On pairwise kernels: An efficient alternative and generalization analysis

Hisashi Kashima, Satoshi Oyama, Yoshihiro Yamanishi, Koji Tsuda

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    17 Citations (Scopus)

    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.

    Original languageEnglish
    Title of host publication13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009
    Pages1030-1037
    Number of pages8
    DOIs
    Publication statusPublished - Jul 23 2009
    Event13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009 - Bangkok, Thailand
    Duration: Apr 27 2009Apr 30 2009

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5476 LNAI
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009
    CountryThailand
    CityBangkok
    Period4/27/094/30/09

    Fingerprint

    Pairwise
    kernel
    Collaborative filtering
    Alternatives
    Cartesian
    Product Graph
    Kronecker Product
    Generalization
    Eigenvalue Analysis
    Collaborative Filtering
    Adjacency Matrix
    Graph in graph theory
    Prediction
    Experimental Results

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Kashima, H., Oyama, S., Yamanishi, Y., & Tsuda, K. (2009). On pairwise kernels: An efficient alternative and generalization analysis. In 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009 (pp. 1030-1037). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5476 LNAI). https://doi.org/10.1007/978-3-642-01307-2_110

    On pairwise kernels : An efficient alternative and generalization analysis. / Kashima, Hisashi; Oyama, Satoshi; Yamanishi, Yoshihiro; Tsuda, Koji.

    13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009. 2009. p. 1030-1037 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5476 LNAI).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Kashima, H, Oyama, S, Yamanishi, Y & Tsuda, K 2009, On pairwise kernels: An efficient alternative and generalization analysis. in 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5476 LNAI, pp. 1030-1037, 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009, Bangkok, Thailand, 4/27/09. https://doi.org/10.1007/978-3-642-01307-2_110
    Kashima H, Oyama S, Yamanishi Y, Tsuda K. On pairwise kernels: An efficient alternative and generalization analysis. In 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009. 2009. p. 1030-1037. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-01307-2_110
    Kashima, Hisashi ; Oyama, Satoshi ; Yamanishi, Yoshihiro ; Tsuda, Koji. / On pairwise kernels : An efficient alternative and generalization analysis. 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2009. 2009. pp. 1030-1037 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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