Bipartite Graph Partition Based Coclustering With Joint Sparsity for Hyperspectral Images

Clustering for hyperspectral images (HSIs) is a very challenging task because HSIs usually have large spectral variability, high dimensionality, and complex structures. Recently, the sparse representation and dictionary-learning-based spectral clustering (SC) approaches have achieved great success in clustering HSIs. However, SC deals with hyperspectral clustering by one-way clustering, i.e., either dictionary atoms or sparse-representation-based clustering, and only clusters the columns information of adjacency matrix. To overcome these problems, we propose a novel coclustering based on bipartite graph partition (BGP) with joint sparsity for two disjoint sets: dictionary atoms and hyperspectral pixels. First, the structured dictionary constraint is incorporated into a unified joint sparsity constrained optimizing model to learn a structured sparse representation by incorporating spectral and contextual characteristics of HSIs where the joint sparsity coefficients provide related information between hyperspectral pixels and dictionary atoms. Then, a BGP-based classifier is proposed to simultaneously group hyperspectral pixels with the learned dictionary atoms by mapping the joint sparsity coefficients to a non-negative affinity matrix of graph, and simultaneously clusters rows and columns information of adjacency matrix. To solve the BGP problem, we use spectral graph partition algorithm, which uses the left and right singular vectors of an appropriately dictionary-signal adjacent matrix to yield good bipartitionings and the singular vectors solve a real relaxation of the NP-complete BGP problem. The proposed algorithm was tested on three widely used hyperspectral datasets, and experimental results demonstrate that the proposed algorithm outperforms other state-of-the-art methods.