Data Filtering for Cluster Analysis by $\ell_0$-Norm Regularization
This work addresses data preprocessing for clustering tasks, offering an incremental improvement by integrating filtering into existing methods.
The paper tackles the problem of data filtering for cluster analysis by proposing a method based on minimizing a least squares function with a weighted ℓ₀-norm penalty, using smooth non-convex approximations to handle discontinuity, and it shows that existing clustering methods can benefit from this filtering strategy in numerical tests on synthetic and real datasets.
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.