Piecewise affine regression via recursive multiple least squares and multicategory discrimination

Valentina Breschi, Dario Piga, Alberto Bemporad

Research output: Contribution to journalArticleAcademicpeer-review

74 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)155-162
Number of pages8
JournalAutomatica
Volume73
DOIs
Publication statusPublished - Nov 2016
Externally publishedYes

Bibliographical note

Funding Information:
This work was partially supported by the European Commission under project H2020-SPIRE-636834 “DISIRE—Distributed In-Situ Sensors Integrated into Raw Material and Energy Feedstock” ( http://spire2030.eu/disire/ ). The material in this paper was partially presented at the 15th European Control Conference, June 29–July 1, 2016, Aalborg, Denmark. This paper was recommended for publication in revised form by Associate Editor Erik Weyer under the direction of Editor Torsten Söderström.

Keywords

  • Clustering
  • Multicategory discrimination
  • PWA regression
  • Recursive multiple least squares
  • System identification

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