Kuboyama Laboratory

About Me

Tetsuji KUBOYAMA, Ph.D.
Professor,

Computer Centre, &
Archival Science, Graduate School of Humanities,
Gakushuin University
1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, JAPAN [MAP]
E-mail: tkuboyama-atmark-tk-dot-cc-dot-gakushuin-dot-ac-dot-jp
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PhD Thesis

Matching and Learning in Trees (PDF 2.7MB)

Ph.D. in Engineering, The University of Tokyo, April 2007

This thesis organizes various approximate matching algorithms for tree structures based on tree edit distance from a unified perspective and applies the results to classification learning using kernel methods. By formalizing the exact meaning of approximate matching of tree structures using ordered algebra, it resolves various errors and problems contained in existing research and clarifies the relationships between existing approximate matching algorithms. As a result, it became clear that tree approximate matching algorithms have a clean class hierarchy according to the sensitivity (degree of approximation) of structural comparison, that there is a close relationship between computational complexity and structural comparison sensitivity, and that multiple algorithms that were thought to be separate algorithms are actually the same algorithm.

Using these results, various similarity measures between tree structures were designed, and kernels were designed for classification learning of tree structures. It also includes a new kernel design framework that goes beyond the conventional convolution kernel framework. Furthermore, by using the concept of tree q-grams, which extends string q-grams, a fast tree kernel was designed and applied to classification learning of glycan structures.

This thesis includes a comprehensive survey of tree edit distance. For an overview of tree edit distance, please refer to Chapter 2 and the last section (summary) of Chapter 4.

Keywords: tree edit distance, alignment of trees, tree kernels, glycans