On Valid Optimal Assignment Kernels and Applications to Graph Classification

On Valid Optimal Assignment Kernels and Applications to Graph Classification

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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Authors
  • Kriege, Nils M.
  • Giscard, Pierre-Louis
  • Wilson, Richard C.
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
The Thirtieth Conference on Neural Information Processing Systems (NIPS)
Divisions
Data Mining and Machine Learning
Event Location
Barcelona, Spanien
Event Type
Conference
Event Dates
05.-10.12.2016
Series Name
Advances in Neural Information Processing Systems 29 (NIPS 2016)
Page Range
pp. 1615-1623
Date
5 December 2016
Official URL
http://papers.nips.cc/paper/6166-on-valid-optimal-...
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