Collaborative and Low-Rank Graph for Discriminant Analysis of Hyperspectral Imagery

Sparse representation can be used for the representation of high-dimensional data into a low-dimensional subspace. Recently, sparse graph-based discriminant analysis that uses l(1)-norm optimization has drawn much attention in dimensionality reduction of hyperspectral imagery. By combining low-rankness and sparsity, sparse and low-rank representation based discriminant analysis (SLGDA) can effectively capture global and local data structures simultaneously. In this article, collaborative and low-rank representation based discriminant analysis (CLGDA) is proposed, which is different from the concept of sparse representation. The more informative graph can be obtained in CLGDA with the combination of both collaborative representation (CR) and low-rank representation (LRR) because global data structure can be preserved by LRR and collaboration among within-class atoms is important than competition in sparse representation. Moreover, CR with l(2)-norm regularization is computationally efficient and competitive to sparse representation. The experimental results conducted on three hyperspectral datasets demonstrate that the proposed CLGDA and its variants can provide better classification performance in comparison to SLGDA counterparts with lower computational complexity.