Clustering in Partially Labeled Stochastic Block Models via Total Variation Minimization

TL;DR

This paper proposes a scalable total variation minimization approach for clustering in partially labeled stochastic block models, providing theoretical conditions for accurate recovery of cluster assignments.

Contribution

It introduces a novel clustering method based on total variation minimization tailored for partially labeled stochastic block models, with scalable message-passing implementation.

Findings

Provides a theoretical condition for accurate clustering

Develops a scalable message-passing clustering algorithm

Demonstrates effectiveness in partially labeled settings

Abstract

A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster assignments are known for at least one data point in each cluster. In such a partially labeled stochastic block model, clustering amounts to estimating the cluster assignments of the remaining data points. We study total variation minimization as a method for this clustering task. We implement the resulting clustering algorithm as a highly scalable message-passing protocol. We also provide a condition on the model parameters such that total variation minimization allows for accurate clustering.