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Algorithms and geometric analysis of data sets that are invariant under a group action

Date

2010

Authors

Smith, Elin Rose, author
Peterson, Christopher Scott, 1963-, advisor
Bates, Daniel J. (Daniel James), 1979-, committee member
Kirby, Michael, 1961-, committee member
McConnell, Ross M., committee member

Journal Title

Journal ISSN

Volume Title

Abstract

We apply and develop pattern analysis techniques in the setting of data sets that are invariant under a group action. We apply Principal Component Analysis to data sets of images of a rotating object in Chapter 5 as a means of obtaining visual and low-dimensional representations of data. In Chapter 6, we propose an algorithm for finding distributions of points in a base space that are (locally) optimal in the sense that subspaces in the associated data bundle are distributed with locally maximal distance between neighbors. In Chapter 7, we define a distortion function that measures the quality of an approximation of a vector bundle by a set of points. We then use this function to compare the behavior of four standard distance metrics and one non-metric. Finally, in Chapter 8, we develop an algorithm to find the approximate intersection of two data sets.

Description

2010 Fall.
Includes bibliographical references.

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Subject

principal component analysis
Geometric group theory
pattern analysis
Geometric analysis
minimal energy configuration
Invariant measures
image analysis
Cluster analysis
group actions
Pattern perception

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