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Piecewise affine regression via recursive multiple least squares and multicategory discrimination

Breschi, Valentina and Piga, Dario and Bemporad, Alberto Piecewise affine regression via recursive multiple least squares and multicategory discrimination. Automatica, 73. 155 - 162. ISSN 0005-1098 (2016)

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In nonlinear regression choosing an adequate model structure is often a challenging problem. While simple models (such as linear functions) may not be able to capture the underlying relationship among the variables, over-parametrized models described by a large set of nonlinear basis functions tend to overfit the training data, leading to poor generalization on unseen data. Piecewise-affine (PWA) models can describe nonlinear and possible discontinuous relationships while maintaining simple local affine regressor-to-output mappings, with extreme flexibility when the polyhedral partitioning of the regressor space is learned from data rather than fixed a priori. In this paper, we propose a novel and numerically very efficient two-stage approach for {PWA} regression based on a combined use of (i) recursive multi-model least-squares techniques for clustering and fitting linear functions to data, and (ii) linear multi-category discrimination, either offline (batch) via a Newton-like algorithm for computing a solution of unconstrained optimization problems with objective functions having a piecewise smooth gradient, or online (recursive) via averaged stochastic gradient descent.

Item Type: Article
Identification Number: 10.1016/j.automatica.2016.07.016
Additional Information: SCOPUS ID: 2-s2.0-84986593950
Uncontrolled Keywords: PWA regression; System identification; Clustering; Recursive multiple least squares; Multicategory discrimination
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 04 Oct 2016 08:56
Last Modified: 04 Oct 2016 08:56
URI: http://eprints.imtlucca.it/id/eprint/3545

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