Regularized Moving-Horizon Piecewise Affine Regression using Mixed-Integer Quadratic Programming

This paper presents a novel two-stage regularized moving-horizon algorithm for PieceWise Affine (PWA) regression. At the first stage, the training samples are processed iteratively, and a Mixed-Integer Quadratic-Programming (MIQP) problem is solved to find the sequence of active modes and the model parameters which best match the training data, within a relatively short time window in the past. According to a moving-horizon strategy, only the last element of the optimal sequence of active modes is kept, and the next sample is processed by shifting forward the estimation horizon. A regularization term on the model parameters is included in the cost of the formulated MIQP problem, to partly take into account also the past training data outside the considered time horizon. At the second stage, linear multi-category discrimination techniques are used to compute a polyhedral partition of the regressor space based on the estimated sequence of active modes.