relation: http://eprints.imtlucca.it/3545/
title: Piecewise affine regression via recursive multiple least squares and multicategory discrimination
creator: Breschi, Valentina
creator: Piga, Dario
creator: Bemporad, Alberto
subject: QA75 Electronic computers. Computer science
description: 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.
publisher: Elsevier
date: 2016
type: Article
type: PeerReviewed
identifier:   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)  
relation: http://www.sciencedirect.com/science/article/pii/S0005109816302849
relation: 10.1016/j.automatica.2016.07.016