Geometrical structure preservation joint with self-expression maintenance for adaptive graph learning

Abstract

Locality preserving projection (LPP) is a subspace learning method that uses pairwise distance to measure the similarity between data points. However, when data points from different clusters are adjacent, the pairwise distance may not accurately reflect the similarity between data points. In this study, a novel graph learning model is proposed to alleviate this problem; it is called adaptive graph learning with geometrical structure preservation and self-expression maintenance (GEAGL), in which a discriminative LPP method is used to extract the geometrical structure of data. By integrating self-expressive learning into the LPP method, a similarity graph that preserves the geometrical structure and self-expressive properties of data can be adaptively learned. The learned similarity graph tends to consist of a block diagonal structure when data points are extracted from independent linear subspaces, which alleviates the cluster interweaving problem. In this study, the relationship between the proposed method and k-means clustering was revealed, and the geometrical structure preservation property of the proposed method was theoretically analyzed. Finally, a graph-based clustering method was developed based on the similarity graph produced by GEAGL. Experimental results of benchmark datasets demonstrate the superiority of the proposed method in comparison with state-of-the-art methods.