**1. Introduction**

Various data mining tools are proposed to extract patterns from data sets [1]. Large, multidimensional data sets impose high requirements as to the precision and efficiency of calculations used to extract patterns (regularities) useful in practice [2]. In this context, there is still a need to develop new algorithms of data mining [3]. New types of patterns are also obtained in result of combining different types of classification or prognosis models [4].

The Simplex algorithm from linear programming is used as an effective big data mining tool [5]. According to the basic theorem of linear programming, the solution to the linear optimization problem with linear constraints can be found at one of the vertices in the parameter space. Narrowing the search area to a finite number of vertices is a source of the efficiency of the Simplex algorithm.

Basis exchange algorithms also look for an optimal solution among a finite number of vertices in the parameter space [6]. The basis exchange algorithms are based on the Gauss - Jordan transformation and, for this reason, are similar to the Simplex algorithm. Controlling the basis exchange algorithm is related to the minimization of convex and piecewise linear (CPL) criterion functions [7].

The perceptron and collinearity criterion functions belong to the family of CPL functions The minimization of the perceptron criterion function allows to check the linear separability of data sets and to design piecewise linear classifiers [8].

Minimizing the collinearity criterion function makes it possible to detect collinear (flat) patterns in data sets and to design multiple interaction models [9].

Data sets consisting of a small number of multivariate feature vectors generate specific problems in data mining [10]. This type of data includes genetic data sets. Minimizing the perceptron criterion function or the collinearity function enables solving problems related to discrimination or regression also in the case of a small set of multidimensional feature vectors by using complex layers of low dimensional linear classifiers or prognostic models [11].
