Robust sparsity and clustering regularization for regression

Based on our previously proposed SPARsity and Clustering (SPARC) regularization, we propose a robust variant of SPARC (RSPARC), which is able to detect observations corrupted by sparse outliers. The proposed RSPARC inherits the ability of SPARC to promote group-sparsity, and combines that ability with robustness to outliers. We propose algorithms of the alternating direction method of multipliers (ADMM) family to solve several regularization formulations involving SPARC regularization. Experiments show that RSPARC is a competitive robust group-sparsity-inducing regularization for regression.