Pursuit of the Cluster Structure of Network Lasso: Recovery Condition and Non-convex Extension

Network lasso (NL for short) is a technique for estimating models by simultaneously clustering data samples and fitting the models to them. It often succeeds in forming clusters thanks to the geometry of the sum of $\ell_2$ norm employed therein, but there may be limitations due to the convexity of the regularizer. This paper focuses on clustering generated by NL and strengthens it by creating a non-convex extension, called network trimmed lasso (NTL for short). Specifically, we initially investigate a …

cluster clustering data extension geometry lasso limitations network norm recovery samples them