The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited
This addresses the need for more effective modeling of higher-order relationships in data, offering a flexible tool for machine learning applications.
The authors tackled the problem of learning on hypergraphs by introducing a new framework that fully utilizes hypergraph structure, based on regularization functionals using total variation on hypergraphs.
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.