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Transitive state alignment for the quantum jensen-shannon kernel

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Title of host publicationStructural, Syntactic, and Statistical Pattern Recognition
DatePublished - 2014
Pages22-31
Number of pages10
PublisherSpringer-Verlag
EditorsPasi Fränti, Gavin Brown, Marco Loog, Francisco Escolano, Marcello Pelillo
Volume8621 LNCS
Original languageEnglish
ISBN (Print)9783662444146

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8621 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Abstract

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks.

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© Springer Verlag 2014. This is an author produced version of a paper accepted for publication in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy.

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