Published on Wed Dec 18 2013

The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited

Matthias Hein, Simon Setzer, Leonardo Jost, Syama Sundar Rangapuram

Hypergraphs allow one to encode higher-order relationships in data. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only applicable under special conditions.

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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.