Manifold learning for robust classification of hyperspectral data

Accurate land cover classification that ensures robust mapping under diverse acquisition conditions is important in environmental studies where the identification of the land cover changes and its quantification have critical implications for management practices, functioning of ecosystems, and impact of climate. While remote sensing data have served as a useful tool for large scale monitoring of the earth, hyperspectral data offer an enhanced capability for more accurate land cover classification. However, constructing a robust classification framework for hyperspectral data poses issues that stem from inherent properties of hyperspectral data, including highly correlated spectral bands, high dimensionality of data, nonlinear spectral responses, and nonstationarity of samples in space and time. This dissertation addresses the issues in hyperspectral data classification by leveraging the concept of manifolds. A manifold is a nonlinear low dimensional subspace that is supported by data samples. Manifolds can be exploited in developing robust feature extraction and classification methods that are pertinent to the aforementioned issues. In this dissertation, various manifold learning algorithms that are widely used in machine learning community are investigated for the classification of hyperspectral data. Performance of global and local manifold learning methods is investigated in terms of (a) parameter values, (b) number of features retained, and (c) scene characteristics of hyperspectral data. The empirical study involving several data sets with diverse characteristics is outlined in Chapter 3. Results indicate that the manifold coordinates produce generally higher classification accuracies compared to those obtained by linear feature extraction methods, when they are used with proper settings. Chapter 4 addresses two limitations in manifold learning—(a) heavy computational requirements and (b) lack of attention to spatial context—which limits the applicability of manifold learning algorithms for large scale remote sensing data. Approximation approaches such as the Nyström methods are employed to mitigate the computation burden, where a set of landmark samples is first selected for the construction of the approximate manifolds, and the remaining samples are then linearly embedded in the manifold. While various landmark selection schemes are possible (e.g. random selection, clustering based approaches), spatially representative samples that are potentially relevant to data on grids can be obtained if the spatial context is considered in the selection scheme. A framework for representing the spatial coherence of samples is proposed using the kernel feature extraction framework. The proposed method produces a set of new features in which a unique spatial coherence pattern for homogeneous regions is captured in the individual features, which yield high classification accuracies and qualitatively superior results. Finally, an adaptive classification framework that exploits manifolds is proposed to obtain robust classification results for hyperspectral data. Spectral signatures can vary significantly across extended areas, often resulting in poor classification of land cover. The proposed adaptive framework employs a manifold regularization classifier, where the classifier is trained with labeled samples in one location and adapted to samples in spatially disjoint areas that exhibit significantly different distributions. In experimental studies, classification accuracies were higher for the proposed approach than for other kernel based semi-supervised classification methods