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A Hilbert-Schmidt Dependence Maximization Approach to Unsupervised Structure Discovery

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83816

Blaschko,  MB
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Blaschko, M., & Gretton, A. (2008). A Hilbert-Schmidt Dependence Maximization Approach to Unsupervised Structure Discovery. Proceedings of the 6th International Workshop on Mining and Learning with Graphs (MLG 2008), 1-3.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C831-4
Abstract
In recent work by (Song et al., 2007), it has been proposed to perform clustering by maximizing a Hilbert-Schmidt independence criterion with respect to a predefined cluster structure Y , by solving for the partition matrix, II. We extend this approach here to the case where the cluster structure Y is not fixed, but is a quantity to be optimized; and we use an independence criterion which has been shown to be more sensitive at small sample sizes (the Hilbert-Schmidt Normalized Information Criterion, or HSNIC, Fukumizu et al., 2008). We demonstrate the use of this framework in two scenarios. In the first, we adopt a cluster structure selection approach in which the HSNIC is used to select a structure from several candidates. In the second, we consider the case where we discover structure by directly optimizing Y.