Theses and Dissertations from UMD

Permanent URI for this communityhttp://hdl.handle.net/1903/2

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

More information is available at Theses and Dissertations at University of Maryland Libraries.

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    A Study of the Relationship Between Spectrum and Geometry Through Fourier Frames and Laplacian Eigenmaps
    (2012) Duke, Kevin W.; Benedetto, John J.; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This thesis has two parts. The first part is a study of Fourier frames. We follow the development of the theory, beginning with its classical roots in non-uniform sampling in Paley-Wiener Spaces, to its current state, the study of the spectral properties of finite measures on locally compact abelian groups. The aim of our study is to understand the relationship between the geometry of the supporting set of a measure and the spectral properties it exhibits. In the second part, we study extensions of the Laplacian Eigenmaps algorithm and their uses in hyperspectral image analysis. In particular, we show that there is a natural way of including spatial information in the analysis that improves classification results. We also provide evidence supporting the use of Schrödinger Eigenmaps as a semisupervised tool for feature extraction. Finally, we show that Schrödinger Eigenmaps provides a platform for fusing Laplacian Eigenmaps with other clustering techniques, such as kmeans clustering.
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    A Performance Characterization of Kernel-Based Algorithms for Anomaly Detection in Hyperspectral Imagery
    (2007-04-25) Goldberg, Hirsh Reid; Chellappa, Rama; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This thesis provides a performance comparison of linear and nonlinear subspace-based anomaly detection algorithms. Using a dual-window technique to separate the local background into inner- and outer-window regions, pixel spectra from each region are projected onto subspaces defined by projection vectors that are generated using three common pattern classification techniques; the detection performances of these algorithms are then compared with the Reed-Xiaoli anomaly detector. Nonlinear methods are derived from each of the linear methods using a kernelization process that involves nonlinearly mapping the data into a high-dimensional feature space and replacing all dot products with a kernel function using the kernel-trick. A projection separation statistic determines how anomalous each pixel is. These algorithms are implemented on five hyperspectral images and performance comparisons are made using receiver operating characteristic (ROC) curves. Results indicate that detection performance is data dependent but that the nonlinear methods generally outperform their corresponding linear algorithms.