  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.
