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Optimal Linear Representations of Images under Diverse Criteria

Title: Optimal Linear Representations of Images under Diverse Criteria.
Name(s): Rubinshtein, Evgenia, author
Srivastava, Anuj, professor directing dissertation
Liu, Xiuwen, outside committee member
Huffer, Fred, committee member
Chicken, Eric, committee member
Department of Statistics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2006
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: Image analysis often requires dimension reduction before statistical analysis, in order to apply sophisticated procedures. Motivated by eventual applications, a variety of criteria have been proposed: reconstruction error, class separation, non-Gaussianity using kurtosis, sparseness, mutual information, recognition of objects, and their combinations. Although some criteria have analytical solutions, the remaining ones require numerical approaches. We present geometric tools for finding linear projections that optimize a given criterion for a given data set. The main idea is to formulate a problem of optimization on a Grassmann or a Stiefel manifold, and to use differential geometry of the underlying space to construct optimization algorithms. Purely deterministic updates lead to local solutions, and addition of random components allows for stochastic gradient searches that eventually lead to global solutions. We demonstrate these results using several image datasets, including natural images and facial images.
Identifier: FSU_migr_etd-1926 (IID)
Submitted Note: A Dissertation Submitted to the Department of Statistics in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2006.
Date of Defense: June 29, 2006.
Keywords: Tangent Spaces of Manifolds, Efficient Algorithm, Matrix Exponent, Gradient Optimization, Entropy
Bibliography Note: Includes bibliographical references.
Advisory committee: Anuj Srivastava, Professor Directing Dissertation; Xiuwen Liu, Outside Committee Member; Fred Huffer, Committee Member; Eric Chicken, Committee Member.
Subject(s): Statistics
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Host Institution: FSU

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Rubinshtein, E. (2006). Optimal Linear Representations of Images under Diverse Criteria. Retrieved from