Robust Correlation Clustering with Asymmetric Noise

TL;DR

This paper introduces a new correlation clustering algorithm robust to asymmetric noise in graphs, supported by a novel generative model and theoretical guarantees for recovering strongly clustered nodes.

Contribution

It proposes the Node Factors Model for generating graphs with asymmetric noise and a semidefinite programming-based algorithm, exttt{$ exttt{ ext{ extbackslash l}_2$-norm-diag}}, with proven robustness.

Findings

exttt{$ exttt{ ext{ extbackslash l}_2$-norm-diag} }$ effectively recovers strongly clustered nodes.

The Node Factors Model captures asymmetric noise in graph generation.

Theoretical analysis demonstrates robustness of the proposed algorithm.

Abstract

Graph clustering problems typically aim to partition the graph nodes such that two nodes belong to the same partition set if and only if they are similar. Correlation Clustering is a graph clustering formulation which: (1) takes as input a signed graph with edge weights representing a similarity/dissimilarity measure between the nodes, and (2) requires no prior estimate of the number of clusters in the input graph. However, the combinatorial optimization problem underlying Correlation Clustering is NP-hard. In this work, we propose a novel graph generative model, called the Node Factors Model (NFM), which is based on generating feature vectors/embeddings for the graph nodes. The graphs generated by the NFM contain asymmetric noise in the sense that there may exist pairs of nodes in the same cluster which are negatively correlated. We propose a novel Correlation Clustering algorithm, called \anormd, using techniques from semidefinite programming. Using a combination of theoretical and computational results, we demonstrate that $\texttt{$\ell_2$-norm-diag}$ recovers nodes with sufficiently strong cluster membership in graph instances generated by the NFM, thereby making progress towards establishing the provable robustness of our proposed algorithm.