On Pairwise Kernels: An Efficient Alternative and Generalization Analysis

Authors:
Hisashi Kashima;Satoshi Oyama;Yoshihiro Yamanishi;Koji Tsuda
Affiliations:
Tokyo Research Laboratory, IBM Research,;Graduate School of Informatics, Kyoto University,;Centre for Computational Biology, Mines ParisTech,;Max Planck Institute for Biological Cybernetics,
Venue:
PAKDD '09 Proceedings of the 13th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining
Year:
2009

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Abstract

Pairwise classification has many applications including network prediction, entity resolution, and collaborative filtering. The pairwise kernel has been proposed for those purposes by several research groups independently, and become successful in various fields. In this paper, we propose an efficient alternative which we call Cartesian kernel . While the existing pairwise kernel (which we refer to as Kronecker kernel) can be interpreted as the weighted adjacency matrix of the Kronecker product graph of two graphs, the Cartesian kernel can be interpreted as that of the Cartesian graph which is more sparse than the Kronecker product graph. Experimental results show the Cartesian kernel is much faster than the existing pairwise kernel, and at the same time, competitive with the existing pairwise kernel in predictive performance.We discuss the generalization bounds by the two pairwise kernels by using eigenvalue analysis of the kernel matrices.