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. / A Dissertation Submitted to the Department of Statistics in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy. / Summer Semester, 2006. / June 29, 2006. / Tangent Spaces of Manifolds, Efficient Algorithm, Matrix Exponent, Gradient Optimization, Entropy / Includes bibliographical references. / Anuj Srivastava, Professor Directing Dissertation; Xiuwen Liu, Outside Committee Member; Fred Huffer, Committee Member; Eric Chicken, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_176393 |
| Contributors | Rubinshtein, Evgenia (authoraut), 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) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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