Year: 2007
Type: dissertation
Abstract: This thesis presents a unified understanding of edit-based approaches to approximate tree matching and introduces new facts on the subject.It also provides a broad view of kernel-based learning methods for trees, and proposes novel methods based on this view.These contributions have a wide range of applications to pattern matching, computational biology, and many other areas of computer science.As an example, this thesis includes an application to computational biology to demonstrate the effectiveness of a novel learning method developed in this work.This thesis is divided into two parts.The first part is devoted to a detailed analysis of the classes of edit-based approximate tree matching such as the tree edit problem and the alignment problem for trees.We focus on the notion of tree mapping in order to describe the semantics of approximate tree matching.We then establish an algebraic model of approximate tree matching.This algebraic model enables us to reveal unknown hidden relationships among a variety of edit-based approximate tree matching problems, which include the equivalence between two problems, the alignment problem and the less-constrained edit problem.Also, we give the tree mapping for the alignment of trees, which has been unknown for the past decade.In addition, we reveal a class hierarchy of edit-based approximate tree matching.The second part focuses on tree kernels for kernel-based learning of trees.We first show that existing tree kernels are formulated by counting functions of tree mappings from the unified view based on the class hierarchy of approximate tree matching established in the first part.In addition, we develop two novel tree kernels more flexible than known tree kernels, and show that the counting function for the alignment of trees does not satisfy a requirement for a tree kernel.The last half of the second part addresses the development of a faster tree kernel without sacrificing its learning performance.We propose two simple tree kernels, a spectrum tree kernel and its variant, a gram distribution kernel.The effectiveness of these methods are demonstrated by applying them to a problem in computational biology.Keywords: approximate pattern matching, tree edit distance, alignment of trees, machine learning, kernel methods, tree kernels, convolution kernel, glycans i I owe immeasurable debts of gratitude to so many people who have supported me along the way.I would especially like to thank my thesis Committee Chair, Hiroshi Yasuda.He has been a generous and superb mentor throughout this work, and gave me an opportunity to have many valuable experiences and to encounter with fabulous people throughout the Information Security Project led by him.I am very grateful for having an exceptional committee for my thesis and wish to thank the other committee members, Koichi Hori, Mina Akaishi, Tetsuo Shibuya, and Terumasa Aoki for sparing their precious time and offering valuable suggestions.Special thanks to Kilho Shin, who could not have been more supportive of me throughout this entire work as a coworker and a reliable friend.His keen logicality and superb mathematical intuition often shed light on my conjectures for achieving tangible results.Thanks also to Koichi Hirata, who is a highly productive researcher with a strong commitment to excellence, for sharing his vast expertise in theoretical computer science, and for encouraging me constantly to write sound and persuasive papers; Hisashi Kashima and Kiyoko Flora Aoki-Kinoshita for their support in their areas of expertise, kernel-based learning and glycomics respectively.It has been a distinct pleasure to have had the opportunity to work with such leading researchers in their fields.I would also like to express my gratitude to: Masaru Kitsuregawa for his patient support and encouragement, and for giving me the opportunity to continue to study at the Institute of Industrial Science (IIS) of the University of Tokyo; All the colleagues at the Computer Center in IIS, Hitomi Fukushima, Hiroshi Hayashi, Kiyomitsu Hirabaru, and Tsuneo Suzuki, who allowed me to concentrate on writing this thesis; Hidetoshi Yokoi, who has made efforts to provide me with such a pleasant working atmosphere at the Center for Collaborative Research of the University of Tokyo; Makoto Amamiya for his endurance while I had been drifting like a jellyfish aimlessly in the depthless abyss without realizing what an ample research environment had been provided by him; Akira Yasuhara for his generosity, a lot of helpful discussions about graph theory, dedicated support, and constant encouragement; Hiroki Arimura, who first appreciated my work in its immature stage, and has since then always been a catalyst for advancing this work; Tetsuhiro Miyahara, whose work on data mining of semistructured data motivated me to start on a part of this work when I almost drifted away from research activities while being swamped with network and database administration tasks.I have had the tremendous fortune to encounter and get (re)acquainted with fabulous researchers active in the front lines in their fields through this work.I would like to return my grateful acknowledgment to
DOI: 10.15083/00002536
Author: 哲二 久保山
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W53241408