Semantic and neighborhood preserving dictionary learning for symmetric positive-definite matrices
Daming Li, Lei Chen, Fei Wang · 2016
The symmetric positive-definite (SPD) matrices form a Riemannian manifold, and sparse representation on the SPD matrix manifold has received increasingly attentions recently. In this paper, we propose a semantic and neighborhood preserving dictionary learning method for the sparse representation on the SPD matrix manifold. The semantic preserving ensures that the semantic similarity information can be kept while sparse representation, and the neighborhood preserving is introduced to better reflect the geometrical structure of the manifold. To effectively model the semantic similarity of the SPD matrices and the geometrical structure, a Laplacian smooth operator is incorporated into the objective function of dictionary learning. With the learned dictionary, the obtained sparse representations of SPD matrices are more discriminative. Experimental results on publicly available datasets demonstrate the effectiveness of the proposed method.