Data Filtering for Cluster Analysis by $\ell_0$-Norm Regularization

TL;DR

This paper introduces a data filtering technique for cluster analysis that uses a smooth approximation of the $\, ext{l}_0$-norm penalty to improve clustering results, with proven convergence and practical effectiveness.

Contribution

It presents a novel filtering method based on $\, ext{l}_0$-norm regularization with non-convex approximations, ensuring convergence and demonstrating improved clustering performance.

Findings

Effective filtering improves clustering accuracy.

Method converges to global minima of the original problem.

Numerical results show advantages over existing methods.

Abstract

A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted $\ell_0$-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the $\ell_0$-norm. The convergence of the global minimum points of the approximating problems towards global minimum points of the original problem is stated. The proposed method also exploits a suitable technique to choose the penalty parameter. Numerical results on synthetic and real data sets are finally provided, showing how some existing clustering methods can take advantages from the proposed filtering strategy.