Department of Mathematics

Time and Place: Tuesdays 3:05-4:20 pm in Room 0231, Love Building

Course: MAP 6939

Scope: The Applied and Computational Math Seminar is series of talks with various topics covering a broad spectrum of not only applied and computational mathematics but also engineering. Researchers outside of the Department of Mathematics and Florida State University, postdocs and senior Ph.D students are also welcomed to share their work. Please contact the organizer if you wish to schedule your talk. For Spring 2023, contact Kyle Gallivan (gallivan"at"math.fsu.edu)

Abstract: Community detection is a popular approach used to analyze large networks and obtain relevant statistical properties by finding community structures in networks. However, community detection algorithms cannot be used to find non-community structures in networks, such as cyclic graph structures which appear in food web networks. The role extraction problem represents large networks by smaller, general graph structures, called role graphs. Two different approaches have been used to solve the role extraction problem: direct approaches, which maximize a quality function to find the role structure and role assignment, and indirect, which transform the network into a similarity graph using a similarity measure and group highly similar nodes together to find the role structure and role assignments. In this talk, we discuss why the neighborhood pattern similarity measure can be used in indirect approaches to solve the role extraction problem. We show under what theoretical assumptions role graphs can be recovered from a low-rank factorization of the similarity matrix due to the relationship between the rank of the similarity matrix and the number of roles. In addition, we show how perturbing the adjacency matrix affects the singular values of the similarity matrix and unify special complex structures in networks as roles structures that can be found using the neighborhood pattern similarity measure.

Bio: Dr. Melissa Marchand graduated as the Outstanding Graduating Senior of the School of Natural Science, Mathematics, and Engineering and the Outstanding Graduating Senior of the Department of Mathematics from California State University of Bakersfield in the Spring of 2011, with a Bachelor's degree in Applied Mathematics and a minor in Computer Science. She obtained her Master's degree in the spring of 2015, and completed her Ph.D in Applied and Computational Mathematics in 2017 at Florida State University. Dr. Marchand currently works at the Naval Surface Warfare Center Panama CIty Division. Her research interests include convex and nonconvex optimization, graph partitioning and numerical linear algebra, and their applications to problems such as low-rank matrix approximation, the role extraction problem, and signal and image processing.