DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** David Marchette, Naval Surface Warfare Center

**Title: ***
Spectral Graph Embedding for Clustering
*

**Abstract:**
Random graphs occur in many scientific disciplines, from biology to the social sciences, physics, chemistry and ecology among many others. One area of interest in the study of random graphs is the study of communities among the nodes of the graph. One of the ways this is currently done is by utilizing the eigenvectors of (a function of) the adjacency matrix to embed the vertices in a (low-dimensional) Euclidean space, in which one subsequently performs inference. I will discuss a particular class of random graph models, the stochastic block model and the related random dot product graph, and describe some of what is known about the distribution of the embedded points under these models. I will discuss a new method for choosing both the embedding dimension and the number of clusters, and show how to fit the cluster model, and discuss some applications of these ideas. I will also briefly describe some of the other research initiatives of our group at NSWC Dahlgren with an aim of fostering discussion and potential collaborations.

**Time:** Friday, October 18, 2019, 1:30-2:30pm

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491