Subspace Clustering Constrained Sparse NMF for Hyperspectral Unmixing

As one of the most important information of hyperspectral images (HSI), spatial information is usually simulated with the similarity among pixels to enhance the unmixing performance of nonnegative matrix factorization (NMF). Nevertheless, the similarity is generally calculated based on the Euclidean distance between pairwise pixels, which is sensitive to noise and fails in capturing subspace information of hyperspectral data. In addition, it is independent of the NMF framework. In this article, we propose a novel unmixing method called subspace clustering constrained sparse NMF (SC-NMF) for hyperspectral unmixing to more accurately extract endmembers and correspond abundances. First, the nonnegative subspace clustering is embedded into the NMF framework to learn a similar graph, which takes full advantage of the characteristics of the reconstructed data itself to extract the spatial correlation of pixels for unmixing. It is noteworthy that the similar graph and NMF will be simultaneously updated. Second, to mitigate the influence of noise in HSI, only the $k$ largest values are retained in each self-expression vector. Finally, we use the idea of subspace clustering to extract endmembers by linearly combining of all pixels in spectral subspace, aiming at giving a reasonable physical significance to the endmembers. We evaluate the proposed SC-NMF on both synthetic and real hyperspectral data, and experimental results demonstrate that the proposed method is effective and superior by comparing with the state-of-the-art methods.