Multi-Objective Sparse Subspace Clustering for Hyperspectral Imagery

Hyperspectral images (HSIs) are typical high-dimensional and complex data. As such, the clustering of HSIs is a challenging task. Out of the motivation to find the low-dimensional structure representation of the high-dimensional data, sparse subspace clustering (SSC) methods have been proposed in recent studies. Sparse representation is an important technique in SSC, which is aimed at obtaining the sparse coefficient matrix of the HSI data. Generally speaking, the acquisition of the sparse coefficient matrix is an ill-posed problem, and the existing methods introduce an extra condition as a regularization term to resolve it. However, the regularization parameter is determined manually, which is difficult and lacks self-adaptability. Hence, in this article, a multi-objective SSC method for hyperspectral imagery is proposed, which simultaneously optimizes the sparse term and the data fidelity term. In addition, the spatial structure information of the HSIs is often neglected in the processing model, and thus, a spatial prior term, as the third optimization objective function, is also tested in this article. As a result, there is no need to manually set a regularization parameter. Furthermore, by using the l
₀
norm as the sparse term, this reduces the error caused by the convex relaxation of the other norms. In the proposed method, a multi-objective optimization model is first used to acquire the sparse coefficient matrix, in which a strategy for constructing the dictionary is proposed for more precise and efficient multi-objective optimization. In addition, a knee point-based selection method is utilized to automatically select the optimal sparse representation solution from the Pareto front. The adjacency matrix is then constructed according to the sparse coefficient matrix. Finally, a spectral clustering method is used to obtain clustering results. Experiments undertaken with four HSI data sets confirm the effectiveness of the proposed method.