Band selection using sparse nonnegative matrix factorization with the thresholded Earth's mover distance for hyperspectral imagery classification

A sparse nonnegative matrix factorization method with the thresholded ground distance (SNMF-TEMD) is proposed to solve the band selection problem in hyperspectral imagery (HSI) classification. The SNMF-TEMD assumes that band vectors are sampled from a union of low-dimensional subspaces and approximates a HSI data matrix with the product of a basis matrix constructed from subspaces and a sparse coefficient matrix. The SNMF-TEMD utilizes the TEMD metric to better measures approximation errors during the optimization of HSI data factorization. The TEMD metric makes up the theoretical drawbacks in the Euclidean distance (ED) and Kullback-Leibler divergence (KLD) metrics when measuring the approximation errors in HSI datasets. The SNMF-TEMD is solved by the combination of min-cost-flow algorithm and multiplicative update rules. The band cluster assignments are found according to positions of largest entries in columns of the coefficient matrix and the desired band subset constitutes with the bands closest to their cluster centers. Three groups of experiments on two HSI datasets are performed to explore the performance of SNMF-TEMD. Four popular band selection methods are used to make comparisons: affinity propagation (AP), maximum-variance principal component analysis (MVPCA), SNMF with ED metric (SNMF-ED) and SNMF with KLD metric (SNMF-KLD). Experimental results show that SNMF-TEMD outperforms all four methods in classification accuracy and its computational speed is slower than SNMF-ED and SNMF-KLD. SNMF-TEMD is a better choice for band selection among all five methods because of its overwhelming advantage in classification and the popular speed remedy scheme from parallel computing and high-performance computers.