Date of Award

Spring 1-1-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Francois Meyer

Second Advisor

James Curry

Third Advisor

Shannon Hughes

Abstract

We investigate the problem of finding a parameterization of a smooth, low-dimensional manifold based on noisy observations from a high-dimensional ambient space. The formulation of such parameterizations sees applications in a variety of areas such as data denoising and image segmentation.

We introduce algorithms inspired by the existing k-svd algorithm for training dictionaries for sparse data representation, and the local best-fit at algorithm for hybrid linear modeling. The output of our algorithm is an assignment of input data points to locally linear models. To demonstrate the applicability of our algorithm, we discuss experiments performed on synthetic datasets.

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