Sparsity-Constrained Deep Nonnegative Matrix Factorization for Hyperspectral Unmixing

Nonnegative matrix factorization (NMF) has been widely used in hyperspectral unmixing (HU). However, most NMF-based methods have single-layer structures, which may achieve poor performance for complex data. Deep learning, with its carefully designed hierarchical structure, has shown great advantages in learning data features. In this letter, we design a deep NMF structure by unfolding NMF into multilayers and present a sparsity-constrained deep NMF method for HU. In each layer, the abundance matrix is directly decomposed into the abundance matrix and endmemher matrix of the next layer. Due to the nonconvexity of the NMF model, sparsity constraint is added to each layer using a L-1 regularizer of the abundance matrix on each layer. To get better initial parameters for the deep NMF network, a layer-wise pretraining strategy based on Nesterov's accelerated gradient algorithm is put forward to initialize the network. An alternative update method is also proposed to further fine-tune the network to get final decomposition results. The experimental results based on synthetic data and real data demonstrate that the proposed method outperforms several other state-of-the-art unmixing approaches.