# Community Detection with Heterogeneous Block Covariance Model

arXiv: https://arxiv.org/abs/2412.03780 · HTML: https://mlsanity.com/paper/2412.03780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 49 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence](https://mlsanity.com/paper/1509.06418/) (2015)
- [A Survey on Theoretical Advances of Community Detection in Networks](https://mlsanity.com/paper/1809.07691/) (2018)
- [Block-diagonal covariance selection for high-dimensional Gaussian graphical models](https://mlsanity.com/paper/1511.04033/) (2015)
- [The Cluster Graphical Lasso for improved estimation of Gaussian graphical models](https://mlsanity.com/paper/1307.5339/) (2013)
- [Significance-based community detection in weighted networks](https://mlsanity.com/paper/1601.05630/) (2016)

## Abstract (arXiv)

Community detection is the task of clustering objects based on their pairwise relationships. Most of the model-based community detection methods, such as the stochastic block model and its variants, are designed for networks with binary (yes/no) edges. In many practical scenarios, edges often possess continuous weights, spanning positive and negative values, which reflect varying levels of connectivity. To address this challenge, we introduce the heterogeneous block covariance model (HBCM) that defines a community structure within the covariance matrix, where edges have signed and continuous weights. Furthermore, it takes into account the heterogeneity of objects when forming connections with other objects within a community. A novel variational expectation-maximization algorithm is proposed to estimate the group membership. The HBCM provides provable consistent estimates of memberships, and its promising performance is observed in numerical simulations with different setups. The model is applied to a single-cell RNA-seq dataset of a mouse embryo and a stock price dataset. Supplementary materials for this article are available online.