Enhancing Hyperspectral Unmixing With Two-Stage Multiplicative Update Nonnegative Matrix Factorization

Abstract

Nonnegative matrix factorization (NMF) is a powerful tool for hyperspectral unmixing (HU). This method factorizes a hyperspectral cube into constituent endmembers and their fractional abundances. In this paper, we propose a two-stage nonnegative matrix factorization algorithm. During the first stage, $k$ -means clustering is first employed to obtain the estimated endmember matrix. This matrix serves as the initial matrix for NMF during the second stage, where we design a new cost function for the purpose of refining the solutions of NMF. The two-stage NMF model is solved with multiplicative update rules, and the monotonic convergence of this algorithm is proven with an auxiliary function. Numerical tests demonstrate that our two-stage NMF algorithm can achieve accurate and stable solutions.