Cut-matching Games for Generalized Hypergraph Ratio Cuts

TL;DR

This paper introduces a fast, approximation algorithm for hypergraph ratio cut clustering that generalizes existing methods, efficiently handling complex multiway interactions in large datasets.

Contribution

It presents a novel $O(\log n)$-approximation algorithm for generalized hypergraph ratio cuts, extending the cut-matching framework to hypergraphs with improved speed and flexibility.

Findings

Algorithm achieves small approximation factors in experiments

Significantly faster than existing hypergraph clustering methods

Handles generalized hypergraph cut functions with different penalties

Abstract

Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data. This paper presents a practical $O(\log n)$-approximation algorithm for a broad class of hypergraph ratio cut clustering objectives. This includes objectives involving generalized hypergraph cut functions, which allow a user to penalize cut hyperedges differently depending on the number of nodes in each cluster. Our method is a generalization of the cut-matching framework for graph ratio cuts, and relies only on solving maximum s-t flow problems in a special reduced graph. It is significantly faster than existing hypergraph ratio cut algorithms, while also solving a more general problem. In numerical experiments on various types of hypergraphs, we show that it quickly finds ratio cut solutions within a small factor of optimality.