Fast and Latent Low-Rank Subspace Clustering for Hyperspectral Band Selection

This article presents a fast and latent low-rank subspace clustering (FLLRSC) method to select hyperspectral bands. The FLLRSC assumes that all the bands are sampled from a union of latent low-rank independent subspaces and formulates the self-representation property of all bands into a latent low-rank representation (LLRR) model. The assumption ensures sufficient sampling bands in representing low-rank subspaces of all bands and improves robustness to noise. The FLLRSC first implements the Hadamard random projections to reduce spatial dimensionality and lower the computational cost. It then adopts the inexact augmented Lagrange multiplier algorithm to optimize the LLRR program and estimates sparse coefficients of all the projected bands. After that, it employs a correntropy metric to measure the similarity between pairwise bands and constructs an affinity matrix based on sparse representation. The correntropy metric could better describe the nonlinear characteristics of hyperspectral bands and enhance the block-diagonal structure of the similarity matrix for correctly clustering all subspaces. The FLLRSC conducts spectral clustering on the connected graph denoted by the affinity matrix. The bands that are closest to their separate cluster centroids form the final band subset. Experimental results on three widely used hyperspectral data sets show that the FLLRSC performs better than the classical low-rank representation methods with higher classification accuracy at a low computational cost.