Discriminative globality and locality preserving graph embedding for dimensionality reduction

Abstract Graph embedding in dimensionality reduction has attracted much attention in the high-dimensional data analysis. Graph construction in graph embedding plays an important role in the quality of dimensionality reduction. However, the discrimination information and the geometrical distributions of data samples are not fully exploited for discovering the essential geometrical and discriminant structures of data and strengthening the pattern discrimination in graph constructions of graph embedding. To overcome the limitations of graph constructions, in this article we propose a novel graph-based dimensionality reduction method entitled discriminative globality and locality preserving graph embedding (DGLPGE) by designing the informative globality and locality preserving graph constructions. In the constructed graphs, bidirectional weights of edges are newly defined by considering both the geometrical distributions of each point of edges and the class discrimination. Using the adjacent weights of graphs, we characterize the intra-class globality preserving scatter, the inter-class globality preserving scatter and the locality preserving scatter to formulate the objective function of DGLPGE in order to optimize the projection of dimensionality reduction. Extensive experiments demonstrate that the proposed DGLPGE often outperforms the state-of-the-art dimensionality reduction methods.