Segmentation of ARX-models using sum-of-norms regularization

Abstract

Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. Here it is formulated as a least-squares problem with sum-of-norms regularization over the state parameter jumps, a generalization of ℓ 1 -regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade-off fit and the number of segments.