Learning on Hypergraphs with Sparsity
This work addresses the challenge of high-order relational learning in domains like social networks or bioinformatics, but it is incremental as it builds on existing smoothness measures and sparse learning frameworks.
The authors tackled the problem of learning smooth functions on hypergraphs by proposing a framework that generalizes existing smoothness measures and introduces new ones, incorporating sparsity at both hyperedge and node levels to handle irrelevant or noisy data, resulting in models that perform similarly or better than dense models in experiments.
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, one wishes to learn a smooth function with respect to its topology. A fundamental issue is to find suitable smoothness measures of functions on the nodes of a graph/hypergraph. We show a general framework that generalizes previously proposed smoothness measures and also gives rise to new ones. To address the problem of irrelevant or noisy data, we wish to incorporate sparse learning framework into learning on hypergraphs. We propose sparsely smooth formulations that learn smooth functions and induce sparsity on hypergraphs at both hyperedge and node levels. We show their properties and sparse support recovery results. We conduct experiments to show that our sparsely smooth models have benefits to irrelevant and noisy data, and usually give similar or improved performances compared to dense models.