Neighborhood preserving Nonnegative Matrix Factorization for spectral mixture analysis

Nonnegative Matrix Factorization (NMF) has been successfully employed to address the mixed-pixel problem of hyperspectral remote sensing images. However, minimizing the representation error by NMF is not sufficient for SMA since the unmixing results of NMF are not unique. Therefore, in this paper, a neighborhood preserving regularization, which preserves the local structure of the hyperspectral data on a low-dimensional manifold, is proposed to constrain NMF for unique solution in SMA. As a result, a Neighborhood Preserving constrained NMF (NP-NMF) algorithm is proposed for SMA of highly mixed hyperspectral data. Finally, experimental results on AVIRIS data demonstrate the effectiveness of our proposed NP-NMF algorithm for SMA applications.