Learning with Hypergraphs: Clustering, Classification, and Embedding

We usually endow the investigated objects with pairwise relationships,\nwhich can be illustrated as graphs. In many real-world problems, however,\nrelationships among the objects of our interest are more complex than pair-\nwise. Naively squeezing the complex relationships into pairwise ones will\ninevitably lead to loss of information which can be expected valuable for\nour learning tasks however. Therefore we consider using hypergraphs in-\nstead to completely represent complex relationships among the objects of\nour interest, and thus the problem of learning with hypergraphs arises. Our\nmain contribution in this paper is to generalize the powerful methodology\nof spectral clustering which originally operates on undirected graphs to hy-\npergraphs, and further develop algorithms for hypergraph embedding and\ntransductive classi¯cation on the basis of the spectral hypergraph cluster-\ning approach. Our experiments on a number of benchmarks showed the\nadvantages of hypergraphs over usual graphs.