Summary of Maximum Likelihood Estimation on Stochastic Blockmodels For Directed Graph Clustering, by Mihai Cucuringu et al.
Maximum Likelihood Estimation on Stochastic Blockmodels for Directed Graph Clustering
by Mihai Cucuringu, Xiaowen Dong, Ning Zhang
First submitted to arxiv on: 28 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Social and Information Networks (cs.SI); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates the directed graph clustering problem, framing it as a statistical estimation task within the directed stochastic block model (DSBM). The authors develop a maximum likelihood estimation (MLE) approach to determine the most probable community assignment given the observed graph structure. Additionally, they show that this MLE formulation is equivalent to a novel flow optimization heuristic that considers edge density and orientation. Building on this foundation, the paper introduces two directed clustering algorithms: spectral clustering and semidefinite programming-based clustering. The authors also provide a theoretical upper bound on the number of misclustered vertices for the spectral clustering algorithm using matrix perturbation theory. The proposed methods are evaluated quantitatively and qualitatively on both synthetic and real-world data, supporting the theoretical contributions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how to group things together in directed graphs. Imagine you have a social network where people interact with each other, and you want to find groups of friends who talk to each other a lot. The authors use statistics to solve this problem by finding the most likely group assignments given what we know about the graph. They also come up with two new ways to do this: one that uses math problems to figure out the groups, and another that uses a special kind of optimization to find the best groups. The authors test these methods on fake data and real-world networks to see how well they work. |
Keywords
* Artificial intelligence * Clustering * Likelihood * Optimization * Spectral clustering
