Hyperspectral Unmixing Using Higher-Order Graph Regularized NMF With Adaptive Feature Selection

Abstract

Recently, graph learning methods have attracted much research attention, which uses first-order nearest-neighbor relation between pixels to construct adjacency graphs for capturing smooth abundance. However, the first-order nearest-neighbor information neglects the shared domain structure of pixels making the higher-order nearest-neighbor relation missing resulting in limited spatial structure learning. Additionally, the feature values in hyperspectral images vary greatly in different bands, tiny value contributions are easily neglected due to the statistical properties of the model, which hinders the learning efficiency of the approach. To address these shortcomings, a higher-order graph regularizer nonnegative matrix factorization with adaptive feature selection method is proposed. Specifically, we introduce pixel second-order nearest-neighbor relation in graph learning to capture the nearest-neighbor domains of pixels with missing connection in first-order neighborhoods and enhance the aggregation of homogeneous regions. Then, the first-order and second-order nearest-neighbor relation are combined to construct higher-order graph regularizer to better preserve the global spatial structure of the image. Additionally, adaptive weight is introduced in the data reconstruction to balance the effects of different feature values by adaptively selecting spectral features to enhance the contribution of tiny features. Finally, the objective function is designed by fusing the higher-order graph regularization, adaptive feature selection and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> sparse regularizer into the nonnegative matrix factorization framework, and the optimization algorithm of the model is derived using a multiplicative update rule. We conducted extensive experiments on synthetic and real datasets, and the effectiveness and superiority of the proposed method were verified by comparing it with several state-of-the-art methods.