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Bioinformatics 2006 22(14):e49-e57; doi:10.1093/bioinformatics/btl242
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© The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact journals.permissions@oxfordjournals.org

Integrating structured biological data by Kernel Maximum Mean Discrepancy

Karsten M. Borgwardt 1,*, Arthur Gretton 2, Malte J. Rasch 3, Hans-Peter Kriegel 1, Bernhard Schölkopf 2 and Alex J. Smola 4

1 Institute for Computer Science, Ludwig-Maximilians-University Munich Germany
2 Max Planck Institute for Biological Cybernetics Tübingen, Germany
3 Graz University of Technology Austria
4 National ICT Australia Canberra, Australia

*To whom correspondence should be addressed.

Motivation: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based statistical test for this problem, based on the fact that two distributions are different if and only if there exists at least one function having different expectation on the two distributions. Consequently we use the maximum discrepancy between function means as the basis of a test statistic.

The Maximum Mean Discrepancy (MMD) can take advantage of the kernel trick, which allows us to apply it not only to vectors, but strings, sequences, graphs, and other common structured data types arising in molecular biology.

Results: We study the practical feasibility of an MMD-based test on three central data integration tasks: Testing cross-platform comparability of microarray data, cancer diagnosis, and data-content based schema matching for two different protein function classification schemas. In all of these experiments, including high-dimensional ones, MMD is very accurate in finding samples that were generated from the same distribution, and outperforms its best competitors.

Conclusions: We have defined a novel statistical test of whether two samples are from the same distribution, compatible with both multivariate and structured data, that is fast, easy to implement, and works well, as confirmed by our experiments.

Availability: http://www.dbs.ifi.lmu.de/~borgward/MMD

Contact: kb{at}dbs.ifi.lmu.de


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