    Abstract We present two input data preprocessing methods for machine learning (ML). The first one consists in extending the set of attributes describing objects in input data table by new attributes and the second one consists in replacing the attributes by new attributes. The methods utilize formal concept analysis (FCA) and boolean factor analysis, recently described by FCA, in that the new attributes are defined by so-called factor concepts computed from input data table. The methods are demonstrated on decision tree induction. The experimental evaluation and comparison of performance of decision trees induced from original and preprocessed input data is performed with standard decision tree induction algorithms ID3 and C4.5 on several benchmark datasets.

    Citations
    1. Bartl Eduard, Belohlavek Radim, Osicka Petr, Řezanková Hana: Dimensionality reduction in boolean data: Comparison of four BMF methods.
      In: 1st International Workshop on Clustering High-Dimensional Data, CHDD 2012, Lecture Notes in Computer Science 7627, 2015, pp. 118–133.
      Sco, GS
    2. Ignatov D. I.: Introduction to formal concept analysis and its applications in information retrieval and related fields.
      In: 8th Russian Summer School on Information Retrieval, RuSSIR 2014, Communications in Computer and Information Science 505, 2015, pp. 42–141.
      WoS, Sco, GS
    3. Belohlavek Radim, Trnecka Martin: From-below approximations in Boolean matrix factorization: Geometry and new algorithm.
      Journal of Computer and System Sciences 81(8)(2015), pp. 1678–1697.
      Sco, GS
    4. Ignatov Dmitry I., Gnatyshak Dmitry V., Kuznetsov Sergei O., Mirkin Boris G.: Triadic Formal Concept Analysis and triclustering: searching for optimal patterns.
      Machine Learning 101(1-3)(2015), pp. 271–302.
      WoS, GS
    5. Belohlavek Radim, Vychodil Vilem: Computing minimal sets of descriptive conditions for binary data.
      International Journal of General Systems 43(5)(2014), pp. 521–534.
      Sco, GS
    6. Belohlavek Radim, Trnecka Martin: From-Below Approximations in Boolean Matrix Factorization: Geometry and New Algorithm.
      arXiv:1306.4905, 2013, 38 pp.
      GS
    7. Belohlavek Radim, Glodeanu Cynthia, Vychodil Vilem: Optimal Factorization of Three-Way Binary Data Using Triadic Concepts.
      Order 30(2)(2013), pp. 437–454.
      Sco, GS
    8. Poelmans Jonas, Kuznetsov Sergei O., Ignatov Dmitry I., Dedene Guido: Formal Concept Analysis in knowledge processing: A survey on models and techniques.
      Expert Systems with Applications 40(16)(2013), pp. 6601–6623.
      WoS, Sco, GS
    9. Kuznetsov Sergei O., Poelmans Jonas: Knowledge representation and processing with formal concept analysis.
      Wiley Interdisciplinary Reviews-Data Mining and Knowledge Discovery 3(3)(2013), pp. 200–215.
      WoS, Sco, GS
    10. Guo Ping, Chen Shuai-Shuai, He Ying: Study on Data Preprocessing for Daylight Climate Data.
      In: Liu B., Ma M., Chang J. (Eds.): Information Computing and Applications, Third International Conference, ICICA 2012, Proceedings, Lecture Notes in Computer Science 7473, 2012, pp. 492–499.
      Sco, GS
    11. Tao Xiaozhen, Zhao Wendong, Wei Yi, Tian Chang: A Layered Recursive Construction Algorithm and a visualization method for concept lattice.
      In: Communication Technology (ICCT), 2012 IEEE 14th International Conference on , Proceedings, 2012, pp. 317–323.
      Sco, GS
    12. Glodeanu Cynthia-Vera: Conceptual Factors and Fuzzy Data.
      Dissertation Thesis, 2012, 172 pp.
      GS
    13. Osička Petr: Concept analysis of three-way ordinal matrices.
      Dissertation Thesis, 2012, 77 pp.
      GS
    14. Belohlavek Radim, Osička Petr, Vychodil Vilem: Factorizing Three-Way Ordinal Data Using Triadic Formal Concepts.
      In: Christiansen H., De Tré G., Yazici A., Zadrozny S., Andreasen T., Larsen H. L. (Eds.): Flexible Query Answering Systems, 9th International Conference, FQAS 2011, Proceedings, Lecture Notes in Computer Science 7022, 2011, pp. 400–411.
      Sco, GS
    15. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
      Annals of Mathematics and Artificial Intelligence 72(1–2)(2014), pp. 3–22.
      WoS, Sco, GS
    16. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
      In: Szathmary L., Priss U. (Eds.): CLA 2012: Proceedings of the 9th International Conference on Concept Lattices and Their Applications, 2012, pp. 305–316.
      Sco
  9. Outrata Jan: Preprocessing input data for machine learning by FCA.
    In: Kryszkiewicz M., Obiedkov S. (Eds.): CLA 2010: Proceedings of the 7th International Conference on Concept Lattices and Their Applications, 2010, pp. 187–198, Sevilla, Spain, 10/2010.
    [University of Sevilla, Sevilla, Spain,
    CEUR WS, Vol. 672, ISBN 978–84614–4027–6]
    DB: Sco, GS, RIV
    PDF | abstract | 6 citations (6 GS) + 2 selfcitations (2 Sco, 2 GS)

    Abstract The paper presents an utilization of formal concept analysis in input data preprocessing for machine learning. Two preprocessing methods are presented. The first one consists in extending the set of attributes describing objects in input data table by new attributes and the second one consists in replacing the attributes by new attributes. In both methods the new attributes are defined by certain formal concepts computed from input data table. Selected formal concepts are so-called factor concepts obtained by boolean factor analysis, recently described by FCA. The ML method used to demonstrate the ideas is decision tree induction. The experimental evaluation and comparison of performance of decision trees induced from original and preprocessed input data is performed with standard decision tree induction algorithms ID3 and C4.5 on several benchmark datasets.

    Citations
    1. Ren Ruisi, Wei Ling: The attribute reductions of three-way concept lattices.
      Knowledge-Based Systems 99(2016), pp. 92–102.
      GS
    2. Trnečka Martin: Decompositions of matrices with relational data: foundations and algorithms.
      Dissertation Thesis, 2016
      GS
    3. Bhalekar Hemangi, Kumbhar Swati, Mewada Hiral, Pokharkar Pratibha, Patil Shriya, Gound Renuka: Pre-processing data using ID3 classifier.
      International Journal of Engineering and Techniques 1(3)(2015).
      GS
    4. Konecny Jan, Osicka Petr: Triadic concept lattices in the framework of aggregation structures.
      Information Sciences 279(2014), pp. 512–527.
      GS
    5. Osička Petr: Concept analysis of three-way ordinal matrices.
      Dissertation Thesis, 2012, 77 pp.
      GS
    6. Belohlavek Radim, Osička Petr, Vychodil Vilem: Factorizing Three-Way Ordinal Data Using Triadic Formal Concepts.
      In: Christiansen H., De Tré G., Yazici A., Zadrozny S., Andreasen T., Larsen H. L. (Eds.): Flexible Query Answering Systems, 9th International Conference, FQAS 2011, Proceedings, Lecture Notes in Computer Science 7022, 2011, pp. 400–411.
      GS
    7. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
      Annals of Mathematics and Artificial Intelligence 72(1–2)(2014), pp. 3–22.
      WoS, Sco, GS
    8. Belohlavek Radim, Outrata Jan, Trnecka Martin: Impact of Boolean factorization as preprocessing methods for classification of Boolean data.
      In: Szathmary L., Priss U. (Eds.): CLA 2012: Proceedings of the 9th International Conference on Concept Lattices and Their Applications, 2012, pp. 305–316.
      Sco
  10. Krajca Petr, Outrata Jan, Vychodil Vilém: Advances in algorithms based on CbO.
    In: Kryszkiewicz M., Obiedkov S. (Eds.): CLA 2010: Proceedings of the 7th International Conference on Concept Lattices and Their Applications, 2010, pp. 325–337, Sevilla, Spain, 10/2010.
    [University of Sevilla, Sevilla, Spain,
    CEUR WS, Vol. 672, ISBN 978–84614–4027–6]
    DB: Sco, GS, RIV
    PDF | abstract | 30 citations (30 GS) + 5 selfcitations (3 Sco, 5 GS)

    Abstract The paper presents a survey of recent advances in algorithms for computing all formal concepts in a given formal context which result as modifications or extensions of CbO. First, we present an extension of CbO, so called FCbO, and an improved canonicity test that significantly reduces the number of formal concepts which are computed multiple times. Second, we outline a parallel version of the proposed algorithm and discuss various scheduling strategies and their impact on the overall performance and scalability of the algorithm. Third, we discuss important data preprocessing issues and their influence on the algorithms. Namely, we focus on the role of attribute permutations and present experimental observations about the efficiency of the proposed algorithms with respect to the number of inversions in such permutations.

