UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

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 given thesis/dissertation in DRUM.

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

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2009 - 200912010 - 20131

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    Data Representation for Learning and Information Fusion in Bioinformatics
    (2013) Rajapakse, Vinodh Nalin; Czaja, Wojciech; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This thesis deals with the rigorous application of nonlinear dimension reduction and data organization techniques to biomedical data analysis. The Laplacian Eigenmaps algorithm is representative of these methods and has been widely applied in manifold learning and related areas. While their asymptotic manifold recovery behavior has been well-characterized, the clustering properties of Laplacian embeddings with finite data are largely motivated by heuristic arguments. We develop a precise bound, characterizing cluster structure preservation under Laplacian embeddings. From this foundation, we introduce flexible and mathematically well-founded approaches for information fusion and feature representation. These methods are applied to three substantial case studies in bioinformatics, illustrating their capacity to extract scientifically valuable information from complex data.
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    Enumeration of Harmonic Frames and Frame Based Dimension Reduction
    (2009) Hirn, Matthew John; Benedetto, John J; Okoudjou, Kasso A; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We investigate two aspects of frame theory, one of a theoretical nature, the other very much on the applied side. In the former, we enumerate all harmonic frames of prime order, and develop partial proofs concerning the structure of the symmetry group for this subset of frames. In the latter, we develop frame theory in the context of kernel eigenmap methods, merging the two theories in a practical manner and applying new algorithms to hyperspectral imagery data for the purposes of material classification. These two problems, while seemingly separate, are united by frame theory and serve to illustrate both the beautiful theoretical nature of frames as well as their practicality in dealing with real world problems.