Abstract
Pattern structures, an extension of FCA to data with complex descriptions, propose an alternative to conceptual scaling (binarization) by giving direct way to knowledge discovery in complex data such as logical formulas, graphs, strings, tuples of numerical intervals, etc. Whereas the approach to classification with pattern structures based on preceding generation of classifiers can lead to double exponent complexity, the combination of lazy evaluation with projection approximations of initial data, randomization and parallelization, results in reduction of algorithmic complexity to low degree polynomial, and thus is feasible for big data.
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References
Aït-Kaci, H., Boyer, R., Lincoln, P., Nasr, R.: Efficient Implementation of Lattice Operations. ACM Transactions on Programming Languages and Systems 11(1), 115–146 (1989)
Arimura, H., Uno, T.: Polynomial-Delay and Polynomial-Space Algorithms for Mining Closed Sequences, Graphs, and Pictures in Accessible Set Systems. In: Proc. SDM, pp. 1087–1098 (2009)
Babin, M.A., Kuznetsov, S.O.: Enumerating Minimal Hypotheses and Dualizing Monotone Boolean Functions on Lattices. In: Jäschke, R. (ed.) ICFCA 2011. LNCS (LNAI), vol. 6628, pp. 42–48. Springer, Heidelberg (2011)
Babin, M.A., Kuznetsov, S.O.: Computing Premises of a Minimal Cover of Functional Depedencies is Intractable. Discr. Appl. Math. 161, 742–749 (2013)
Baixeries, J., Kaytoue, M., Napoli, A.: Computing Functional Dependencies with Pattern Structures. In: Proc. 9th International Conference on Concept Lattices and Their Applications (CLA 2012), Malaga (2012)
Birkhoff, B.: Lattice Theory. ACM (1991)
Chaudron, L., Maille, N.: Generalized Formal Concept Analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867, pp. 357–370. Springer, Heidelberg (2000)
Coulet, A., Domenach, F., Kaytoue, M., Napoli, A.: Using pattern structures for analyzing ontology-based annotations of biomedical data. In: Cellier, P., Distel, F., Ganter, B. (eds.) ICFCA 2013. LNCS (LNAI), vol. 7880, pp. 76–91. Springer, Heidelberg (2013)
Distel, F., Sertkaya, B.: On the Complexity of Enumerating Pseudo-intents. Discrete Applied Mathematics 159(6), 450–466 (2011)
Férré, S., Ridoux, O.: A Logical Generalization of Formal Concept Analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867, pp. 371–385. Springer, Heidelberg (2000)
Férré, S., King, R.D.: Finding Motifs in Protein Secondary Structure for Use in Function Prediction. Journal of Computational Biology 13(3), 719–731 (2006)
Ferré, S.: The Efficient Computation of Complete and Concise Substring Scales with Suffix Trees. In: Kuznetsov, S.O., Schmidt, S. (eds.) ICFCA 2007. LNCS (LNAI), vol. 4390, pp. 98–113. Springer, Heidelberg (2007)
Finn, V.K.: Plausible Reasoning in Systems of JSM Type. Itogi Nauki i Tekhniki, Seriya Informatika 15, 54–101 (1991) (in Russian)
Galitsky, B.A., Kuznetsov, S.O., Samokhin, M.V.: Analyzing Conflicts with Concept-Based Learning. In: Dau, F., Mugnier, M.-L., Stumme, G. (eds.) ICCS 2005. LNCS (LNAI), vol. 3596, pp. 307–322. Springer, Heidelberg (2005)
Galitsky, B.A., Kuznetsov, S.O., Usikov, D.: Parse Thicket Representation for Multi-sentence Search. In: Pfeiffer, H.D., Ignatov, D.I., Poelmans, J., Gadiraju, N. (eds.) ICCS 2013. LNCS, vol. 7735, pp. 153–172. Springer, Heidelberg (2013)
Ganter, B., Kuznetsov, S.O.: Pattern Structures and Their Projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)
Ganter, B., Grigoriev, P.A., Kuznetsov, S.O., Samokhin, M.V.: Concept-based Data Mining with Scaled Labeled Graphs. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 94–108. Springer, Heidelberg (2004)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Garriga, G., Khardon, R., De Raedt, L.: Mining Closed Patterns in Relational, Graph and Network Data, Annals of Mathematics and Artificial Intelligence (2013)
Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de donnees binaires. Math. Sci. Humaines 95, 5–18 (1986)
Hullermeier, E.: Case-Based Approximate Reasoning. Springer (2007)
Kautz, H.A., Kearns, M.J., Selman, B.: Reasoning with characteristic models. In: Proc. AAAI 1993, pp. 1–14 (1993)
Kaytoue, M., Duplessis, S., Kuznetsov, S.O., Napoli, A.: Two FCA-Based Methods for Mining Gene Expression Data. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS (LNAI), vol. 5548, pp. 251–266. Springer, Heidelberg (2009)
Kaytoue, M., Kuznetsov, S.O., Napoli, A.: Revisiting Numerical Pattern Mining with Formal Concept Analysis. In: Proc. 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 1342–1347 (2011)
Kaytoue, M., Kuznetsov, S.O., Napoli, A., Duplessis, S.: Mining gene expression data with pattern structures in formal concept analysis. Inf. Sci. 181(10), 1989–2001 (2011)
Kuznetsov, S.O.: Stability as an Estimate of the Degree of Substantiation of Hypotheses on the Basis of Operational Similarity. Nauchno-Tekhnicheskaya Informatsiya, Ser. 2 24(12), 21–29 (1990)
Kuznetsov, S.O.: JSM-method as a machine learning method. Itogi Nauki i Tekhniki, Ser. Informatika 15, 17–50 (1991) (in Russian)
Kuznetsov, S.O.: Mathematical aspects of concept analysis. J. Math. Sci. 80(2), 1654–1698 (1996)
Kuznetsov, S.O.: Learning of Simple Conceptual Graphs from Positive and Negative Examples. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 384–391. Springer, Heidelberg (1999)
Kuznetsov, S.O.: Complexity of Learning in Concept Lattices from Positive and Negative Examples. Discr. Appl. Math. 142, 111–125 (2004)
Kuznetsov, S.O.: Pattern Structures for Analyzing Complex Data. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS (LNAI), vol. 5908, pp. 33–44. Springer, Heidelberg (2009)
Kuznetsov, S.O.: Computing Graph-Based Lattices from Smallest Projections. In: Wolff, K.E., Palchunov, D.E., Zagoruiko, N.G., Andelfinger, U. (eds.) KONT/KPP 2007. LNCS (LNAI), vol. 6581, pp. 35–47. Springer, Heidelberg (2011)
Kuznetsov, S.O., Obiedkov, S.A.: Some Decision and Counting Problems of the Duquenne-Guigues Basis of Implications. Discrete Applied Mathematics 156(11), 1994–2003 (2008)
Kuznetsov, S.O., Samokhin, M.V.: Learning Closed Sets of Labeled Graphs for Chemical Applications. In: Kramer, S., Pfahringer, B. (eds.) ILP 2005. LNCS (LNAI), vol. 3625, pp. 190–208. Springer, Heidelberg (2005)
Kuznetsov, S.O., Revenko, A.: Finding Errors in Data Tables: An FCA-based Approach. Annals of Mathematics and Artificial Intelligence (2013)
Liquiere, M., Sallantin, J.: Structural Machine Learning with Galois Lattice and Graphs. In: Proc. ICML 1998 (1998)
Luxenburger, M.: Implications partielle dans un contexte. Math. Sci. Hum. (1991)
Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Efficient Minining of Association Rules Based on Using Closed Itemset Lattices. J. Inf. Systems 24, 25–46 (1999)
Ryssel, U., Distel, F., Borchmann, D.: Fast computation of proper premises. In: Proc. CLA 2011 (2011)
Yan, X., Han, J.: CloseGraph: Mining closed frequent graph patterns. In: Proc. KDD 2003, pp. 286–295. ACM Press, New York (2003)
Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search - The Metric Space Approach. Springer (2006)
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Kuznetsov, S.O. (2013). Fitting Pattern Structures to Knowledge Discovery in Big Data. In: Cellier, P., Distel, F., Ganter, B. (eds) Formal Concept Analysis. ICFCA 2013. Lecture Notes in Computer Science(), vol 7880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38317-5_17
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DOI: https://doi.org/10.1007/978-3-642-38317-5_17
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