A Difference of Convex Functions Algorithm for Switched Linear Regression

• Published in: IEEE transactions on automatic control Vol. 59; no. 8; pp. 2277 - 2282
• Main Authors: Tao Pham Dinh, Hoai Minh Le, Hoai An Le Thi, Lauer, Fabien
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Automatic; Computational efficiency; Computational modeling; Computer Science; Convergence; Data models; Data points; DC programming; DCA; Direct current; Engineering Sciences; Linear systems; Machine Learning; Mathematical analysis; Mathematical models; Mathematics; nonconvex optimization; nonsmooth optimization; Optimization; Optimization and Control; piecewise affine systems; Programming; Regression; switched linear systems; switched regression; Switches; system identification; Vectors; Switched linear systems; Nonconvex optimization; DCA; Piecewise affine systems; Switched regression; DC programming; Nonsmooth optimization; System identification
• ISSN: 0018-9286; 1558-2523; 2334-3303; 1558-2523
• DOI: 10.1109/TAC.2014.2301575

This technical note deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The technical note proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.