Fuad Aleskerov – Head of Department of Mathematics, Faculty of Economics, National Research University Higher School of Economics; head of laboratory, Trapeznikov Institute of Control Sciences, Russian Academy of Sciences.  
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: alesk@hse.ru

Veronika Belousova – Head of Budgeting Methodology Department, Institute for Statistical Studies and Economics of Knowledge, National Research University Higher School of Economics.
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: vbelousova@hse.ru

Ludmila Egorova – Lecturer, Department of Mathematics, Faculty of Economics, National Research University Higher School of Economics.
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: legorova@hse.ru

Boris Mirkin – Professor, Department of Data Analysis and Artificial Intelligence, School of Applied Mathematics and Information Science, National Research University Higher School of Economics.
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: bmirkin@hse.ru

In this paper the term “pattern” refers to a combination of values of some features such that objects with these feature values ​​significantly differ from other objects. Although some works related to finding and using patterns have been published in the literature, this paper probably is the first to consider the concept as a general tool for the analysis of behavior of objects in both statics and dynamics.

The concept of “pattern” is defined here in three equivalent mathematical frameworks that appeal to different cognitive subsystems pertaining to image, logics and geometry, respectively. The first approach utilizes parallel coordinates for the visual analysis in order to determine different patterns, the second approach uses conjunctive interval predicates that define a set of classifiers separating the patterns from each other and from the rest, and the third approach represents a pattern as the Cartesian product of the corresponding intervals.

The paper proposes a two-stage method for automation of the process of patterns formation. At the first stage we use classical cluster analysis to find clusters of objects; at the second stage we find patterns that adequately represent the obtained clusters. If the data describes functioning of various socio-economic objects in time, we add the third stage at which we analyze pattern changing behavior of the objects. Objects with a stable pattern over time are of a special interest because they can represent objects well adapted to their environment.

We present a review of the literature on each of the three stages: a review of cluster analysis methods, examples of the usage of the term “pattern” in various subject areas of science as a template data structure, and the dynamics of multi-dimensional objects through the examples from several theoretical and practical works similar to the dynamic pattern analysis.