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University of Colorado

1. Bertrand, Nicholas. Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations.

Degree: MS, Applied Mathematics, 2012, University of Colorado

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. Advisors/Committee Members: Francois Meyer, James Curry, Shannon Hughes.

Subjects/Keywords: k-svd algorithm; MLBF; Applied Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Bertrand, N. (2012). Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/55

Chicago Manual of Style (16th Edition):

Bertrand, Nicholas. “Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations.” 2012. Masters Thesis, University of Colorado. Accessed March 06, 2021. https://scholar.colorado.edu/appm_gradetds/55.

MLA Handbook (7th Edition):

Bertrand, Nicholas. “Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations.” 2012. Web. 06 Mar 2021.

Vancouver:

Bertrand N. Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations. [Internet] [Masters thesis]. University of Colorado; 2012. [cited 2021 Mar 06]. Available from: https://scholar.colorado.edu/appm_gradetds/55.

Council of Science Editors:

Bertrand N. Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations. [Masters Thesis]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/appm_gradetds/55

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