On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms
SIAM Journal on Computing
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
A Decomposition Theorem for Maximum Weight Bipartite Matchings
SIAM Journal on Computing
Kernels for Semi-Structured Data
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Glycan classification with tree kernels
Bioinformatics
A generalization of Haussler's convolution kernel: mapping kernel
Proceedings of the 25th international conference on Machine learning
Journal of Computer Science and Technology
The kernel of maximum agreement subtrees
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
The Kernel of Maximum Agreement Subtrees
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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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 | ·|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.