    Citations
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      Biologically Inspired Cognitive Architectures (2017).
      GS
    2. Kodagoda Nuwan, Pulasinghe Koliya: Comparision Between Features of CbO based Algorithms for Generating Formal Concepts.
      International Journal of Conceptual Structures and Smart Applications 4(1)(2016).
      GS
    3. Bazin Alexandre: Comparing Algorithms for Computing Lower Covers of Implication-closed Sets.
      In: Huchard M., Kuznetsov S. O. (Eds.): Proc. CLA 2016, 2016, pp. 21–31.
      GS
    4. Rodríguez-Jiménez Jose Manuel, Cordero Pablo, Enciso Manuel, Mora Angel: Data mining algorithms to compute mixed concepts with negative attributes: an application to breast cancer data analysis.
      Mathematical Methods in the Applied Sciences (2016).
      GS
    5. Alam Mehwish: Interactive Knowledge Discovery over Web of Data.
      Dissertation Thesis, 2015, 159 pp.
      GS
    6. Buzmakov Aleksey: Formal Concept Analysis and Pattern Structures for mining Structured Data.
      Dissertation Thesis, 2015, 193 pp.
      GS
    7. Ol'shanskii D. L.: WEBCHEM-JSM: an information environment for implementation of the JSM method in pharmacology.
      Automatic Documentation and Mathematical Linguistics 49(5)(2015), pp. 153–162.
      GS
    8. Ol'shanskii D. L.: Selection of an algorithm for the parallel implementation of the similarity method in intelligent DSM systems.
      Automatic Documentation and Mathematical Linguistics 49(4)(2015), pp. 109–116.
      GS
    9. Andrews Simon: A ‘Best-of-Breed’ approach for designing a fast algorithm for computing fixpoints of Galois Connections.
      Information Sciences 295(2015), pp. 633–649.
      WoS, GS
    10. Wu Chao: Intelligent Data Mining on Large-scale Heterogeneous Datasets and its Application in Computational Biology.
      Dissertation Thesis, 2014
      GS
    11. Kaburlasos V. G., Moussiades L.: Induction of formal concepts by lattice computing techniques for tunable classification.
      Journal of Engineering Science and Technology Review 7(1)(2014), pp. 1–8.
      GS
    12. Bazin Alexandre: On the enumeration of pseudo-intents : choosing the order and extending to partial implications.
      Dissertation Thesis, 2014
      GS
    13. Котельников E.B.: ПОВЫШЕНИЕ БЫСТРОДЕЙСТВИЯ ДСМ-МЕТОДА В ЗАДАЧАХ ОБРАБОТКИ ТЕКСТОВОЙ ИНФОРМАЦИИ.
      In: КИИ-2014, Том 2, 2014, pp. 274–282.
      GS
    14. Veroneze Rosana, Banerjee Arindam, Von Zuben Fernando J.: Enumerating all maximal biclusters in numerical datasets.
      arXiv:1403.3562v3, 2014, 35 pp.
      GS
    15. Buzmakov Aleksey, Kuznetsov Sergei O., Napoli Amedeo: Is Concept Stability a Measure for Pattern Selection?.
      Procedia Computer Science 31(2014), pp. 918–927.
      GS
    16. Buzmakov Aleksey, Kuznetsov Sergei O., Napoli Amedeo: Scalable Estimates of Concept Stability.
      In: Glodeanu C. V., Kaytoue M., Sacarea Ch. (Eds.): Formal Concept Analysis, 12th International Conference, ICFCA 2014. Proceedings, Lecture Notes in Computer Science 8478, 2014, pp. 157–172.
      GS
    17. Alam Mehwish, Napoli Amedeo: Lattice-Based View Access: A way to Create Views over SPARQL Query for Knowledge Discovery.
      Research Report, 2014, 28 pp.
      GS
    18. Kaburlasos V.G., Tsoukalas V., Moussiades L.: FCknn: A granular knn classifier based on formal concepts.
      In: IEEE (Ed.): 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2014, pp. 61–68.
      GS
    19. Andrews Simon: A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms.
      In: Hernandez N., Jäschke R., Croitoru M. (Eds.): Graph-Based Representation and Reasoning, 21st International Conference on Conceptual Structures, ICCS 2014. Proceedings, Lecture Notes in Artificial Intelligence 8577, 2014, pp. 37–50.
      WoS, GS
    20. Ferrandin Mauri, Nievola Júlio César, Enembreck Fabrício, Scalabrin Edson Emílio, Kredens Kelvin Vieira, Ávila Bráulio Coelho: Hierarchical Classification Using FCA and the Cosine Similarity Function.
      In: Proceedings of The 2013 World Congress in Computer Science, Computer Engineering, and Applied Computing, 2013.
      GS
    21. Selmi Afef, Gammoudi Mohamed Mohsen, Harrathi Farah: A method for improving Algorithms of Formal Concepts extraction using Prime Numbers.
      ResearchGate, 2013
      GS
    22. Pisková Lenka, Horváth Tomáš: Comparing Performance of Formal Concept Analysis and Closed Frequent Itemset Mining Algorithms on Real Data.
      In: Ojeda-Aciego M., Outrata J. (Eds.): Proc. CLA 2013, 2013, pp. 299–304.
      GS
    23. Ferreira Tiago: Redes Sociais e Classificação Conceptual: Abordagem Complementar para um sistema de Recomendação de Coautorias.
      Dissertation Thesis, 2013, 91 pp.
      GS
    24. Hashikami Hidenobu, Tanabata Takanari, Hirose Fumiaki, Hasanah Nur, Sawase Kazuhito, Nobuhara Hajime: An Algorithm for Recomputing Concepts in Microarray Data Analysis by Biological Lattice.
      Journal of Advanced Computational Intelligence and Intelligent Informatics 17(5)(2013), pp. 761–771.
      GS
    25. Poelmans Jonas, Kuznetsov Sergei O., Ignatov Dmitry I., Dedene Guido: Formal Concept Analysis in knowledge processing: A survey on models and techniques.
      Expert Systems with Applications 40(16)(2013), pp. 6601–6623.
      WoS, GS
    26. Ferrandin Mauri: Classificação hierárquica utilizando análise formal de conceitos.
      Dissertation Thesis, 2012
      GS
    27. Osička Petr: Concept analysis of three-way ordinal matrices.
      Dissertation Thesis, 2012, 77 pp.
      GS
    28. Kirchberg Markus, Leonardi Erwin, Tan Yu Shyang, Link Sebastian, Ko Ryan K. L., Lee Bu Sung: Formal Concept Discovery in Semantic Web Data.
      In: Domenach F., Ignatov D. I., Poelmans J. (Eds.): Formal Concept Analysis, 10th International Conference, ICFCA 2012. Proceedings, Lecture Notes in Computer Science 7278, 2012, pp. 164–179.
      GS
    29. Kaytoue Mehdi, Kuznetsov Sergei O., Napoli Amedeo: Biclustering Numerical Data in Formal Concept Analysis.
      In: Valtchev P., Jäschke R. (Eds.): Formal Concept Analysis, 9th International Conference, ICFCA 2011. Proceedings, Lecture Notes in Computer Science 6628, 2011, pp. 135–150.
      GS
    30. Andrews Simon: In-Close2, a High Performance Formal Concept Miner.
      In: Andrews S., Polovina S., Hill R., Akhgar B. (Eds.): Conceptual Structures for Discovering Knowledge, 19th International Conference on Conceptual Structures, ICCS 2011, Lecture Notes in Computer Science 6828, 2011, pp. 50–62.
      GS
    31. Wray Tim, Outrata Jan, Eklund Peter: Scalable Performance of FCbO Update Algorithm on Museum Data.
      In: Huchard M., Kuznetsov S. O. (Eds.): CLA 2016: Proceedings of the 13th International Conference on Concept Lattices and Their Applications, 2016, pp. 363–376.
      GS
    32. Outrata Jan: A lattice-free concept lattice update algorithm.
      Int. Journal of General Systems 45(2)(2016), pp. 211–231.
      WoS, Sco, GS
    33. Outrata Jan: A lattice-free concept lattice update algorithm based on *CbO.
      In: Ojeda-Aciego M., Outrata J. (Eds.): CLA 2013: Proceedings of the 10th International Conference on Concept Lattices and Their Applications, 2013, pp. 261–274.
      Sco, GS
    34. Krajca Petr, Outrata Jan, Vychodil Vilém: Computing formal concepts by attribute sorting.
      Fundamenta Informaticae 115(4)(2012), pp. 395–417.
      WoS, Sco, GS
    35. Outrata Jan, Vychodil Vilém: Fast Algorithm for Computing Fixpoints of Galois Connections Induced by Object-Attribute Relational Data.
      Information Sciences 185(1)(2012), pp. 114–127.
      WoS, Sco, GS
  11. Krajca Petr, Outrata Jan, Vychodil Vilém: Parallel Recursive Algorithm for FCA.
    In: Belohlavek R., Kuznetsov S. O. (Eds.): CLA 2008: Proceedings of the Sixth International Conference on Concept Lattices and Their Applications, 2008, pp. 71–82, Olomouc, Czech Rep., 10/2008.
    [Palacký University, Olomouc, Czech Rep.,
    CEUR WS, Vol. 433, ISBN 978–80–244–2111–7]
    DB: Sco, GS, RIV
    PDF | abstract | 53 citations (2 Sco, 53 GS) − 1 co-citation (1 GS) + 1 selfcitation (1 Sco, 1 GS)

