Sparse PCA via ℓ 2,0 -Norm Constrained Optimization for Unsupervised Feature Selection
Anning Yang, Xinrong Li, Xianchao Xiu · 2024
Unsupervised feature selection is widely applied in machine learning and pattern recognition. Although many methods based on sparse representation have been proposed to obtain discriminative features, we found that their dimensionality reduction capabilities are not sufficient. In this paper, we propose and study a novel unsupervised feature selection method by integrating $\ell_{2,0}$-norm constrained optimization with the classical principal component analysis (PCA). However, this is a noncon-vex and nonsmooth problem, which brings great computational challenges. To this end, we design an alternating minimization algorithm with convergence guarantees. Technically, the hard thresholding method is utilized to exploit the sparsity, and an exact penalty function method is adopted to ensure the efficiency of the manifold optimization. Finally, we validate the effectiveness through extensive numerical experiments. Especially on the lung dataset, the clustering accuracy (ACC) is improved by at least 4.55% and the normalized mutual information (NMI) by at least 9.16% compared to existing methods. Our code is available at https://github.com/yan921.