Unsupervised feature selection via row-sparse local preserving projection

In order to effectively process high-dimensional unlabeled data, an increasing number of researchers are focusing on unsupervised dimensionality reduction methods, which consist of two types: feature extraction and feature selection. Local Preserving Projection (LPP) is a widely used unsupervised dimensionality reduction technique that performs feature extraction rather than feature selection. Some methods perform feature selection by applying sparse constraints to the projection matrix of the LPP method. Because the ℓ_2,0-norm is difficult to optimize, these LPP-based feature selection methods introduce sparse regularization terms in the objective function by considering the ℓ_2,p-norm (0 < p ≤ 1) in the projection matrix. Since the ℓ_2,p-norm is only an approximation of the ℓ_2,0-norm, the feature subset selected in this way is often suboptimal. To directly handle the ℓ_2,0-norm constraint problem to obtain the optimal feature subset, we propose an unsupervised feature selection method termed Unsupervised Feature Selection via Row-Sparse Local Preserving Projection (UFSLP) in this paper. The proposed method preserves the local neighborhood structure in the feature selection process and effectively balances local and global information by introducing principal component analysis (PCA) as a regularization term. To optimize the ℓ_2,0-norm problem, we reformulate it as an equivalent form and solve it via a coordinate descent method. Extensive experiments on nine benchmark datasets demonstrate that UFSLP outperforms other state-of-the-art unsupervised feature selection methods in terms of clustering accuracy and normalized mutual information.