Structure Preserving Non-negative Feature Self-Representation for Unsupervised Feature Selection

Inspired by the importance of self-representation and structure-preserving ability of features, in this paper, we propose a novel unsupervised feature selection algorithm named structure-preserving non-negative feature self-representation (SPNFSR). In this algorithm, each feature in high-dimensional data can be represented by the linear combination of other features. Then, to exploit the structure-preserving ability of features, we construct a low-rank representation graph, which takes the local and global structures into consideration to maintain the intrinsic structure of the data space. Finally, an l_2,1-norm regularization and the non-negative constraint are imposed on the representation coefficient matrix with the goal of achieving feature selection in the batch mode. Moreover, we provide a simple yet efficient iterative update algorithm to solve SPNFSR, as well as the convergence analysis of the proposed algorithm. The performance of the proposed approach is illustrated by six publicly available databases. In comparison with the state-of-the-art approaches, the extensive experimental results show the advantages and effectiveness of our approach.