Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning

Abstract

Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically involve finding a well-connected set of nodes near a given set of labeled vertices. Although many methods for local clustering exist for graphs, there are relatively few for localized clustering in hypergraphs. Moreover, those that exist often lack flexibility to model a general class of hypergraph cut functions or cannot scale to large problems. To tackle these issues, this paper proposes a new diffusion-based hypergraph clustering algorithm that solves a quadratic hypergraph cut based objective akin to a hypergraph analog of Andersen-Chung-Lang personalized PageRank clustering for graphs. We prove that, for graphs with fixed maximum hyperedge size, this method is strongly local, meaning that its runtime only depends on the size of the output instead of the size of the hypergraph and is highly scalable. Moreover, our method enables us to compute with a wide variety of cardinality-based hypergraph cut functions. We also prove that the clusters found by solving the new objective function satisfy a Cheeger-like quality guarantee. We demonstrate that on large realworld hypergraphs our new method finds better clusters and runs much faster than existing approaches. Specifically, it runs in few seconds for hypergraphs with a few million hyperedges compared with minutes for flow-based technique. We furthermore show that our framework is general enough that can also be used to solve other p-norm based cut objectives on hypergraphs. Our code is available github.com/MengLiuPurdue/LHQD.

A nonlinear diffusion method for semi-supervised learning on hypergraphs

“…Directly modeling these higher-order interactions has led to improvements in a number of machine learning problems [42,6,22,23,39,32,2]. Along this line, there are a number of diffusions or label spreading techniques for semi-supervised learning on hypergraphs [42,14,40,21,24,37,35], which are also built on principles of similarity or assortativity. However, these methods are designed for cases where only labels are available, and do not take advantage of rich features or metadata associated with hypergraphs that are potentially useful for making accurate predictions.…”

Hyperedge Prediction using Tensor Eigenvalue Decomposition

“…Hypergraphs relax this assumption of pairwise interaction and provide the freedom to model the interaction among k nodes. Such networks commonly occur in social networks [7,15], metabolic networks [32], recommender systems [17,28] and multi-actor collaboration [25].…”