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)

## 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.

Item Type: | Article |
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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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