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Capturing complex high-order interactions among data is an important task inmany scenarios. A common way to model high-order interactions is to usehypergraphs whose topology can be mathematically represented by tensors.Existing methods use a fixed-order tensor to describe the topology of the wholehypergraph, which ignores the divergence of different-order interactions. Inthis work, we take this divergence into consideration, and propose amulti-order hypergraph Laplacian and the corresponding total variation. Takingthis total variation as a regularization term, we can utilize the topologyinformation contained by it to smooth the hypergraph signal. This can helpdistinguish different-order interactions and represent high-order interactionsaccurately.

Regularized Recovery by Multi-order Partial Hypergraph Total Variation