Landing Probabilities of Random Walks for Seed-Set Expansion in Hypergraphs

TL;DR

This paper presents a mean-field analysis of landing probabilities for random walks on hypergraphs, comparing clique-expansion and tensor methods, and proposing a hybrid approach for seed-set community expansion.

Contribution

It is the first to analyze landing probabilities on hypergraphs using mean-field theory and introduces a hybrid method combining clique-expansion and tensor techniques.

Findings

Clique-expansion outperforms tensor methods in certain regimes.

Tensor methods are more effective in other parameter regimes.

The hybrid method improves seed-set expansion accuracy and efficiency.

Abstract

We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe parameter regimes in which the two methods outperform each other and propose a hybrid expansion method that uses partial clique-expansion to reduce the projection distortion and low-complexity tensor methods applied directly on the partially expanded hypergraphs.