    Abstract This paper presents a parallel algorithm for computing formal concepts. Presented is a sequential version upon which we build the parallel one.We describe the algorithm, its implementation, scalability, and provide an initial experimental evaluation of its efficiency. The algorithm is fast, memory efficient, and can be optimized so that all critical operations are reduced to low-level bit-array operations. One of the key features of the algorithm is that it avoids synchronization which has positive impacts on its speed and implementation.

    Citations
    1. Kodagoda Nuwan, Pulasinghe Koliya: Comparision Between Features of CbO based Algorithms for Generating Formal Concepts.
      International Journal of Conceptual Structures and Smart Applications 4(1)(2016).
      GS
    2. Ren Xiang, Xie Rong, Du Juan, He Xiang-Yi: Modeling of Spatial-Temporal Associations on a Mobile Trajectory.
      In: Hussain A. (Ed.): Proc. 5th International Conference on Electronics, Communications and Networks (CECNet 2015), Lecture Notes in Electrical Engineering 382, 2016, pp. 251–262.
      GS
    3. Andrews Simon, Hirsch Laurence: A Tool for Creating and Visualising Formal Concept Trees.
      In: Andrews S., Polovina S. (Eds.): Proc. Fifth Conceptual Structures Tools & Interoperability Workshop (CSTIW 2016), 22nd International Conference on Conceptual Structures (ICCS 2016), 2016, pp. 1–9.
      Sco, GS
    4. Benito-Picazo F., Cordero Pablo, Enciso Manuel, Mora Angel: Reducing the search space by closure and simplification paradigms, A parallel key finding method.
      The Journal of Supercomputing (2016), pp. 1–13.
      GS
    5. de Moraes Nilander R. M., Dias Sergio M., Freitas Henrique C., Zarate Luis E.: Parallelization of the next Closure algorithm for generating the minimum set of implication rules.
      Artificial Intelligence Research 5(2)(2016).
      GS
    6. Rodríguez-Jiménez Jose Manuel, Cordero Pablo, Enciso Manuel, Mora Angel: Data mining algorithms to compute mixed concepts with negative attributes: an application to breast cancer data analysis.
      Mathematical Methods in the Applied Sciences (2016).
      GS
    7. Singh Prem Kumar, Kumar Cherukuri Aswani, Gani Abdullah: A Comprehensive Survey on Formal Concept Analysis, its Research Trends and Applications.
      International Journal of Applied Mathematics and Computer Science 26(2)(2016), pp. 495–516.
      WoS, GS
    8. Ol'shanskii D. L.: WEBCHEM-JSM: an information environment for implementation of the JSM method in pharmacology.
      Automatic Documentation and Mathematical Linguistics 49(5)(2015), pp. 153–162.
      GS
    9. Ol'shanskii D. L.: Selection of an algorithm for the parallel implementation of the similarity method in intelligent DSM systems.
      Automatic Documentation and Mathematical Linguistics 49(4)(2015), pp. 109–116.
      GS
    10. Mimouni Nada: Interrogation d'un réseau sémantique de documents: l'intertextualité dans l'accés á l'information juridique.
      Dissertation Thesis, 2015, 245 pp.
      GS
    11. Kriegel Francesco, Borchmann Daniel: NextClosures: Parallel Computation of the Canonical Base.
      In: Ben Yahia S., Konecny J. (Eds.): Proc. CLA 2015, 2015, pp. 181–192.
      GS
    12. Tovar Mireya, Pinto David, Montes Azucena, Serna Gabriel, Vilariño Darnes: Patterns Used to Identify Relations in Corpus Using Formal Concept Analysis.
      In: Carrasco-Ochoa J. A., Martínez-Trinidad J. F., Sossa-Azuela J. H., Olvera López J. A., Famili F. (Eds.): Pattern Recognition, 7th Mexican Conference, MCPR 2015, Proceedings, Lecture Notes in Computer Science 9116, 2015, pp. 236–245.
      GS
    13. Güner Edip Serdar: Makine çevirisinde yeni bir bilgisayımsal yaklaşım.
      Doctoral Thesis, 2015, 107 pp.
      GS
    14. Tovar Vidal Mireya, Pinto David, Montes Azucena, Serna Gabriel Gonzalez, Vilarino Ayala Darnes: Identification of Ontological Relations in Domain Corpus Using Formal Concept Analysis.
      Engineering Letters 23(2)(2015).
      GS
    15. Andrews Simon: A ‘Best-of-Breed’ approach for designing a fast algorithm for computing fixpoints of Galois Connections.
      Information Sciences 295(2015), pp. 633–649.
      WoS, GS
    16. Tovar Vidal Mireya, Pinto David, Montes Azucena, Serna Gabriel Gonzalez, Vilarino Ayala Darnes: Identification of Ontological Relations Using Formal Concept Analysis.
      In: Acosta Guadarrama J. C., De Ita Luna G., Marcial Romero R., Osorio M., Zepeda C. (Eds.): Proceedings of the Ninth Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning, LANMR 2014, 2014.
      GS
    17. de Fréin Ruairí: Multilayered, Blocked Formal Concept Analyses for Adaptive Image Compression.
      In: Glodeanu C. V., Kaytoue M., Sacarea Ch. (Eds.): Formal Concept Analysis, 12th International Conference, ICFCA 2014. Proceedings, Lecture Notes in Computer Science 8478, 2014, pp. 251–267.
      GS
    18. Andrews Simon: A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms.
      In: Hernandez N., Jäschke R., Croitoru M. (Eds.): Graph-Based Representation and Reasoning, 21st International Conference on Conceptual Structures, ICCS 2014. Proceedings, Lecture Notes in Artificial Intelligence 8577, 2014, pp. 37–50.
      WoS, GS
    19. Kilicaslan Yilmaz, Tuna Gurkan: An Nlp-Based Approach for Improving Human-Robot Interaction.
      Journal of Artificial Intelligence and Soft Computing Research 3(3)(2013), pp. 189–200.
      GS
    20. Heckmann Paul, Speicher Daniel: Interactive Exploration of Structural Concepts in Code.
      In: Fred A., Dietz J. L. G., Liu K., Filipe J. (Eds.): Knowledge Discovery, Knowledge Engineering and Knowledge Management, 4th International Joint Conference, IC3K 2012. Revised Selected Papers, Communications in Computer and Information Science 415, 2013, pp. 260–270.
      GS
    21. Wray Tim, Eklund Peter, Kautz Karlheinz: Pathways through Information Landscapes: Alternative Design Criteria for Digital Art Collections.
      In: The 34th International Conference on Information Systems (ICIS 2013), 2013.
      GS
    22. Pei Zheng, Ruan Da, Meng Dan, Liu Zhicai: Formal concept analysis based on the topology for attributes of a formal context.
      Information Sciences 236(2013), pp. 66–82.
      GS
    23. Sawase Kazuhito, Nobuhara Hajime: The transformation method between tree and lattice for file management system.
      Evolving Systems 4(3)(2013), pp. 183–193.
      GS
    24. Hashikami Hidenobu, Tanabata Takanari, Hirose Fumiaki, Hasanah Nur, Sawase Kazuhito, Nobuhara Hajime: An Algorithm for Recomputing Concepts in Microarray Data Analysis by Biological Lattice.
      Journal of Advanced Computational Intelligence and Intelligent Informatics 17(5)(2013), pp. 761–771.
      GS
    25. Barkstrom Bruce R.: Using Formal Concept Analysis for Categorizing Earth Science Data and Object Collections.
      In: The 17th World Multi-Conference on Systemics, Cybernetics and Informatics: WMSCI 2013, 2013.
      GS
    26. Hachana Safaà, Cuppens Frédéric, Cuppens-Boulahia Nora, Atluri Vijay, Morucci Stephane: Policy Mining: A Bottom-Up Approach toward a Model Based Firewall Management.
