Non-negative matrix factorization with local preservation for hyperspectral image dimensionality reduction

Abstract

This letter presents a non-negative matrix factorization (NMF) with local preservation framework for hyperspectral image dimensionality reduction. The proposed method combines the NMF and local manifold learning techniques. It overcomes the drawback that the NMF does not consider local spatial information of the data space. In this framework, we take the local spatial information into the low-dimensional representations. In order to do that, we introduce two local manifold learning approaches: locally linear embedding and local tangent space alignment. The local geometric structure can be effectively modelled through these approaches. This framework is a general framework which also includes the NMF with Laplacian Eigenmaps method. The gradient descent approach is used to find the solution of the proposed models. In order to evaluate the developed method, the support vector machine (SVM) and the k-nearest neighbour (k-NN) approaches are used for hyperspectral image classification. Experiments are done on a hyperspectral image and the classification accuracies are compared. The proposed methods can improve the classification accuracies (by at least for SVM and by at least for k-NN) when comparing with the other approaches.