Nonsmooth optimization algorithm for solving clusterwise linear regression problems
- Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 164, no. 3 (2015), p. 755-780
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
- Reviewed:
- Description: 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 Spath and the incremental algorithms on several publicly available datasets for regression analysis.
Nonsmooth nonconvex optimization approach to clusterwise linear regression problems
- Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
- Date: 2013
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 229, no. 1 (2013), p. 132-142
- Full Text: false
- Reviewed:
- Description: Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis. © 2013 Elsevier B.V. All rights reserved.
- Description: 2003011018