Local manifold learning has been successfully applied to hyperspectral dimensionality reduction in order to embed nonlinear and non-convex manifolds in the data. Local manifold learning is mainly characterized by affinity matrix construction, which is composed of two steps: neighbor selection and computation of affinity weights. There is a challenge in each step: (1) neighbor selection is sensitive to complex spectral variability due to non-uniform data distribution, illumination variations, and sensor noise; (2) the computation of affinity weights is challenging due to highly correlated spectral signatures in the neighborhood. To address the two issues, in this work a novel manifold learning methodology based on locally linear embedding (LLE) is proposed through learning a robust local manifold representation (RLMR). More specifically, a hierarchical neighbor selection (HNS) is designed to progressively eliminate the effects of complex spectral variability using joint normalization (JN) and to robustly compute affinity (or reconstruction) weights reducing collinearity via refined neighbor selection (RNS). Additionally, an idea that combines spatial-spectral information is introduced into the proposed manifold learning methodology to further improve the robustness of affinity calculations. Classification is explored as a potential application for validating the proposed algorithm. Classification accuracy in the use of different dimensionality reduction methods is evaluated and compared, while two kinds of strategies are applied in selecting the training and test samples: random sampling and region-based sampling. Experimental results show the classification accuracy obtained by the proposed method is superior to those state-of-the-art dimensionality reduction methods.
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