Learning with Hypergraphs: Clustering, Classification, and Embedding
Dengyong Zhou, Jiayuan Huang and Bernhard Schölkopf
In: 20th Annual Conference on Neural Information Processing Systems, 4-9 Dec 2006, Vancouver / Whistler, Canada.
We usually endow the investigated objects with pairwise relationships, which can be illustrated as graphs. In many real-world problems, however, relationships among the objects of our interest are more complex than pair-
wise. Naively squeezing the complex relationships into pairwise ones will inevitably lead to loss of information which can be expected valuable for our learning tasks however. Therefore we consider using hypergraphs instead to completely represent complex relationships among the objects of our interest, and thus the problem of learning with hypergraphs arises. Our main contribution in this paper is to generalize the powerful methodology of spectral clustering which originally operates on undirected graphs to hy-
pergraphs, and further develop algorithms for hypergraph embedding and transductive classification on the basis of the spectral hypergraph clustering approach. Our experiments on a number of benchmarks showed the advantages of hypergraphs over usual graphs.