ON CORRECT SUPERVISED CLASSIFICATION OVER THE PRODUCT OF PARTIAL ORDERS
N. A. Dragunov, E. V. Djukova
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia
Keywords: supervised classification, correct classification, regular representative elementary classifier, Cartesian product of partial orders, metric properties of the set of elementary classifiers, irredundant covering of integer matrix
Abstract
We consider the issues of creating algorithmic support for supervised classification problem which is the one of the central tasks of machine learning. Original procedures of logical analysis and classification of integer data represented as a set of elements of Cartesian product of finite partially ordered sets (product of partial orders) are constructed and investigated. At the training stage of the proposed procedures, the search for so-called regular representative elementary classifiers (special fragments in feature descriptions of precedents that distinguish objects belonging to different classes) is performed. An asymptotically optimal algorithm for enumerating the required elementary classifiers over a product of antichains is constructed and the results of its testing on real-world tasks are presented. Theoretical and experimental justifications for the efficiency of the new classification procedures are provided for the case when linear orders on sets of feature values are defined. The theoretical conclusions are based on the study of the metric (quantitative) properties of the set of regular representative elementary classifiers.
|