      In: Bagchi A., Ray I. (Eds.): Information Systems Security, 9th International Conference, ICISS 2013. Proceedings, Lecture Notes in Computer Science 8303, 2013, pp. 133–147.
      GS
    27. Ying Wen, Mingqing Xiao: Diagnosis Rule Mining of Airborne Avionics Using Formal Concept Analysis.
      In: Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC), 2013 International Conference on, 2013, pp. 259–265.
      GS
    28. Andrews Simon: Discovering Knowledge in Data Using Formal Concept Analysis.
      International Journal of Distributed Systems and Technologies (IJDST) 4(2)(2013).
      GS
    29. de Fréin Ruairí: Formal Concept Analysis via Atomic Priming.
      In: Cellier P., Distel F., Ganter B. (Eds.): Formal Concept Analysis, 11th International Conference, ICFCA 2013. Proceedings, Lecture Notes in Computer Science 7880, 2013, pp. 92–108.
      GS
    30. Zlotnikova Irina, van der Weide Theo: An approach to modeling ICT educational policies in African countries.
      International Journal of Education and Development using ICT 7(3)(2012), pp. 50–73.
      GS
    31. Osička Petr: Concept analysis of three-way ordinal matrices.
      Dissertation Thesis, 2012, 77 pp.
      GS
    32. Heckmann Paul, Speicher Daniel: Assisted Software Exploration using Formal Concept Analysis.
      In: Exman I., Llorens J., Fraga A. (Eds.): 3rd International Workshop on Software Knowledge - SKY 2012, 2012.
      GS
    33. Shan Bo, Qi Jianjun, Liu Wei: A CUDA-Based Algorithm for Constructing Concept Lattices.
      In: Yao JT., Yang Y., Słowiński R., Greco S., Li H., Mitra S., Polkowski L. (Eds.): Rough Sets and Current Trends in Computing, 8th International Conference, RSCTC 2012. Proceedings, Lecture Notes in Computer Science 7413, 2012, pp. 297–302.
      GS
    34. Andrews Simon, Orphanides Constantinos: Knowledge discovery through creating formal contexts.
      International Journal of Space-Based and Situated Computing 2(2)(2012), pp. 123–138.
      GS
    35. Doerfel Stephan, Jäschke Robert, Stumme Gerd: Publication Analysis of the Formal Concept Analysis Community.
      In: Domenach F., Ignatov D. I., Poelmans J. (Eds.): Formal Concept Analysis, 10th International Conference, ICFCA 2012. Proceedings, Lecture Notes in Computer Science 7278, 2012, pp. 77–95.
      GS
    36. Xu Biao, de Fréin Ruairí, Robson Eric, Foghlú Mícheál Ó: Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework.
      In: Domenach F., Ignatov D. I., Poelmans J. (Eds.): Formal Concept Analysis, 10th International Conference, ICFCA 2012. Proceedings, Lecture Notes in Computer Science 7278, 2012, pp. 292–308.
      GS
    37. Kirchberg Markus, Leonardi Erwin, Tan Yu Shyang, Link Sebastian, Ko Ryan K. L., Lee Bu Sung: Formal Concept Discovery in Semantic Web Data.
      In: Domenach F., Ignatov D. I., Poelmans J. (Eds.): Formal Concept Analysis, 10th International Conference, ICFCA 2012. Proceedings, Lecture Notes in Computer Science 7278, 2012, pp. 164–179.
      GS
    38. Wild Marcel: Compactly generating all satisfying truth assignments of a Horn formula.
      Journal on Satisfiability, Boolean Modeling and Computation 8(2012), pp. 63–82.
      GS
    39. Kirchberg Markus, Leonardi Erwin, Tan Yu Shyang, Ko Ryan K L, Link Sebastian, Lee Bu Sung: Beyond RDF Links – Exploring the Semantic Web with the Help of Formal Concepts.
      In: The 10th International Semantic Web Conference, ISWC 2011, 2011.
      GS
    40. Xu Biao: Distributed Algorithms for Computing Closed Itemsets Based on an Iterative MapReduce Framework.
      Master Thesis, 2011, 97 pp.
      GS
    41. Kılıçaslan Yılmaz, Güner Edip Serdar: Filtering Machine Translation Results with Automatically Constructed Concept Lattices.
      In: Napoli A., Vychodil V. (Eds.): Proc. CLA 2011, 2011, pp. 59–73.
      GS
    42. Langdon W. B., Yoo Shin, Harman Mark: Formal Concept Analysis on Graphics Hardware.
      In: Napoli A., Vychodil V. (Eds.): Proc. CLA 2011, 2011, pp. 413–416.
      Sco, GS
    43. Andrews Simon, Orphanides Constantinos, Polovina Simon: Visualising Computational Intelligence through Converting Data into Formal Concepts.
      In: Bessis N., Xhafa F. (Eds.): Next Generation Data Technologies for Collective Computational Intelligence, Studies in Computational Intelligence 352, 2011, pp. 139–165.
      GS
    44. Andrews Simon: In-Close2, a High Performance Formal Concept Miner.
      In: Andrews S., Polovina S., Hill R., Akhgar B. (Eds.): Conceptual Structures for Discovering Knowledge, 19th International Conference on Conceptual Structures, ICCS 2011, Lecture Notes in Computer Science 6828, 2011, pp. 50–62.
      GS
    45. Sawase Kazuhito, Nobuhara Hajime: A Method of Transformation Between Tree and Lattice Structure for File Management.
      In: SCIS & ISIS 2010, 2010.
      GS
    46. Andrews Simon, Orphanides Constantinos: Analysis of Large Data Sets using Formal Concept Lattices.
      In: Kryszkiewicz M., Obiedkov S. (Eds.): Proc. CLA 2010, 2010, pp. 104–115.
      GS
    47. Molloy Ian, Chen Hong, Li Tiancheng, Wang Qihua, Li Ninghui, Bertino Elisa, Calo Seraphin, Lobo Jorge: Mining Roles with Multiple Objectives.
      ACM Transactions on Information and System Security (TISSEC) 13(4)(2010).
      GS
    48. Fang Peici, Zheng Siyao: A Research on Fuzzy Formal Concept Analysis Based Collaborative Filtering Recommendation System.
      In: Knowledge Acquisition and Modeling, 2009. KAM '09. Second International Symposium on, 2009, pp. 352–355.
      GS
    49. Andrews Simon: Data conversion and interoperability for FCA.
      In: Conceptual Structures Tools Interoperability Workshop at the 17th International Conference on Conceptual Structures, 2009.
      GS
    50. Krajca Petr, Vychodil Vilem: Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework.
      In: Adams N. M., Robardet C., Siebes A., Boulicaut J.-F. (Eds.): Advances in Intelligent Data Analysis VIII, 8th International Symposium on Intelligent Data Analysis, IDA 2009, Lecture Notes in Computer Science 5772, 2009, pp. 333–344.
      GS
    51. Andrews Simon: In-Close, a fast algorithm for computing formal concepts.
      In: International Conference on Conceptual Structures (ICCS), 2009.
      GS
    52. Speicher Daniel, Heckmann Paul: Interaktive Exploration von Softwaremustern.
      , 2 pp.
      GS
    53. Коробко А. В., Пенькова Т. Г.: Интегральная OLAP-модель предметной области для аналитической поддержки принятия решений.
      Информационные технологии 12(), pp. 8–13.
      GS
    54. Krajca Petr, Outrata Jan, Vychodil Vilém: Advances in algorithms based on CbO.
      In: Kryszkiewicz M., Obiedkov S. (Eds.): CLA 2010: Proceedings of the 7th International Conference on Concept Lattices and Their Applications, 2010, pp. 325–337.
      Sco, GS
  12. Outrata Jan: Drawing lattices with a geometric heuristic.
    In: Yager R. R., Sgurev V. S., Jotsov V. S. (Eds.): Proceedings of IEEE CIS 2008: The Fourth International IEEE Conference on Intelligent Systems, 2008, pp. 1535–1541, Varna, Bulgaria, 9/2008.
    [IEEE, New York, USA,
    DOI 10.1109/IS.2008.4670536, ISBN 978–1–4244–1740–7]
    DB: WoS (WOS:000263194700112), Sco, GS, RIV
    PDF | abstract | 2 citations (2 GS)

