Nikolay G. Zagoruiko

Methods of recognition based on the function of rival similarity

A unified approach to the development of pattern recognition methods is proposed. The approach is based on the employment of the function of rival similarity (FRiS-function), which adequately represents human methods of evaluation of similarity and difference. Methods of recognition based on this approach are briefly described. Examples of solution of actual and benchmark problems using FRiS-function are given.

Use of the FRiS-function for taxonomy, attribute selection and decision rule construction

The task of simultaneous taxonomy (task S), decision rule construction (task D) and most informative attributes selection (task X) is the combined-type task SDX. We offer a way to solve this type of task with a function of rival similarity (FRiS-function). As a result the set of analyzed objects is divided into K classes (clusters) in the selected subspace of informative attributes according to principles of natural classification. Every cluster is described by a necessary and sufficient set of typical representatives (stolps), which provide maximal similarity of all objects of the training dataset with the nearest stolps. In this paper advantages of the criterion based on the FRiS-function for solving SDX task and other combined-type problems in data mining are shown.

Feature selection by using the FRiS function in the task of generalized classification

The task of generalized classification combines three well-known problems of machine learning: recognition, taxonomy, and semi-supervised learning. Usually these problems are examined separately, and for solving each of them, special algorithms are developed. The FRiS-TDR algorithm, based on the function of rival similarity, examines these three problems as special cases of the generalized classification problem and solves all of them. In this paper we show how to choose the sets of informative features in the task of generalized classification. For this purpose the measure of compactness for combined (mixed) dataset is developed. It consists of both objects with known labels (class names) and nonclassified objects.

Measure of Similarity and Compactness in Competitive Space

The given work is devoted to measures of similarity which are used at discovering of empirical regularities (knowledge). The function of competitive (rival) similarity (FRiS) is proposed as a similarity measure for classification and pattern recognition applications. This function allows one to design effective algorithms for solving all basic data mining tasks, obtain quantitative estimates of the compactness of patterns and the informativeness of feature spaces, and construct easily interpretable decision rules. The method is suitable for any number of patterns regardless of the nature of their distributions and conditionality of training samples (the ratio of the numbers of objects and features). The usefulness of the FRiS is shown by solving a problems of molecular biology.

Feature selection in the task of medical diagnostics on microarray data

In view of the active use of DNA microarrays in solving various problems in medicine, bioinformatics, and molecular biology, there is a growing need of data mining algorithms capable of handling tasks in which the number of analyzed objects is smaller than the number of attributes by orders of magnitude. However, most of the currently existing algorithms were originally not intended to solving such complex, ill-conditioned problems. We have developed an approach based on the idea of rival similarity, which makes it possible to develop algorithms better suited for this purpose. We proposed one such algorithm, FRiS-GRAD, which simultaneously solves the problem of recognizing and selecting the system of informative features. Its efficiency is illustrated in a variety of medical problems compared to the most popular algorithms for the selection of informative features and recognition.

Problems in constructing an empirical theory of data mining

The paper describes the structure of empirical theories and analyzes the nature of problems inherent in data mining. A formal description an empirical theory of data mining is given. A general approach to the construction of data mining methods based on the function of rival similarity (FRiS-function) is presented. Application of this function allows the construction of a new class of data mining methods and strengthens empirical theory.