Neighborhood Preserving Orthogonal PNMF Feature Extraction for Hyperspectral Image Classification

In this paper, we propose a manifold geometry based projective nonnegative matrix factorization linear dimensionality reduction method, called neighborhood preserving orthogonal projective nonnegative matrix factorization (NPOPNMF), for feature extraction of hyperspectral image. By adding constraints on projective nonnegative matrix factorization (PNMF) that each data point can be represented as a linear combination of its neighbors, NPOPNMF preserves local neighborhood geometrical structure of hyperspectral data in the reduced space, and overcomes the Euclidean limitation of PNMF. The metric structure of original high-dimensional hyperspectral data space is preserved due to the orthogonality of projection matrix. NPOPNMF can be performed in either supervised or unsupervised mode according to the construction of adjacency graph and it can improve the discriminant performance of PNMF. Theoretical analysis and experimental results on hyperspectral data sets demonstrate that the proposed method is an effective and promising method for hyperspectral image feature extraction.