Regularized Recovery by Multi-order Partial Hypergraph Total Variation

TL;DR

This paper introduces a novel multi-order hypergraph Laplacian and total variation to better model and regularize high-order interactions in hypergraphs, improving the accuracy of hypergraph signal smoothing.

Contribution

It proposes a new multi-order hypergraph Laplacian and total variation that consider divergence among different interaction orders, enhancing high-order interaction modeling.

Findings

Effective in capturing diverse high-order interactions

Improves hypergraph signal smoothing accuracy

Provides a new regularization framework for hypergraph learning

Abstract

Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods use a fixed-order tensor to describe the topology of the whole hypergraph, which ignores the divergence of different-order interactions. In this work, we take this divergence into consideration, and propose a multi-order hypergraph Laplacian and the corresponding total variation. Taking this total variation as a regularization term, we can utilize the topology information contained by it to smooth the hypergraph signal. This can help distinguish different-order interactions and represent high-order interactions accurately.