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arXiv · 2102.09771

Regularized Recovery by Multi-order Partial Hypergraph Total Variation

Ruyuan Qu·Jiaqi He·Hui Feng·Chongbin Xu·Bo Hu
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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.

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Ruyuan Qu, Jiaqi He, Hui Feng, Chongbin Xu, Bo Hu. 2021-02-19. Regularized Recovery by Multi-order Partial Hypergraph Total Variation. https://arxiv.org/abs/2102.09771

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