Learning on Hypergraphs with Sparsity

TL;DR

This paper introduces a new framework for learning smooth functions on hypergraphs that incorporates sparsity to handle irrelevant or noisy data, improving performance over traditional dense models.

Contribution

It proposes sparsely smooth formulations for hypergraph learning that induce sparsity at hyperedge and node levels, extending existing smoothness measures.

Findings

Sparsely smooth models effectively handle noisy data.

Models show comparable or improved performance over dense models.

The framework generalizes previous smoothness measures.

Abstract

Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, one wishes to learn a smooth function with respect to its topology. A fundamental issue is to find suitable smoothness measures of functions on the nodes of a graph/hypergraph. We show a general framework that generalizes previously proposed smoothness measures and also gives rise to new ones. To address the problem of irrelevant or noisy data, we wish to incorporate sparse learning framework into learning on hypergraphs. We propose sparsely smooth formulations that learn smooth functions and induce sparsity on hypergraphs at both hyperedge and node levels. We show their properties and sparse support recovery results. We conduct experiments to show that our sparsely smooth models have benefits to irrelevant and noisy data, and usually give similar or improved performances compared to dense models.