Adaptive Weighted Sparse Principal Component Analysis for Robust Unsupervised Feature Selection

Current unsupervised feature selection methods cannot well select the effective features from the corrupted data. To this end, we propose a robust unsupervised feature selection method under the robust principal component analysis (PCA) reconstruction criterion, which is named the adaptive weighted sparse PCA (AW-SPCA). In the proposed method, both the regularization term and the reconstruction error term are constrained by the $\ell _{2,1}$ -norm: the $\ell _{2,1}$ -norm regularization term plays a role in the feature selection, while the $\ell _{2,1}$ -norm reconstruction error term plays a role in the robust reconstruction. The proposed method is in a convex formulation, and the selected features by it can be used for robust reconstruction and clustering. Experimental results demonstrate that the proposed method can obtain better reconstruction and clustering performance, especially for the corrupted data.