Two-stage Nonnegative Matrix Factorization in Hyperspectral Un-mixing

Nonnegative matrix factorization (NMF) has been applied to hyperspectral un-mixing (HU) due to its simplicity and effectiveness. There are two shortcomings when applying NMF in HU. First, the solution space of NMF is large, which is caused by the nonconvex objective function. Second, the part-based property NMF is not strong enough for the HU problem, resulting in a less expressive estimation of endmembers. We present a two-stage active set type NMF algorithm, which uses k-means and obtains an estimation of the endmember matrix. Then, the estimated endmember matrix starts the alternative least squares stage as the initialization matrix. Two reasonable constraints are added in our cost function of NMF, it controls the similarity between the first-factor matrix and the endmember matrix, and the sparsity of the second-factor matrix. Numerical tests show that the accuracy and the stabilization of the solution are achieved when applying our new algorithms in HU.