    Abstract Lattices play an important role in many areas of computer science andapplied mathematics. The information, extracted from data in dataanalysis or operated with in intelligent systems, is usuallyrepresented by hierarchical structures, where relationships aredescribed by lattices. To visualize the information, one needs tovisualize lattices. We mention the existing methods of automateddrawing of lattices and focus on the geometric method introduced byWille et al. Diagrams drawn by the geometric method achieve a goodlevel of readability and aesthetic criteria while satisfying commonconventions and constraints, even for larger lattices. We discussseveral questions regarding the method and show the diagram drawingsproduced by two software programs developed at Dept. Computer Science,Palacky University, Czech Republic.

    Citations
    1. Kester Quist-Aphetsi: Using Formal Concepts Analysis Techniques in Mining Data from Criminal Databases and Profiling Events Based on Factors to Understand Criminal Environments.
      In: Gervasi O., Murgante B., Misra S., Rocha A. M. A. C., Torre C. M., Taniar D., Apduhan B. O., Stankova E., Wang S. (Eds.): Proc. Computational Science and Its Applications, 16th International Conference (ICCSA 2016), Lecture Notes in Computer Science 9790, 2016, pp. 480–496.
      GS
    2. Drda Adam: Demonstration of lattice drawing algorithms (in Czech).
      Bachelor Thesis, 2015, 40 pp.
      GS
  13. Outrata Jan: Inducing decision trees via concept lattices.
    In: Trappl R. (Ed.): Cybernetics and Systems 2008: Proceedings of the 19th European Meeting on Cybernetics and Systems Research, 2008, pp. 9–14, Vienna, Austria, 3/2008.
    [Austrian Society for Cybernetics Studies, Vienna, Austria, ISBN 978–3–85206–175–7]
    DB:
    RIV
    abstract

    Abstract The paper presents a new machine learning method of decision tree induction based on formal concept analysis (FCA). FCA is a data mining technique the output of which is a hierarchical structure of clusters extracted from data describing objects by attributes. The decision tree is derivedusing the structure of clusters (called concept lattice). The idea behind is tolook at a concept lattice as a collection of overlapping trees. The main purpose of the paper is to explore the possibility of using FCA in theproblem of decision tree induction. We present our method and providecomparisons with selected methods of decision tree induction and machine learning on testing datasets.

  14. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: Direct factorization by similarity of fuzzy concept lattices by factorization of input data.
    In: Ben Yahia S., Mephu Nguifo E., Belohlavek R. (Eds.): Concept Lattices and their Applications, Lecture Notes in Artificial Intelligence 4923, 2008, pp. 68–79, Hammamet, Tunisia, 10–11/2006.
    [Springer-Verlag, Berlin Heidelberg, Germany,
    DOI 10.1007/978-3-540-78921-5_4, ISBN 978–3–540–78920–8, ISSN 0302-9743 (paper), 1611–3349 (online)]
    DB: WoS (WOS:000254857000004), Sco, GS, RIV
    PDF | abstract | 4 citations (1 WoS, 2 Sco, 4 GS)

    Abstract The paper presents additional results on factorization by similarity of fuzzyconcept lattices. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concept lattice, its factor lattice. The factor lattice contains less clusters than the original concept lattice but, at the same time, represents a reasonable approximation of the original concept lattice and provides us with a granular view on the original concept lattice. The factor lattice results by factorization of the original fuzzy concept lattice by a similarity relation. The similarity relation is specified by a user by means of a single parameter, called a similarity threshold. Smaller similarity thresholds lead to smaller factor lattices, i.e. to morecomprehensible but less accurate approximations of the original concept lattice. Therefore, factorization by similarity provides a trade-off between comprehensibility and precision. We first recall the notion of factorization. Second, we present a way to compute the factor lattice of a fuzzy concept lattice directly from input data, i.e. without the need to compute the possibly large original concept lattice.

    Citations
    1. Konecny Jan, Krupka Michal: Block relations in formal fuzzy concept analysis.
      International Journal of Approximate Reasoning 73(2016), pp. 27–55.
      Sco, GS
    2. Konecny Jan: Closure and Interior Structures in Relational Data Analysis and Their Morphisms.
      Dissertation Thesis, 2012, 86 pp.
      GS
    3. Shu Chang, Mo Zhi Wen: On Fuzzy Rough Concept Lattices.
      In: Kahraman C., Kerre E. E., Bozbura F. T. (Eds.): Uncertainty Modeling in Knowledge Engineering and Decision Making, World Scientific Proceedings Series on Computer Engineering and Information Science 7, 2012, pp. 652–657.
      WoS, GS
    4. Konecny Jan, Krupka Michal: Block Relations in Fuzzy Setting.
      In: Napoli A., Vychodil V. (Eds.): Proc. CLA 2011, 2011, pp. 115–130.
      Sco, GS
  15. Bělohlávek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Inducing decision trees via concept lattices.
    In: Diatta J., Eklund P., Liquière M. (Eds.): Proc. CLA 2007, 2007, pp. 274–285, Montpellier, France, 10/2007.
    [LIRMM & University of Montpellier II, Montpellier, France,
    CEUR WS, Vol. 331]
    DB: Sco
    PDF | abstract | 1 citation ()

    Abstract The paper presents a new method of decision tree induction based on formalconcept analysis (FCA). The decision tree is derived using a concept lattice,i.e.a hierarchy of clusters provided by FCA. The idea behind is to lookat a concept lattice as a collection of overlapping trees.The main purpose of the paper is to explore the possibility of using FCA in theproblem of decision tree induction. We present our method and providecomparisonswith selected methods of decision tree induction on testing datasets.

