ESTIMATION OF PARAMETERS OF CLUSTER MIXED LOOP-LINEAR REGRESSION
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 Transport University
(Candidate of Economic Sciences, Assistant Professor; Head of the Department of Information Systems and Information Security)
Russian Federation
Russian Federation
Type:
Article
Pages:
from 136
to 140
Status:
Published
Received:
23.12.2025
Accepted:
23.12.2025
Published:
23.12.2025
Language:
Russian
Keywords:
CLUSTERED MIXED PIECEWISE LINEAR REGRESSION, LOSS FUNCTION, LEAST SQUARES METHOD, LINEAR-BOOLEAN PROGRAMMING, AND PETROLEUM PRODUCTION
Abstract (English):
The paper provides a brief overview of publications on the use of nonlinear cluster regressions in modeling complex objects. In particular, the following are considered: an algorithm for cluster nonlinear regression of center and range for interval-significant data; methods of nonlinear regression analysis developed for analyzing clustered data; a method of nonlinear subspace clustering for grouping images; methods for modeling and evaluating nonlinear conditional quantile functions when data is clustered in two-level nested plans; an approach to clustering data in two-level nested plans; a new clustering algorithm based on an interval-valued stable fuzzy model; a clustering algorithm for fuzzy c-regression models; clustering of the Gaussian mixture model based on a genetic version of the expectation maximization algorithm and the minimum description length criterion. It is shown that if the sum of the modulus of deviations of the calculated values of the dependent variable from the actual values is used as a loss function when calculating estimates of the parameters of a cluster mixed piecewise linear regression, this problem can be reduced to a linear Boolean programming problem. A cluster mixed piecewise linear regression model of oil product production in the Russian Federation is constructed. The volumes of oil and condensate production are involved as independent factors. The model has high approximation characteristics, as indicated by the adequacy criteria used - the sum of error modules and the average relative error. The analysis of the model shows that the index sets on which particular linear models are defined have different capacities. In addition, the second partial regression does not contain components corresponding to the Leontiev function, since the corresponding parameters turned out to be zero.
The paper provides a brief overview of publications on the use of nonlinear cluster regressions in modeling complex objects. In particular, the following are considered: an algorithm for cluster nonlinear regression of center and range for interval-significant data; methods of nonlinear regression analysis developed for analyzing clustered data; a method of nonlinear subspace clustering for grouping images; methods for modeling and evaluating nonlinear conditional quantile functions when data is clustered in two-level nested plans; an approach to clustering data in two-level nested plans; a new clustering algorithm based on an interval-valued stable fuzzy model; a clustering algorithm for fuzzy c-regression models; clustering of the Gaussian mixture model based on a genetic version of the expectation maximization algorithm and the minimum description length criterion. It is shown that if the sum of the modulus of deviations of the calculated values of the dependent variable from the actual values is used as a loss function when calculating estimates of the parameters of a cluster mixed piecewise linear regression, this problem can be reduced to a linear Boolean programming problem. A cluster mixed piecewise linear regression model of oil product production in the Russian Federation is constructed. The volumes of oil and condensate production are involved as independent factors. The model has high approximation characteristics, as indicated by the adequacy criteria used - the sum of error modules and the average relative error. The analysis of the model shows that the index sets on which particular linear models are defined have different capacities. In addition, the second partial regression does not contain components corresponding to the Leontiev function, since the corresponding parameters turned out to be zero.
Keywords:
CLUSTERED MIXED PIECEWISE LINEAR REGRESSION, LOSS FUNCTION, LEAST SQUARES METHOD, LINEAR-BOOLEAN PROGRAMMING, AND PETROLEUM PRODUCTION
CLUSTERED MIXED PIECEWISE LINEAR REGRESSION, LOSS FUNCTION, LEAST SQUARES METHOD, LINEAR-BOOLEAN PROGRAMMING, AND PETROLEUM PRODUCTION
