Low-rank unsupervised graph feature selection via feature self-representation

Feature selection and subspace learning are two popular approaches of dimensionality reduction for solving the issue of 'curse of dimensionality' in high-dimensional data. However, most of previous methods of feature selection and subspace learning ignore the fact that there exist noise and outliers in high-dimensional data, which increase the rank of the data matrix so that decreasing the stability of learning models. In this paper, we integrate a feature-level self-representation loss function, a low-rank constraint, a graph Laplacian regularizer, and a sparsity regularizer into a unified framework to conduct unsupervised feature selection for solving mentioned issues. Specifically, we first propose a new feature-level self-representation loss function plus a sparsity regularizer (a (2,1)-norm regularizer) to select representative features, and then push a low-rank constraint on the coefficient matrix which considers the response variables as a whole group to avoid the impact of noise and outliers, and a graph regularizer to preserve the local structures of the data to conduct subspace learning in the framework of feature selection. Experimental results on real databases implied that the proposed method effectively selected the most representative features and removed the adverse effect of irrelevant features, compared to the state-of-the-art methods.