NDLI: A Generalization of Haussler's Convolution Kernel — Mapping Kernel and Its Application to Tree Kernels

Content Provider	Springer Nature Link
Author	Shin, Kilho Kuboyama, Tetsuji
Copyright Year	2010
Abstract	Haussler's convolution kernel provides an effective framework for engineering positive semidefinite kernels, and has a wide range of applications. On the other hand, the mapping kernel that we introduce in this paper is its natural generalization, and will enlarge the range of application significantly. Our main theorem with respect to positive semidefiniteness of the mapping kernel (1) implies Haussler's theorem as a corollary, (2) exhibits an easy-to-check necessary and sufficient condition for mapping kernels to be positive semidefinite, and (3) formalizes the mapping kernel so that significant flexibility is provided in engineering new kernels. As an evidence of the effectiveness of our results, we present a framework to engineer tree kernels. The tree is a data structure widely used in many applications, and tree kernels provide an effective method to analyze tree-type data. Thus, not only is the framework important as an example but also as a practical research tool. The description of the framework accompanies a survey of the tree kernels in the literature, where we see that 18 out of the 19 surveyed tree kernels of different types are instances of the mapping kernel, and examples of novel interesting tree kernels.
Starting Page	1040
Ending Page	1054
Page Count	15
File Format	PDF
ISSN	10009000
Journal	Journal of Computer Science and Technology
Volume Number	25
Issue Number	5
e-ISSN	18604749
Language	English
Publisher	Springer US
Publisher Date	2010-09-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	kernel convolution kernel tree edit distance Information Systems Applications (incl.Internet) Artificial Intelligence (incl. Robotics) Data Structures, Cryptology and Information Theory Theory of Computation Software Engineering Computer Science
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computer Science Applications Software Hardware and Architecture

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