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Signals and Telecommunications Journal

FCA-based Approach to Machine Learning

Dmitry V Vinogradov
Federal Research Center for Computer Science and Control Russian Academy of Science, Moscow 119333, Russia, Russian State University for Humanities, Intelligent Robotics Laboratory Moscow 125993, Russia

Abstract: The main result of the paper provides a lower bound on sufficient number of randomly generated formal concepts to correctly predict all important positive test examples with given confidence level. The technique coincides with modern approach to the famous theorem of V.N. Vapnik and A.Ya. Chervonenkis. However the situation is dual to the classical one: in our case test examples correspond to fixed subsets and probabilistically generated formal concepts must fall into selected areas of sufficient large volume.

Keywords: Formal Context, Formal Concept, Boolean Hypercube, Lower Half-space, Prediction, Condence FCA-based Approach to Machine Learning

DOI:https://doi.org/10.6025/stj/2020/9/25-30

Full_Text PDF 513 KB Download: 299 times

References:

[1] Ganter, Bernard and Wille, Rudolf. (1999). Formal Concept Analysis: Mathematical Foundations, Springer-Verlag, 1999.
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[4] Kuznetsov, S.O. (2004). Machine Learning and Formal Concept Analysis. Proceedings 2nd International Conference on Formal Concept Analysis: Springer LNAI, Volume 2961 p 287-312.
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[6] Vinogradov, D.V. (2013). A Markov Chain Approach to Random Generation of Formal Concepts. Proceedings of the Workshop Formal Concept Analysis Meets Information Retrieval (FCAIR 2013): CEUR Workshop Proceedings, 977, p. 127–133.
[7] Vinogradov, D.V. (2017). Accidental Formal Concepts in the Presence of Counterexamples. Proceedings of International Workshop on Formal Concept Analysis for Knowledge Discovery (FCA4KD 2017): CEUR Workshop Proceedings, Volume 1921, p 104–112.
[8] Vorontsov, K.V., Ivahnenko, A. (2011). Tight Combinatorial Generalization Bounds for Threshold Conjunction Rules. Proceedings of 4th International Conference on Pattern Recognition and Machine Intelligence. p 66-73.

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