IDENTIFICATION OF PARAMETERS OF THE CLUSTER PIECEWISE LINEAR REGRESSION FUNCTION OF LEONTIEV BY THE METHOD OF LEAST MODULES

The paper provides a brief overview of publications on the application of both linear and nonlinear methods in data clustering. In particular, the following are considered: four groups of nonlinear clustering algorithms: kernel-based clustering, multi-sample model, graph-based method, and support vector clustering; an overview of kernel and spectral clustering methods; an approach to divisive hierarchical clustering that is capable of identifying clusters in nonlinear manifolds; the use of a functional neural network for transforming data samples into a nonlinear domain; a method for clustering nonlinear and non-stationary time series; a method for improving the efficiency of the false nearest neighbor algorithm for estimating the order of linear and nonlinear systems based on clustering; a method of fuzzy modeling of nonlinear systems with non-uniform sampling; methods for clustering time series with common dependent and nonlinear structure; an approach based on fuzzy c-means clustering and kernel principal component analysis for solving the problem of multispectral images. a method of clustering time series based on their structural characteristics. An algorithmic method for constructing a Leontief cluster piecewise linear model has been developed, based on solving a linear-Boolean programming problem when choosing a loss function in the form of a sum of absolute values of approximation errors. In this case, two problems are solved simultaneously - calculating parameter estimates and forming compositions of index sets containing numbers of sample observations included in clusters. A cluster piecewise linear model of zinc production in the Russian Federation with high approximation quality has been developed. The following factors have been used as independent factors: zinc prices, financing of geological exploration work at the expense of subsoil users' own funds and federal budget funds.