    Citations
    1. Girard Nathalie: Vers une approche hybride mêlant arbre de classification et treillis de Galois pour de l'indexation d'images.
      Dissertation Thesis, 2013
  16. Bělohlávek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Trees in concept lattices.
    In: Torra V., Narukawa Y., Yoshida Y. (Eds.): Modeling Decisions for Artificial Intelligence: 4th International Conference, Lecture Notes in Artificial Intelligence 4617, 2007, pp. 174–184, Kitakyushu, Japan, 8/2007.
    [Springer-Verlag, Berlin Heidelberg, Germany,
    DOI 10.1007/978-3-540-73729-2_17, ISBN 978–3–540–73728–5, ISSN 0302-9743]
    DB: WoS (WOS:000249325800017), Sco, GS, RIV
    PDF | abstract | 2 citations (2 WoS, 1 Sco, 2 GS) + 1 selfcitation (1 WoS, 1 Sco, 1 GS)

    Abstract The paper presents theorems characterizing concept lattices which happen to be trees after removing the bottom element. Concept lattices are the clustering/classification systems provided as an output of formal concept analysis. In general, a concept latticemay contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several classification methods as the output. This paper attempts to help establish a bridge between concept lattices and tree-based classification methods. We present results presenting conditions for input data which are sufficient and necessary for the output concept lattice to form a tree after one removes its bottom element. In addition, we present illustrative examples and several remarks on related efforts and future research topics.

    Citations
    1. Apollonio Nicola, Caramia Massimiliano, Franciosa Paolo Giulio: On the Galois Lattice of Bipartite Distance Hereditary Graphs.
      Discrete Applied Mathematics 190(2015), pp. 13–23.
      WoS, GS
    2. Abudawood Tarek: Improving Predictions of Multiple Binary Models in ILP.
      The Scientific World Journal (2014).
      WoS, Sco, GS
    3. Belohlavek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Inducing decision trees via concept lattices.
      Int. Journal of General Systems 38(4)(2009), pp. 455–467.
      WoS, Sco, GS
  17. Bělohlávek Radim, De Baets Bernard, Outrata Jan, Vychodil Vilém: Lindig's algorithm for concept lattices over graded attributes.
    In: Torra V., Narukawa Y., Yoshida Y. (Eds.): Modeling Decisions for Artificial Intelligence: 4th International Conference, Lecture Notes in Artificial Intelligence 4617, 2007, pp. 156–167, Kitakyushu, Japan, 8/2007.
    [Springer-Verlag, Berlin Heidelberg, Germany,
    DOI 10.1007/978-3-540-73729-2_15, ISBN 978–3–540–73728–5, ISSN 0302-9743]
    DB: WoS (WOS:000249325800015), Sco, GS, RIV
    PDF | abstract | 14 citations (9 WoS, 8 Sco, 13 GS) − 1 co-citation (1 WoS, 1 GS)

    Abstract Formal concept analysis (FCA) is a method of exploratory data analysis. The data is in the form of a table describing relationship between objects (rows) and attributes (columns), where table entries are grades representing degrees to which objects have attributes. The main output of FCA is a hierarchical structure (so-called concept lattice) of conceptual clusters (so-called formal concepts) present in the data. This paper focuses on algorithmic aspects of FCA of data with graded attributes. Namely, we focus on the problem of generating efficiently all clusters present in the data together with their subconcept-superconcept hierarchy. We present theoretical foundations, the algorithm, analysis of its efficiency, and comparison with other algorithms.

    Citations
    1. Shemis Ebtesam E., Gadallah Ahmed M.: Enhanced algorithms for fuzzy formal concepts analysis.
      In: Hassanien A. E., Shaalan K., Azar A. T., Gaber T.,Tolba M. F. (Eds.): 2nd International Conference on Advanced Intelligent Systems and Informatics, AISI 2016, 2017, pp. 781–792.
      GS
    2. Singh Prem Kumar, Kumar C. Aswani, Li Jinhai: Knowledge representation using interval-valued fuzzy formal concept lattice.
      Soft Computing 20(4)(2016), pp. 1485–1502.
      WoS, Sco, GS
    3. De Maio C., Fenza G., Gallo M., Loia V., Senatore S.: Formal and relational concept analysis for fuzzy-based automatic semantic annotation.
      Applied Intelligence 40(1)(2014), pp. 154–177.
      WoS, Sco, GS
    4. Carlos Diaz Juan, Medina Jesus: Multi-adjoint relation equations: Definition, properties and solutions using concept lattices.
      Information Sciences 253(2013), pp. 100–109.
      WoS, Sco, GS
    5. Medina Jesus, Ojeda-Aciego Manuel: Dual multi-adjoint concept lattices.
      Information Sciences 225(2013), pp. 47–54.
      WoS, Sco, GS
    6. Carlos Diaz Juan, Medina Jesus: Solving systems of fuzzy relation equations by fuzzy property-oriented concepts.
      Information Sciences 222(2013), pp. 405–412.
      WoS, Sco, GS
    7. Loia V., Fenza G., De Maio C., Salerno S.: Hybrid methodologies to foster Ontology-based Knowledge Management Platform.
      In: IEEE (Ed.): 2013 IEEE Symposium on Intelligent Agent (IA), 2013, pp. 36–43.
      WoS
    8. Carlos Diaz Juan, Garcia Bosco, Medina Jesus, Rodriguez, Rafael: Building multi-adjoint concept lattices.
      In: Pasi G., Montero J., Ciucci D. (Eds.): Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13), Advances in Intelligent Systems Research 32, 2013, pp. 340–346.
      WoS, Sco, GS
    9. Díaz Juan Carlos, Medina Jesús, Rodríguez Rafael: Solving General Fuzzy Relation Equations Using Property-Oriented Concept Lattices.
      In: Greco S., Bouchon-Meunier B., Coletti G., Fedrizzi M., Matarazzo B., Yager R. R. (Eds.): Advances in Computational Intelligence, 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Proceedings, Part II, Communications in Computer and Information Science 298, 2012, pp. 395–404.
      GS
    10. Medina Jesus, Ojeda-Aciego Manuel: On multi-adjoint concept lattices based on heterogeneous conjunctors.
      Fuzzy Sets and Systems 208(2012), pp. 95–110.
      WoS, Sco, GS
    11. Díaz Juan Carlos, Medina-Moreno Jesús: Concept lattices in fuzzy relation equations.
      In: Napoli A., Vychodil V. (Eds.): Proc. CLA 2011, 2011, pp. 75–86.
      Sco, GS
    12. Majidian Andrei, Martin Trevor, Cintra Marcos E.: Fuzzy formal concept analysis and algorithm.
      In: Proceedings of the 11th UK Workshop on Computational Intelligence, 2011, pp. 61–67.
      GS
    13. Belohlavek Radim: Optimal decompositions of matrices with grades.
      In: IEEE (Ed.): 2008 4th International IEEE Conference Intelligent Systems, Vols 1 and 2, 2008, pp. 628–633.
      WoS, GS
    14. Ghosh Partha, Kundu Krishna: Rules for Computing Fixpoints of a Fuzzy Closure Operator.
      Annals of Fuzzy Mathematics and Informatics (2015).
      GS
  18. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: On factorization by similarity of fuzzy concept lattices with hedges.
    In: Ben Yahia S., Mephu Nguifo E. (Eds.): Proc. 4th Int. Conf. on Concept Lattices and Their Applications, CLA 2006, 2006, pp. 57–69, Hammamet, Tunisia, 10–11/2006.
    [Faculté des Sciences de Tunis, Université Centrale, Tunis, Tunisia, ISBN 978–9973–61–481–0]
    DB:
    GS, RIV
    PDF | abstract | 1 selfcitation (1 GS)

    Abstract The paper presents results on factorization by similarity of fuzzy concept lattices with hedges. Factorization of fuzzy concept lattices including a fast way to compute the factor lattice was presented in our earlier papers. The basic idea is to have, instead of a whole fuzzy concept lattice, its factor lattice. The factor lattice results by factorizingthe original fuzzy concept lattice by a similarity relation which is specified by a user by a single parameter (similarity threshold). The main purpose is to have a smaller lattice which can be seen as a reasonable approximation of the original, possibly large, fuzzy concept lattice. In this paper, we extend the existing results to the case of fuzzy concept lattices with hedges, i.e. with parameters controlling the size of a fuzzy concept lattice.

