Kernels Based on Distributions of Agreement Subtrees

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| ·|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.KeywordsIndex StructureDynamic Programming AlgorithmGlycan StructureInput TreeReduction FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.