Classification algorithms based on formal concept analysis (FCA) differ in how they process nonbinary descriptions of objects: using them directly as given or after transforming them to binary attributes by a scaling procedure. A common weakness of classifiers of the second type is that they forget the metric structure of the initial attribute space. The main idea of this article is how to utilize the original metric information alongside with order-theoretical relations between objects and attributes. The metric approach substantially reduces the number of classification failures and provides additional information about the objects, thus opening new options for classifier construction. A classifier model is proposed that generalizes some of the existing FCA-based classification algorithm and opens new possibilities for their modification. The article also considers an alternative metric-based approach: specifically, introduction of a distance measure between formal concepts and its use for classifier modification.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. O. Kuznetsov, “Complexity of learning in concept lattices from positive and negative examples,” Discrete Applied Mathematics, No. 142(1–3), 111–125 (2004).
M. Sahami, “Learning classification rules using lattices,” in N. Lavrac and S. Wrobel, eds., Proc. ECML, Heraclion, Crete, Greece (April 1995), pp. 343–346.
C. Caprineto and G. Romano, “GALOIS: An order-theoretic approach to conceptual clustering,” Proc. ICML93, Amherst, USA (July 1993), pp. 33–40.
M. Kaytoue, S. O. Kuznetsov, A. Napoli, and S. Duplessis, “Mining gene expression data with pattern structures in formal concept analysis,” Information Sciences, 181, No. 10, 1989–2001 (2011).
S. O. Kuznetsov, “Scalable knowledge discovery in complex data with pattern structures,” in: P. Maji, A. Ghosh, M. N. Murty, K. Ghosh, and S. K. Pal, eds., Proc. 5 th Int. Conf. Pattern Recognition and Machine Intelligence (PReMI2013), Lecture Notes in Computer Science, Springer, vol. 8251, pp. 30–41 (2013).
O. Prokasheva, A. Onishchenko, and S. Gurov, “Classification methods based on Formal Concept Analysis,” FCAIR 2013 — Formal Concept Analysis Meets Information Retrieval, Workshop Co-Located with the 35 th European Conference on Information Retrieval (ECIR 2013), Moscow Russia (24 March 2013), pp. 95–104.
Yu. I. Zhuravlev, “Algebraic approach to recognition or classification problems,” Probl. Kibernet., 33, 5–68 (1978).
D. A. Simovici, “Betweenness, metrics, and entropies in lattices,” Proc. 38 th Int. Symp. on Multiple Valued Logic, Dallas, TX, IEEE Computer Society (22–24 May 2008), pp. 26–31.
K. Bache and M. Lichman, UCI Machine Learning Repository [http://archive.ics.uci.edu/ml], University of California, School of Information and Computer Science, Irvine, CA (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 47, 2014, pp. 122–136.
Rights and permissions
About this article
Cite this article
Kolmakov, E.A. Metric Generalization of Classification Algorithms Based on Formal Concept Analysis. Comput Math Model 26, 566–576 (2015). https://doi.org/10.1007/s10598-015-9293-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-015-9293-y