Cartesian Kernel : An Efficient Alternative to the Pairwise Kernel

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概要

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• 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 has been used successfully in several fields. In this paper, we propose an efficient alternative which we call a Cartesian kernel. While the existing pairwise kernel (which we refer to as the 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. We discuss the generalization bounds of the two pairwise kernels by using eigenvalue analysis of the kernel matrices. Also, we consider the N-wise extensions of the two pairwise kernels. Experimental results show the Cartesian kernel is much faster than the Kronecker kernel, and at the same time, competitive with the Kronecker kernel in predictive performance.

• （社）電子情報通信学会の論文
• 2010-10-01

著者

• KASHIMA Hisashi

  Department of Mathematical Informatics, the University of Tokyo

• Oyama Satoshi

  Graduate School Of Information Science And Technology Hokkaido University

• Tsuda Koji

  Aist Computational Biology Research Center

• YAMANISHI Yoshihiro

  Mines ParisTech, Centre for Computational Biology

• Yamanishi Yoshihiro

  Mines Paristech Centre For Computational Biology

• Kashima Hisashi

  Department Of Mathematical Informatics Graduate School Of Information Science And Technology The Uni

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• Cartesian Kernel : An Efficient Alternative to the Pairwise Kernel
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