Globally maximizing, locally minimizing: Regularized Nonnegative Matrix Factorization for hyperspectral data feature extraction

In order to find a compact representation which uncovers the hidden topics and simultaneously respects the intrinsic geometric structure of hyperspectral data, a novel algorithm, named GLNMF (Globally maximizing, Locally minimizing, regularized Nonnegative Matrix Factorization) feature extraction algorithm, is proposed. The proposed algorithm is a linear approximation of a multi-manifolds-based learning framework which imposes an additional constraint on NMF that both the local and non-local quantities are considered. GLNMF characterizes the local scatter as well as the non-local scatter, seeking to find a projection that simultaneously maximizes the non-local scatter and minimizes the local scatter. This characteristic makes GLNMF more intuitive and more powerful than some up-to-date methods. An iterative multiplicative updating algorithm is proposed to optimize the objective. Experiments on a benchmark hyperspectral dataset demonstrate that the proposed method outperforms NMF as well as a few current dimensionality reduction methods.