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Cartesian Kernel : An Efficient Alternative to the Pairwise Kernel

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Title: Cartesian Kernel : An Efficient Alternative to the Pairwise Kernel
Authors: KASHIMA, Hisashi Browse this author
OYAMA, Satoshi Browse this author →KAKEN DB
YAMANISHI, Yoshihiro Browse this author
TSUDA, Koji Browse this author
Keywords: kernel methods
pairwise kernels
link prediction
Issue Date: Oct-2010
Publisher: Institute of Electronics, Information and Communication Engineers
Journal Title: IEICE Transactions on Information and Systems
Volume: E93-D
Issue: 10
Start Page: 2672
End Page: 2679
Publisher DOI: 10.1587/transinf.E93.D.2672
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 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.
Rights: Copyright ©2010 The Institute of Electronics, Information and Communication Engineers
Relation: https://search.ieice.org/
Type: article
URI: http://hdl.handle.net/2115/62276
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 小山 聡

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