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Dimension reduction (DR) is an essential preprocessing for hyperspectral image (HSI) classification. Recently, nonnegative matrix factorization (NMF) has been shown as an effective tool for the DR of hyperspectral data given the fact that it provides interpretable results. However, the basic NMF ignores the geometric structure information of the HSI data, thus limiting its performance. To this end, a novel regularized NMF method, termed NMF with adaptive graph regularizer (NMFAGR), is proposed for the spectral-spatial dimension reduction of hyperspectral data in this paper. Specifically, to enhance the preservation ability of the geometric structure information, the NMFAGR performs the dimension reduction and graph learning simultaneously. Regarding the mutual correlation between these two tasks, a graph regularizer is added as an interaction. Moreover, to effectively utilize complementary information among spectral-spatial features, the NMFAGR allocates feature weight factors automatically without requiring any additional parameters. An efficient algorithm is utilized to solve the optimization problem. The effectiveness of the proposed method is demonstrated on three benchmark hyperspectral data sets through experimentation.

A Novel Regularized Nonnegative Matrix Factorization for Spectral-Spatial Dimension Reduction of Hyperspectral Imagery