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Over the past decade, manifold and graph representations of hyperspectral imagery (HSI) have been explored widely in HSI applications. Among many data-driven approaches to deriving manifold coordinate representations including Isometric Mapping (ISOMAP), Local Linear Embedding (LLE), Laplacian Eigenmaps (LE), and Diffusion Kernels (DK), ISOMAP is the only global method that well represents the large scale nonlinear geometric structure of the data. In recent years, methods such as ENH-ISOMAP as well as its parallel computing accelerations makes ISOMAP practical for hyperspectral image dimensionality reduction. However, the noise problem in these methods has not been well addressed, which is critical to classification accuracy based on the manifold coordinates derived from these methods. While standard linear techniques to reduce the effects of noise can be applied as a preliminary step, these are based on global statistics and are applied globally across the entire data set, resulting in the risk of losing subtle nonlinear features before classification. To solve this problem, in this paper, we explore several approaches to modeling and mitigating noise in HSI in a local sense to improve the performance of the ENH-ISOMAP algorithm, aiming to reduce the noise effect on the manifold representations of the HSI. A new method to split data into local spectral subsets is introduced. Based on the local spectral subsets obtained with this method, a local noise model guided landmark selection scheme is proposed. In addition, a new robust adaptive neighborhood method using intrinsic dimensionality information to construct the k-Nearest Neighbor graph is introduced to increase the fidelity of the graph, based on the same framework of local spectral subsetting. The improved algorithm produces manifold coordinates with less noise, and shows a better classification accuracy using k-Nearest Neighbor classifier.
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