TY  - JOUR
SN  - 0005-1098
Y1  - 2016///
N2  - 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.
JF  - Automatica
N1  - SCOPUS ID: 2-s2.0-84986593950
VL  - 73
EP  -  162
PB  - Elsevier
A1  - Breschi, Valentina
A1  - Piga, Dario
A1  - Bemporad, Alberto
SP  - 155 
ID  - eprints3545
TI  - Piecewise affine regression via recursive multiple least squares and multicategory discrimination
AV  - none
KW  - PWA regression; System identification; Clustering; Recursive multiple least squares; Multicategory discrimination
UR  - http://www.sciencedirect.com/science/article/pii/S0005109816302849
ER  -