A subpath kernel for rooted unordered trees

Authors:
Daisuke Kimura;Tetsuji Kuboyama;Tetsuo Shibuya;Hisashi Kashima
Affiliations:
Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan;Computer Centre, Gakushuin University, Toyoshima-ku, Tokyo, Japan;Human Genome Center, Institute of Medical Science, The University of Tokyo, Tokyo, Japan;Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan
Venue:
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part I
Year:
2011

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Abstract

Kernel method is one of the promising approaches to learning with tree-structured data, and various efficient tree kernels have been proposed to capture informative structures in trees. In this paper, we propose a new tree kernel function based on "subpath sets" to capture vertical structures in rooted unordered trees, since such tree-structures are often used to code hierarchical information in data. We also propose a simple and efficient algorithm for computing the kernel by extending the multikey quicksort algorithm used for sorting strings. The time complexity of the algorithm is O((|T1|+|T2|)log(|T1|+|T2|)) time on average, and the space complexity is O(|T1| + |T2|), where |T1| and |T2| are the numbers of nodes in two trees T1 and T2. We apply the proposed kernel to two supervised classification tasks, XML classification in web mining and glycan classification in bioinformatics. The experimental results show that the predictive performance of the proposed kernel is competitive with that of the existing efficient tree kernel for unordered trees proposed by Vishwanathan et al. [1], and is also empirically faster than the existing kernel.