Sparsity and Geometry Preserving Graph Embedding for Dimensionality Reduction

Jianping Gou, Zhang Yi, David Zhang, Yongzhao Zhan, Xiangjun Shen, Lan Du

Abstract: Graph embedding is a very useful dimensionality reduction technique in pattern recognition. In this paper, we develop a novel discriminative dimensionality reduction technique entitled sparsity and geometry preserving graph embedding (SGPGE). SGPGE can not only capture the sparse reconstructive relationships among training samples but also discover the intrinsic geometry and latent discrimination from high-dimensional data. In SGPGE, the novel ways of constructing global and local adjacent graphs are developed. The built graphs with discriminant and geometrical information are more informative in graph embedding. Integrating the sparse reconstruction with the designed local and global adjacent graph constructions, SGPGE newly characterizes with-class sparsity and geometry preserving scatter, between class sparsity and geometry preserving scatter and local sparsity and geometry preserving scatter to formulate the objective function of dimensionality reduction, and learns the discriminative transformation matrix using maximum margin criterion. Moreover, we also propose three variants of SGPGE. Experimental results on six public face datasets have demonstrated that the proposed methods are effective dimensionality reduction techniques with very good performance for classification in the embedding subspace.