IDENTIFICATION OF PARAMETERS OF THE CLUSTER PIECEWISE LINEAR REGRESSION FUNCTION OF LEONTIEV BY THE METHOD OF LEAST MODULES
Authors:
1.
Irkutsk State University of Railway Transport
(Doctor of Technical Sciences, Professor; Professor of the Department of Information Systems and Information Security)
Irkutsk, Irkutsk region, Russian Federation
Irkutsk, Irkutsk region, Russian Federation
2.
Irkutsk State University of Railway Transport
Type:
Article
eLocation:
Status:
Published
Received:
05.08.2025
Accepted:
07.08.2025
Published:
07.08.2025
Language:
Russian
Keywords:
LEONTIEF CLUSTER PIECEWISE LINEAR REGRESSION MODEL, LEAST ABSOLUTE VALUES METHOD, LINEAR BOOLEAN PROGRAMMING PROBLEM, APPROXIMATION QUALITY, AVERAGE PERCENTAGE ERROR, CEMENT PRODUCTION
Abstract (English):
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.
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.
Keywords:
LEONTIEF CLUSTER PIECEWISE LINEAR REGRESSION MODEL, LEAST ABSOLUTE VALUES METHOD, LINEAR BOOLEAN PROGRAMMING PROBLEM, APPROXIMATION QUALITY, AVERAGE PERCENTAGE ERROR, CEMENT PRODUCTION
LEONTIEF CLUSTER PIECEWISE LINEAR REGRESSION MODEL, LEAST ABSOLUTE VALUES METHOD, LINEAR BOOLEAN PROGRAMMING PROBLEM, APPROXIMATION QUALITY, AVERAGE PERCENTAGE ERROR, CEMENT PRODUCTION
