Regularized Recovery by Multi-order Partial Hypergraph Total Variation
This work addresses a domain-specific issue in hypergraph modeling for data analysis, offering an incremental improvement over existing methods.
The paper tackles the problem of modeling complex high-order interactions in data by proposing a multi-order hypergraph Laplacian and total variation to account for divergent interactions across different orders, which helps in accurately representing these interactions.
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.