Abstract
We often meet the tree decomposition task in the tree kernel computing. And tree decomposition tends to vary under different tree mapping constraint. In this paper, we first introduce the general tree decomposition function, and compare the three variants of the function corresponding to different tree mapping. Then we will give a framework to generalize the kernels based on tree-to-tree decomposition with the decomposition function.
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References
Kuboyama, T., Shin, K., Kashima, H.: Flexible Tree Kernels based on Counting the Number of Tree Mapping. In: Proceedings of the International Workshop on Mining and Learning with Graphs, pp. 61–72 (2006)
Collins, M., Duffy, N.: Convolution Kernels for Natural Language. Advances in Neural Information Processing Systems 14, 625–632 (2001)
Shawe-Taylor, J., Cristinini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Kashima, H., Koyanagi, T.: Kernels for Semi-Structured Data. In: Proceeding of the 9th International Conference on Machine Learning, pp. 291–298 (2002)
Zhang, K., Shasha, D.: Simple Fast Algorithm for the Editing Distance between Trees and Related Problems. SIAM Journal of Computing 18, 1245–1262 (1989)
Tai, K.C.: The Tree-to-Tree Correction Problem. JACM 26, 422–433 (1979)
Zhang, K.: Algorithms for the Constrained Editing Distance between Ordered Labeled Tree and Related Problems. Pattern Recognition 28, 463–474 (1995)
Lu, C.L., Su, Z.-Y., Tang, C.Y.: A New Measure of Edit Distance between Labeled Trees. In: Wang, J. (ed.) COCOON 2001. LNCS, vol. 2108, pp. 338–348. Springer, Heidelberg (2001)
Haussler, D.: Convolution kernels on Discrete Structures. USSC-CRL 99–10, Dept. of Computer Science, Univ. of California at Santa Cruz (1999)
Kuboyama, T., Shin, K., Miyahara, T., Yasuda, H.: A Theoretical Analysis of Alignment and Edit Problems for Trees. In: Coppo, M., Lodi, E., Pinna, G.M. (eds.) ICTCS 2005. LNCS, vol. 3701, pp. 323–337. Springer, Heidelberg (2005)
Dulucq, S., Touzet, H.: Analysis of Tree Edit Distance Algorithms. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 83–95. Springer, Heidelberg (2003)
Boser, B.E., Guyon, I.M., Vapnik, V.N.: A Training Algorithm for Optimal Margin Classifiers. In: Haussler, D. (ed.) Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, pp. 144–152 (1992)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)
Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)
Gärtner, T., Lloyd, J., Flach, P.A.: Kernels and Distances for Structured Data. Machine Learning 57, 205–232 (2004)
Dzeroski, S., Lavrac, N. (eds.): Relational Data Mining. Springer, Heidelberg (2001)
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Huang, P., Zhu, J. (2007). Decomposition Method for Tree Kernels. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72393-6_71
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DOI: https://doi.org/10.1007/978-3-540-72393-6_71
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72392-9
Online ISBN: 978-3-540-72393-6
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