Cartesian kernel: An efficient alternative to the pairwise kernel

Hisashi Kashima, Satoshi Oyama, Yoshihiro Yamanishi, Koji Tsuda

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)2672-2679
    Number of pages8
    JournalIEICE Transactions on Information and Systems
    Issue number10
    Publication statusPublished - Oct 2010

    All Science Journal Classification (ASJC) codes

    • Software
    • Hardware and Architecture
    • Computer Vision and Pattern Recognition
    • Electrical and Electronic Engineering
    • Artificial Intelligence


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