Nonsmooth Optimization Algorithm for Solving Clusterwise Linear Regression Problems

Adil M. Bagirov (), Julien Ugon and Hijran G. Mirzayeva
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Adil M. Bagirov: Federation University Australia
Julien Ugon: Federation University Australia
Hijran G. Mirzayeva: Federation University Australia

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 3, No 3, 755-780

Abstract: Abstract Clusterwise linear regression consists of finding a number of linear regression functions each approximating a subset of the data. In this paper, the clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem and an algorithm based on an incremental approach and on the discrete gradient method of nonsmooth optimization is designed to solve it. This algorithm incrementally divides the whole dataset into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate good starting points for solving global optimization problems at each iteration of the incremental algorithm. The algorithm is compared with the multi-start Späth and the incremental algorithms on several publicly available datasets for regression analysis.

Keywords: Nonsmooth optimization; Nonconvex optimization; Clusterwise linear regression; Discrete gradient method; 65K05; 90C25 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-014-0566-y

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