Typical Hypergraph Computation Tasks

Abstract

Abstract After hypergraph structure generation for the data, the next step is how to conduct data analysis on the hypergraph. In this chapter, we introduce four typical hypergraph computation tasks, including label propagation, data clustering, imbalance learning, and link prediction. The first typical task is label propagation, which is to predict the labels for the vertices, i.e., assigning a label to each unlabeled vertex in the hypergraph, based on the labeled information. In general cases, label propagation is to propagate the label information from labeled vertices to unlabeled vertices through structural information of the hyperedges. In this part, we discuss the hypergraph cut on hypergraphs and random walk interpretation of label propagation on hypergraphs. The second typical task is data clustering, which is formulated as dividing the vertices into several parts in a hypergraph. In this part, we introduce a hypergraph Laplacian smoothing filter and an embedded model for hypergraph clustering tasks. The third typical task is cost-sensitive learning, which targets on learning with different mis-classification costs. The fourth typical task is link prediction, which aims to discover missing relations or predict new coming hyperedges based on the observed hypergraph.