Title of dissertation : Dimensionality Reduction for Hyperspectral Data

Title of dissertation: Dimensionality Reduction for Hyperspectral Data David P. Widemann, Doctor of Philosophy, 2008 Dissertation directed by: Professor John Benedetto Department of Mathematics Professor Wojciech Czaja Department of Mathematics This thesis is about dimensionality reduction for hyperspectral data. Special emphasis is given to dimensionality reduction techniques known as kernel eigenmap methods and manifold learning algorithms. Kernel eigenmap methods require a nearest neighbor or a radius parameter be set. A new algorithm that does not require these neighborhood parameters is given. Most kernel eigenmap methods use the eigenvectors of the kernel as coordinates for the data. An algorithm that uses the frame potential along with subspace frames to create nonorthogonal coordinates is given. The algorithms are demonstrated on hyperspectral data. The last two chapters include analysis of representation systems for LIDAR data and motion blur estimation, respectively. Dimensionality Reduction for Hyperspectral Data by David P. Widemann Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2008 Advisory Committee: Professor John Benedetto, Chair/Advisor Professor Wojciech Czaja, Co-Advisor Professor Kasso Okoudjou Professor Konstantina Trivisa Professor Denny Gulick c © Copyright by David P. Widemann 2008 For Mariam and Tarahneh