By the same authors

On Valid Optimal Assignment Kernels and Applications to Graph Classification

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Publication details

Title of host publicationNIPS'16 Proceedings of the 30th International Conference on Neural Information Processing Systems
DatePublished - 6 Dec 2016
Pages1623-1631
Number of pages9
PublisherCurran Associates Inc.
EditorsDaniel D. Lee, Ulrike von Luxburg, Roman Garnett, Masashi Sugiyama, Isabelle Guyon
Original languageEnglish
ISBN (Print)978-1-5108-3881-9

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Abstract

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are obtained from an optimal bijection between parts, which can provide a more valid notion of similarity. In general however, optimal assignments yield indefinite functions, which complicates their use in kernel methods. We characterize a class of base kernels used to compare parts that guarantees positive semidefinite optimal assignment kernels. These base kernels give rise to hierarchies from which the optimal assignment kernels are computed in linear time by histogram intersection. We apply these results by developing the Weisfeiler-Lehman optimal assignment kernel for graphs. It provides high classification accuracy on widely-used benchmark data sets improving over the original Weisfeiler-Lehman kernel.

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