Local discriminant non-negative matrix factorization feature extraction for hyperspectral image classification

Non-negative matrix factorization (NMF) ignores both the local geometric structure of and the discriminative information contained in a data set. A manifold geometry-based NMF dimension reduction method called local discriminant NMF (LDNMF) is proposed in this paper. LDNMF preserves not only the non-negativity but also the local geometric structure and discriminative information of the data. The local geometric and discriminant structure of the data manifold can be characterized by a within-class graph and a between-class graph. An efficient multiplicative updating procedure is produced, and its global convergence is guaranteed theoretically. Experimental results on two hyperspectral image data sets show that the proposed LDNMF is a powerful and promising tool for extracting hyperspectral image features.