Geometric Nonnegative Matrix Factorization (GNMF) for Hyperspectral Unmixing

In the available hyperspectral unmixing approaches, hyperspectral images are often treated as a list of spectral measurements with no geometric organization. In this paper, we explore the geometric structure of hyperspectral images in both the spatial domain and the spectral domain to advance a geometric nonnegative matrix factorization (GNMF) for more accurate endmember extraction and abundance estimation. In the proposed GNMF, we define the “spatial geometric distance” and “spectral geometric distance” to reveal the affinity between pixels. Both the spatial geometric homogeneity of hyperspectral vectors in a local region, and the geometry manifold structure in the spectral domain, are explored to formulate spatial-spectral manifold regularizer for NMF. Some experiments are taken on some synthetic data and real hyperspectral data to investigate the performance of GNMF, and the results show that it can present state-of-the-art unmixing results.