Adaptive Hypergraph Regularized Multilayer Sparse Tensor Factorization for Hyperspectral Unmixing

Abstract

Hyperspectral unmixing with tensor models has received great attention in recent years. A tensor-based decomposition method can effectively represent the structural feature of hyperspectral images; however, the obtained results may be physically uninterpretable. To overcome this limitation, a novel adaptive hypergraph regularized multilayer sparse tensor factorization (AHGMLSTF) algorithm is proposed. First, a modified hypergraph is incorporated into tensor factorization, and the modified hypergraph uses spectral angle distance (SAD) instead of Euclidean distance to construct hyperedges to better represent the joint spatial and spectral information. Then, the hypergraph is constructed adaptively by hyperedges of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> neighborhoods. Second, the concept of multilayer decomposition is introduced to explore the hierarchical features of hyperspectral images, and a sparse constraint is imposed on each layer to make the unmixing results more consistent with the physical mechanism of mixed spectral pixels. With these constraints, the proposed method established a spectral–spatial joint tensor decomposition model that represents not only the local neighborhood similarity but also the heterogeneity of adjacent edges. Experiments on simulated data and real hyperspectral data demonstrate the effectiveness of the proposed method.