Non-convex feature selection based on feature correlation representation and dual manifold optimization

Abstract

The existing feature selection algorithms often utilize local structure of data, but do not fully mine internal structure and ignore potential correlation information between samples. To address the problems and fully utilize manifold information of data, this paper proposes non-convex feature selection based on feature correlation representation and dual manifold optimization (FDNFS). Firstly, FDNFS constructs feature graph of original data, which can obtain feature correlation representation to represent the interconnection information. Based on the obtained interconnection information, FDNFS unifies feature correlation representation learning and feature selection through feature transformation matrix, so that the interconnection information between data guides feature selection. Secondly, to make multivariate frameworks guide feature selection, FDNFS introduces self-representation on the improved sparse regression model. Using self-representation can make basis matrix and reconstruction coefficient matrix reconstruct original data more accurately. Next, in order to preserve local structure information abundantly, FDNFS has two-part manifold regularization on the pseudo-label matrix in sparse regression model and the reconstructed coefficient matrix in self-representation framework. This can fully use the manifold information of data. In addition, FDNFS imposes the non-convex constraints. It can ensure the sparsity of feature selection matrix. In turn, this can select features with lower redundancy, and then select a better feature subset. Finally, this paper adopts an iterative optimization method. FDNFS is compared with nine algorithms on seven datasets. The clustering results reflect better performance of FDNFS.