Alignment Kernels Based on a Generalization of Alignments

Kilho SHIN  

IEICE TRANSACTIONS on Information and Systems   Vol.E97-D   No.1   pp.1-10
Publication Date: 2014/01/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E97.D.1
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Fundamentals of Information Systems
edit distance,  kernel,  tree,  graph,  

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This paper shows a way to derive positive definite kernels from edit distances. It is well-known that, if a distance d is negative definite, e-λd is positive definite for any λ > 0. This property provides us the opportunity to apply useful techniques of kernel multivariate analysis to the features of data captured by means of the distance. However, the known instances of edit distance are not always negative definite. Even worse, it is usually not easy to examine whether a given instance of edit distance is negative definite. This paper introduces alignment kernels to present an alternative means to derive kernels from edit distance. The most important advantage of the alignment kernel consists in its easy-to-check sufficient condition for the positive definiteness. In fact, when we surveyed edit distances for strings, trees and graphs, all but one are instantly verified to meet the condition and therefore proven to be positive definite.