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Nonsmooth nonconvex optimization approach to clusterwise linear regression problems. (English) Zbl 1317.90242
Summary: 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.

90C26 Nonconvex programming, global optimization
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62J05 Linear regression; mixed models
Algorithm 39; UCI-ml
Full Text: DOI
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