This article is cited in 30 papers

Logical regularities in pattern recognition (parametric approach)

V. V. Ryazanov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: The search for logical regularities of classes in the recognition by precedents problems and the use of logical regularities for solving recognition and prediction problems are considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of a value of a feature in a certain interval of the real axis. The conjunctions are true on the subsets of reference objects of a certain class and are optimal. Various optimality criteria are considered and the problem of finding logical regularities is formulated as an integer programming problem. A qualitative analysis of these problems is performed. Models for evaluating estimates on the basis of systems of logical regularities are considered. Modifications of linear decision rules for finding estimates of how close the reference objects are to classes are proposed that are based on the search for the maximum gap. Approximations of logical regularities of classes by smooth functions is proposed. The concept of the dynamic logical regularity of classes is introduced, an algorithm for finding dynamic logical regularities is proposed, and a prediction method is developed.

Key words: logical class regularities, precedent-based recognition, prediction, estimate evaluation algorithm, integer programming, decision rule, dynamic regularity.

UDC: 519.6:519.712

Received: 04.05.2007

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:10, 1720–1735

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