# Clustering Degree-Corrected Stochastic Block Model with Outliers

## TL;DR

This paper introduces a convex-optimization clustering algorithm for degree-corrected stochastic block models that effectively handles outliers, achieving exact recovery and lower error rates in heterogeneous networks.

## Contribution

It presents a novel convex-optimization method with penalization for clustering in the presence of outliers, improving accuracy over existing algorithms.

## Key findings

- Achieves exact cluster recovery under mild conditions.
- Performs well on networks with Pareto degree distributions.
- Reduces error rates compared to prior methods.

## Abstract

For the degree corrected stochastic block model in the presence of arbitrary or even adversarial outliers, we develop a convex-optimization-based clustering algorithm that includes a penalization term depending on the positive deviation of a node from the expected number of edges to other inliers. We prove that under mild conditions, this method achieves exact recovery of the underlying clusters. Our synthetic experiments show that our algorithm performs well on heterogeneous networks, and in particular those with Pareto degree distributions, for which outliers have a broad range of possible degrees that may enhance their adversarial power. We also demonstrate that our method allows for recovery with significantly lower error rates compared to existing algorithms.