Papers Published
- Reeves, G; Mayya, V; Volfovsky, A, The Geometry of Community Detection via the MMSE Matrix,
IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July
(July, 2019),
pp. 400-404 [doi] .
(last updated on 2024/04/19)Abstract:
The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study 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. Our 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. We provide explicit formulas for the asymptotic per-node mutual information and upper bounds on the minimum mean-squared error. The theoretical results are supported by numerical simulations.