The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited

TL;DR

This paper introduces a new hypergraph learning framework utilizing total variation regularization, enabling more accurate modeling of higher-order data relationships without relying on graph approximations or tensor methods.

Contribution

It proposes a novel total variation-based regularization functional specifically designed for hypergraphs, fully leveraging their structure for learning tasks.

Findings

New hypergraph total variation regularization functional

Framework improves modeling of higher-order relationships

Applicable to various learning scenarios without approximations

Abstract

Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only applicable under special conditions. In this paper, we present a new learning framework on hypergraphs which fully uses the hypergraph structure. The key element is a family of regularization functionals based on the total variation on hypergraphs.