This dissertation uses Riemannian optimization theory to increase our understanding of the role extraction problem and algorithms.
Recent ideas of using the low-rank projection of the neighborhood pattern similarity measure and our theoretical analysis of the relationship
between the rank of the similarity measure and the number of roles in the graph motivates our proposal to use Riemannian optimization to
compute a low-rank approximation of the similarity measure. We propose two indirect approaches to use to solve the role extraction problem.
The first uses the standard two-phase process. For the first phase, we propose using Riemannian optimization to compute a low-rank
approximation of the similarity of the graph, and for the second phase using k-means clustering on the low-rank factor of the similarity
matrix to extract the role partition of the graph. This approach is designed to be efficient in time and space complexity while still being
able to extract good quality role partitions. We use basic experiments and applications to illustrate the time, robustness, and quality of
our two-phase indirect role extraction approach. The second indirect approach we propose combines the two phases of our first approach into a
one-phase approach that iteratively approximates the low-rank similarity matrix, extracts the role partition of the graph, and updates the
rank of the similarity matrix. We show that the use of Riemannian rank-adaptive techniques when computing the low-rank similarity matrix
improves robustness of the clustering algorithm. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the
degree of Doctor of Philosophy. / Fall Semester 2017. / September 21, 2017. / blockmodeling, graph partitioning, networks, Riemannian optimization, role extraction problem / Includes bibliographical references. / Kyle A. Gallivan, Professor Co-Directing Dissertation; Paul Van Dooren, Professor Co-Directing
Dissertation; Gordon Erlebacher, University Representative; Giray Ökten, Committee Member; Mark Sussman, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_604988 |
| Contributors | Marchand, Melissa Sue (author), Gallivan, Kyle A., 1958- (professor co-directing dissertation), Dooren, Paul van (professor co-directing dissertation), Erlebacher, Gordon, 1957- (university representative), Sussman, Mark (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (176 pages), computer, application/pdf |
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