The Geometry of Community Detection via the MMSE Matrix

Presented on September 4, 2019 at 12:15 p.m. in the Marcus Nanotechnology Building, Room 1116.Galen Reeves joined the faculty at Duke University in Fall 2013, and is currently an Assistant Professor with a joint appointment in the Department of Electrical & Computer Engineering and the Department of Statistical Science.Runtime: 39:39 minutesThe information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. In this talk, Reeves will present a new approach that applies to a broader class of network models that allow for variability in the sizes and behaviors of the different communities, and thus better reflect the behaviors observed in real-world networks. The results show that the ability to detect communities can be described succinctly in terms of a matrix of effective signal-to-noise ratios that provides a geometrical representation of the relationships between the different communities. This characterization follows from a matrix version of the I-MMSE relationship and generalizes the concept of an effective scalar signal-to-noise ratio introduced in previous work. This work can be found online at https://arxiv.org/abs/1907.0249