    Citations
    1. Outrata Jan: Factorizing Fuzzy Concept Lattices by Similarity.
      Dissertation Thesis, 2006, 77 pp.
      GS
  19. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: Thresholds and shifted attributes in formal concept analysis of data with fuzzy attributes.
    In: Schärfe H., Hitzler P., Øhrstrøm P. (Eds.): Proc. 14th International Conference on Conceptual Structures, ICCS 2006, Lecture Notes in Artificial Intelligence 4068, 2006, pp. 117–130, Aalborg, Denmark, 7/2006.
    [Springer-Verlag, Berlin Heidelberg, Germany,
    DOI 10.1007/11787181_9, ISBN 3–540–35893–5, ISSN 0302-9743]
    DB: WoS (WOS:000239625500008), Sco, GS, RIV
    PDF | abstract | 16 citations (9 WoS, 9 Sco, 16 GS) − 2 co-citations (1 WoS, 1 Sco, 2 GS) + 3 selfcitations (1 WoS, 1 Sco, 3 GS)

    Abstract We focus on two approaches to formal concept analysis (FCA) of data with fuzzy attributes recently proposed in the literature, namely, on the approach via hedges and the approach via thresholds. Both of the approaches present parameterized ways to FCA of data with fuzzy attributes. Our paper shows basic relationships between the two of the approaches. Furthermore, we show that the approaches can be combined in a natural way, i.e. we present an approach in which one deals with both thresholds and hedges. We argue that while the approach via thresholds is intuitively appealing, it can be considered a special case of the approach via hedges. An important role in this analysis is played by so-called shifts of fuzzy attributes which appeared earlier in the study of factorization of fuzzy concept lattices. In addition to fuzzy concept lattices, we consider the idea of thresholds for the treatment of attribute implications from tables with fuzzy attributes and prove basic results concerning validity and non-redundant bases.

    Citations
    1. Cornejo M. E., Medina J., Ramirez-Poussa E.: Cuts or thresholds, what is the best reduction method in fuzzy formal concept analysis?.
      In: IEEE (Ed.): 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), IEEE International Conference on Fuzzy Systems, 2015.
      Sco, GS
    2. Zhai Yanhui, Li Deyu, Qu Kaishe: Decision implication canonical basis: a logical perspective.
      Journal of Computer and System Sciences 81(1)(2015), pp. 208–218.
      WoS, GS
    3. Cornejo M. Eugenia, Medina Jesús, Ramírez-Poussa Eloisa: On the use of irreducible elements for reducing multi-adjoint concept lattices.
      Knowledge-based Systems 89(2015), pp. 192–202.
      WoS, Sco, GS
    4. Cornejo M. Eugenia, Medina Jesús, Ramírez-Poussa Eloisa: On the use of thresholds in multi-adjoint concept lattices.
      International Journal of Computer Mathematics 92(9)(2015), pp. 1855–1873.
      WoS, GS
    5. Zhai Yanhui, Li Deyu, Qu Kaishe: Decision implications: a logical point of view.
      International Journal of Machine Learning and Cybernetics 5(4)(2014), pp. 509–516.
      GS
    6. Poelmans Jonas, Ignatov Dmitry I., Kuznetsov Sergei O., Dedene Guido: Fuzzy and rough formal concept analysis: a survey.
      International Journal of General Systems 43(2)(2014), pp. 105–134.
      WoS, Sco, GS
    7. Yao Yanqing, Mi Jusheng, Li Zhoujun, Xie Bin: The Construction of Fuzzy Concept Lattices Based on (theta, sigma)-Fuzzy Rough Approximation Operators.
      Fundamenta Informaticae 111(1)(2011), pp. 33–45.
      WoS, Sco, GS
    8. Poelmans Jonas: Essays on using formal concept analysis in information engineering.
      Dissertation Thesis, 2010, 297 pp.
      GS
    9. Li Lifeng, Zhang Jianke: Attribute reduction in fuzzy concept lattices based on the T implication.
      Knowledge-Based Systems 23(6)(2010), pp. 497–503.
      WoS, Sco, GS
    10. Krupka Michal: Factorization of fuzzy concept lattices with hedges by modification of input data.
      Annals of Mathematics and Artificial Intelligence 59(2)(2010), pp. 187–200.
      WoS, Sco, GS
    11. Krupka Michal: Factorization of residuated lattices.
      Logic Journal of the IGPL 17(2)(2009), pp. 205–223.
      WoS, Sco, GS
    12. Yao Yan-Qing, Mi Ju-Sheng: Fuzzy Concept Lattices Determined by (theta, sigma)-Fuzzy Rough Approximation Operators.
      In: Wen P., Li Y,, Polkowski L., Yao Y., Tsumoto S., Wang G. (Eds.): Rough Sets and Knowledge Technology, Proceedings, Lecture Notes in Artificial Intelligence 5589, 2009, pp. 601–609.
      WoS, GS
    13. Krupka Michal: Factorization of Concept Lattices with Hedges by Means of Factorization of Residuated Lattices.
      In: Belohlavek R., Kuznetsov S. O. (Eds.): Proc. CLA 2008, 2008, pp. 231–241.
      Sco, GS
    14. Belohlavek Radim: Relational Data, Formal Concept Analysis, and Graded Attributes.
      In: Galindo J. (Ed.): Handbook of Research on Fuzzy Information Processing in Databases, 2008, pp. 462–489.
      GS
    15. Belohlavek Radim: A note on variable threshold concept lattices: Threshold-based operators are reducible to classical concept-forming operators.
      Information Sciences 177(15)(2007), pp. 3186–3191.
      WoS, Sco, GS
    16. Yang B., Xu B., Li Y.: A Theoretical Framework for Distributed Reduction in Concept Lattice.
      GS
    17. Belohlavek Radim, Outrata Jan, Vychodil Vilém: Fast factorization by similarity of fuzzy concept lattices with hedges.
      Int. Journal of Foundations of Computer Science 19(2)(2008), pp. 255–269.
      WoS, Sco, GS
    18. Outrata Jan: Factorizing Fuzzy Concept Lattices by Similarity.
      Dissertation Thesis, 2006, 77 pp.
      GS
    19. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: On factorization by similarity of fuzzy concept lattices with hedges.
      In: Ben Yahia S., Mephu Nguifo E. (Eds.): Proc. 4th Int. Conf. on Concept Lattices and Their Applications, CLA 2006, 2006, pp. 57–69.
      GS
  20. Outrata Jan: Similarity clarification in formal concept analysis.
    In: Zajac M. (Ed.): International Conference in Applied mathematics for undergraduate and graduate students, ISCAM 2005, 2005, pp. 41–45, Bratislava, Slovak Rep., 4/2005.
    [Slovak University of Technology]
    abstract | 1 selfcitation (1 GS)

    Abstract Formal concept analysis (FCA) is an algebraic method of data miningwhich aims at extracting a hierarchical structure (so-called conceptlattice) of clusters (so-called formal concepts) from object-attributedata tables. One of the hottest problems in application of FCA is alarge number of clusters extracted from data. We try to cope withthis problem by reducing the amount of input data by the well-knownmethod called clarification, extended to fuzzy setting. This reductionhas the effect of clustering of similar formal concepts and therebymakes the concept lattice smaller.

