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Seminar Details

Date 18-11-2005
Time 14:30
Room/Location Sala conferenze 322, 3 piano
Title Kernels on Probability Measures
Speaker Dott. Matthias Hein
Affiliation MPI for Biological Cybernetics , Dept. Schölkopf , Spemannstraße 38 , 72076 Tübingen
Link http://www.kyb.mpg.de/~mh
Abstract We consider two ways of constructing Hilbertian metrics and positive definite kernels on probability measures. The first one leads to covariant kernels. These are kernels which are invariant with respect to coordinate changes in the probability space. As an example take color histograms of images. Covariance then means that the kernel will be invariant with respect to the choice of the color space RGB, HSV, CIE Lab etc. We extend a family of covariant Hilbertian metrics recently proposed by Fuglede and Topsoe which interpolates between the following well-known measures: the chi2-measure, the Hellinger distance, the Jensen-Shannon divergence and the total variation. The second way deals with so called structural kernels. These are kernels which incorporate similarity information of the probability space into the kernel. For example one might have a similarity measure on the space of colors which one would like to be incorporated into the kernel for color histograms of images. Two different structural kernels are considered. Finally the performance of all these kernels versus linear and Gaussian kernels is compared on two text datasets and two image datasets.
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