Constrained nonnegative matrix factorization and hyperspectral image dimensionality reduction

This letter presents a constrained nonnegative matrix factorization (NMF)-based method for hyperspectral image dimensionality reduction. The proposed method combines the NMF and Laplacian Eigenmaps (LE). It overcomes the drawback that NMF does not consider the intrinsic geometric structure of the data space. In LE framework, an affinity graph is constructed to encode the geometrical information. The proposed technique seeks a matrix factorization which considers the graph structure. We also use the smoothness constraint and the sparsity constraint on the lower dimensional matrices. The gradient descent approach is used to find solution of the proposed model. In order to evaluate the developed method, we use the support vector machine and the k-nearest neighbourhood (KNN) approach for hyperspectral image classification. Experiments are done on a hyperspectral image. The results are compared with those obtained using other hyperspectal image dimensionality reduction methods. The classification accuracy using the proposed method is higher than that of the alternative approaches.