Graph-Regularized Fast and Robust Principal Component Analysis for Hyperspectral Band Selection

A fast and robust principal component analysis on Laplacian graph (FRPCALG) method is proposed to select bands of hyperspectral imagery (HSI). The FRPCALG assumes that a clean band matrix lies in a unified manifold subspace with low-rank and clustering properties, whereas sparse noise does not lie in the same subspace. It estimates the clean low-rank approximation of the original HSI band matrix while uncovering the clustering structure of all bands. Specifically, a structured random projection is adopted to reduce the high spatial dimensionality of the original data for computational cost saving, and then a Laplacian graph (LG) term is regularized into the regular robust principal component analysis (RPCA) to formulate the FRPCALG model for the submatrix of bands to be selected. The RPCA term ensures the clean and low-rank approximation of original data, and the LG term guarantees the clustering quality of a low-rank matrix in the low-dimensional manifold subspace. The alternating direction method of multipliers' algorithm is utilized to optimize the convex program of the FRPCALG. The K-means algorithm is to group all columns of submatrix into clusters, and corresponding bands closest to their cluster centroids finally constitute the desired band subset. Experimental results show that FRPCALG outperforms state-of-the-art methods with lower computational cost. A moderate regularization parameter lambda and a small mu could guarantee satisfying the classification accuracy of FRPCALG, and a small projected dimension greatly reduces the computational cost and does not affect the classification performance. Therefore, the FRPCALG can be an alternative method for hyperspectral band selection.