Abstract
The MAST (maximum agreement subtrees) problem has been extensively studied, and the size of the maximum agreement subtrees between two trees represents their similarity. This similarity measure, however, only takes advantage of a very small portion of the agreement subtrees, that is, the maximum agreement subtrees, and agreement subtrees of smaller size are neglected at all. On the other hand, it is reasonable to consider that the distributions of the sizes of the agreement subtrees may carry useful information with respect to similarity. Based on the notion of the size-of-index-structure-distribution kernel introduced by Shin and Kuboyama, the present paper introduces positive semidefinite tree-kernels, which evaluate distributional features of the sizes of agreement subtrees, and shows efficient dynamic programming algorithms to calculate the kernels. In fact, the algorithms are of O(|x| ยท|y|)-time for labeled and ordered trees x and y. In addition, the algorithms are designed so that the agreement subtrees have roots and leaves with labels from predetermined sub-domains of an alphabet. This design will be very useful for important applications such as the XML documents.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Shin, K., Kuboyama, T.: A generalization of hausslerโs convolution kernel - mapping kernel. In: Proc. of The 25th International Conference On Machine Learning, ICML (2008)
Kashima, H., Koyanagi, T.: Kernels for Semi-Structured Data. In: Proc. of The 9th International Conference on Machine Learning (ICML), pp. 291โ298 (2002)
Berry, V., Nicolas, F.: Maximum Agreement and Compatible Supertrees (Extended Abstract). In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol.ย 3109, pp. 205โ219. Springer, Heidelberg (2004)
Hein, J., Jiang, T., Wang, L., Zhang, K.: On the complexity of comparing evolutionary trees. Discrete Applied Mathematicsย 71, 153โ169 (1996)
Amir, A., Keselman, D.: Maximum agreement subtree in a set of evolutionary trees: Metrics and efficient algorithm. SIAM J. Computingย 26(6), 1656โ1669 (1997)
Kao, M.Y., Lam, T.W., Sung, W.-K., Ting, H.F.: An even faster and more unifying algorithm for comparing trees via unbalanced bipartite matching. J. Algorithmsย 40(2), 212โ233 (2001)
Kao, M.Y., Lam, T.W., Sung, W.-K., Ting, H.F.: A decomposition theorem for maximum weight bipartite matching with applications to evolutionary trees. SIAM J. Computingย 31(1), 18โ26 (2001)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other kernel-based learning methods. Cambridge University Press, Cambridge (2000)
Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines, Software (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm/
Hashimoto, K., Goto, S., Kawano, S., Aoki-Kinoshita, K.F., Ueda, N.: KEGG as a glycome informatics resource. Glycobiologyย 16, 63Rโ70R (2006)
Doubet, S., Albersheim, P.: CarbBank. Glycobiologyย 2(6), 505 (1992)
Yamanishi, Y., Bach, F., Vert, J.-P.: Glycan classification with tree kernels. Bioinformaticsย 23(10), 1211โ1216 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
ยฉ 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shin, K., Kuboyama, T. (2008). Kernels Based on Distributions of Agreement Subtrees. In: Wobcke, W., Zhang, M. (eds) AI 2008: Advances in Artificial Intelligence. AI 2008. Lecture Notes in Computer Science(), vol 5360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89378-3_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-89378-3_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89377-6
Online ISBN: 978-3-540-89378-3
eBook Packages: Computer ScienceComputer Science (R0)