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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 lowrank 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 …