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.
Highlights
The goal of hyperspectral imaging is to obtain the spectrum for each pixel in an image to find physical objects, identify land cover materials, or detect processes
Hyperspectral unmixing can be readily formulated as a nonnegative matrix factorization (NMF) problem, which is a linear transformation process
Real Data Experiments In this experiments, we evaluate the performances of multiplicative update (MU), Orthogonal nonnegative matrix factorization (ONMF), minvol, TSMU1, TSMU2 and TSMU3 in real data experiments with the benchmark metric spectral angle distance (SAD)
Summary
The goal of hyperspectral imaging is to obtain the spectrum for each pixel in an image to find physical objects, identify land cover materials, or detect processes. Hyperspectral unmixing can be readily formulated as a nonnegative matrix factorization (NMF) problem, which is a linear transformation process. Based on singular value decomposition, Boutsidis and Gallopoulos [14] initiated NMF with a basic form that contains no randomization and converges to the same solution This warm start method can be combined with all of the existing NMF algorithms. To find a decomposition in which the hidden components are sparse, Hoyer proposed nonnegative sparse coding: the regularized term is defined as J2(V ) = ij Vij, and the factor matrices are updated using the MU method [18], [19]. We present two-stage multiplicative update nonnegative matrix factorization algorithms. TWO-STAGE MULTIPLICATIVE UPDATE ALGORITHM FOR NONNEGATIVE MATRIX FACTORIZATION A. We are ready to state our two-stage multiplicative update algorithm for nonnegative matrix factorization
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