    Citations
    1. Outrata Jan: Factorizing Fuzzy Concept Lattices by Similarity.
      Dissertation Thesis, 2006, 77 pp.
      GS
  21. Bělohlávek Radim, Dvořák Jiří, Outrata Jan: Direct factorization in formal concept analysis by factorization of input data.
    In: Proc. 5th Int. Conf. on Recent Advances in Soft Computing, RASC 2004, 2004, pp. 578–583, Nottingham, UK, 12/2004.
    [, ISBN 1–84233–110–8]
    DB:
    GS, RIV
    PDF | abstract | 2 citations (2 GS) + 4 selfcitations (4 GS)

    Abstract Formal concept analysis aims at extracting a hierarchical structure(so-called concept lattice) of clusters (so-called formal concepts)from object-attribute data tables. We present an algorithm forcomputing a factor lattice of a concept lattice from the data and auser-specified similarity threshold a. The presented algorithmcomputes the factor lattice directly from the data, without firstcomputing the whole concept lattice and then computing the collectionsof clusters. We present theoretical insight and examples.

    Citations
    1. Poelmans Jonas, Ignatov Dmitry I., Kuznetsov Sergei O., Dedene Guido: Fuzzy and rough formal concept analysis: a survey.
      International Journal of General Systems 43(2)(2014), pp. 105–134.
      WoS, GS
    2. Poelmans Jonas: Essays on using formal concept analysis in information engineering.
      Dissertation Thesis, 2010, 297 pp.
      GS
    3. Belohlavek Radim, Outrata Jan, Vychodil Vilém: Fast factorization by similarity of fuzzy concept lattices with hedges.
      Int. Journal of Foundations of Computer Science 19(2)(2008), pp. 255–269.
      WoS, Sco, GS
    4. Outrata Jan: Factorizing Fuzzy Concept Lattices by Similarity.
      Dissertation Thesis, 2006, 77 pp.
      GS
    5. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: On factorization by similarity of fuzzy concept lattices with hedges.
      In: Ben Yahia S., Mephu Nguifo E. (Eds.): Proc. 4th Int. Conf. on Concept Lattices and Their Applications, CLA 2006, 2006, pp. 57–69.
      GS
    6. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: Thresholds and shifted attributes in formal concept analysis of data with fuzzy attributes.
      In: Schärfe H., Hitzler P., Øhrstrøm P. (Eds.): Proc. 14th International Conference on Conceptual Structures, ICCS 2006, Lecture Notes in Artificial Intelligence 4068, 2006, pp. 117–130.
      WoS, Sco, GS
  22. Bělohlávek Radim, Dvořák Jiří, Outrata Jan: Fast factorization by similarity in formal concept analysis.
    In: AISTA 2004 in Cooperation with the IEEE Computer Society Proceedings, 2004, pp. ?–?, Kirchberg – Luxembourg, Luxembourg, 11/2004.
    [University of Canberra, Canberra, Australia, ISBN 2–9599776–8–8]
    DB:
    GS
    PDF | abstract

    Abstract Formal concept analysis aims at extracting a hierarchical structure(so-called concept lattice) of clusters (so-called formal concepts)from object-attribute data tables. An important problem inapplications of formal concept analysis is a possibly large number ofclusters extracted from data. Factorization is one of the methodsbeing used to cope with the number of clusters. We present analgorithm for computing a factor lattice of a concept lattice from thedata and a user-specified similarity threshold $a$. The factor latticeis smaller than the original concept lattice and its size depends onthe similarity threshold. The elements of the factor lattice arecollections of clusters which are pairwise similar in degree at least$a$. The presented algorithm computes the factor lattice directly fromthe data, without first computing the whole concept lattice and thencomputing the collections of clusters. We present theoretical insightand examples for demonstration.

  23. Bělohlávek Radim, Dvořák Jiří, Outrata Jan: Fast factorization of concept lattices by similarity: solution and an open problem.
    In: Snášel V., Bělohlávek R. (Eds.): CLA 2004, Concept Lattice and their Applications, proceedings of the 2nd international workshop, 2004, pp. 47–57, Ostrava, Czech Rep., 9/2004.
    [VŠB – Technical University of Ostrava, Ostrava, Czech Rep.,
    CEUR WS, Vol. 110, ISBN 80–248–0597–9]
    DB: GS
    PDF | abstract | 10 citations (10 GS) + 2 selfcitations (2 GS)

    Abstract An important problem in applications of formal concept analysis is a possibly large number of clusters extracted from data. Factorization is one of the methods being used to cope with the number of clusters. We present an algorithm for computing a factor lattice of a concept lattice from the data and a user-specified similarity threshold $a$. The elements of the factor lattice are collections of clusters which are pairwise similar in degree at least $a$. The presented algorithm computes the factor lattice directly from the data, without first computing the whole concept lattice and then computing the collections of clusters. We present theoretical insight and examples for demonstration, and an open problem.

    Citations
    1. Xia Hong: Semantic Web Ontology Integration Based on Formal Concept Analysis.
      Applied Mechanics and Materials 373-375(2013), pp. 1714–1718.
      GS
    2. Xia Hong: Concept Lattice-Based Semantic Web Service Ontology Merging.
      In: Zheng F. (Ed.): Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013), Advances in Intelligent Systems Research 41, 2013, pp. 233–236.
      GS
    3. Subramanian Hema: Summarization Of Real Valued Biclusters.
      Master Thesis, 2011, 72 pp.
      GS
    4. Guoa Lankun, Huangb Fangping, Lia Qingguo, Zhangb Guo-Qiang: Power contexts and their concept lattices.
      Discrete Mathematics 311(18-19)(2011), pp. 2049–2063.
      GS
    5. Alqadah Faris, Bhatnagar Raj: Similarity measures in formal concept analysis.
      Annals of Mathematics and Artificial Intelligence 61(3)(2011), pp. 245–256.
      GS
    6. Xia Hong, Chen Yan, Gao Haichang, Li Zengzhi, Chen Yanping: Concept Lattice-Based Semantic Web Service Matchmaking.
      In: Wen D., Wang R., Zhou J. (Eds.): Communication Software and Networks, 2010. ICCSN '10. Second International Conference on, 2010, pp. 439–443.
      GS
    7. Formica Anna: Concept Similarity in Fuzzy Formal Concept Analysis for Semantic Web.
      2009, 17 pp.
      GS
    8. Formica Anna: Concept similarity in Formal Concept Analysis: An information content approach.
      Knowledge-Based Systems 21(1)(2008), pp. 80–87.
      GS
    9. Formica Anna: Ontology-based concept similarity in Formal Concept Analysis.
      Information Sciences 176(18)(2006), pp. 2624–2641.
      GS
    10. Guoa L., Huangb F., Lia Q., Zhangb G. Q.: Towards a Theory of Power Concept Lattices.
      GS
    11. Belohlavek Radim, Outrata Jan, Vychodil Vilém: Fast factorization by similarity of fuzzy concept lattices with hedges.
      Int. Journal of Foundations of Computer Science 19(2)(2008), pp. 255–269.
      WoS, Sco, GS
    12. Bělohlávek Radim, Outrata Jan, Vychodil Vilém: On factorization by similarity of fuzzy concept lattices with hedges.
      In: Ben Yahia S., Mephu Nguifo E. (Eds.): Proc. 4th Int. Conf. on Concept Lattices and Their Applications, CLA 2006, 2006, pp. 57–69.
      GS

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