||Sala conferenze 322, 3 piano
||Kernels on Probability Measures
||Dott. Matthias Hein
||MPI for Biological Cybernetics , Dept. Schölkopf , Spemannstraße 38 , 72076 Tübingen
||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
invariant with respect to coordinate changes in the probability
space. As an example take color histograms of images. Covariance
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
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
which incorporate similarity information of the probability space
For example one might have a similarity measure on the space of
one would like to be incorporated into the kernel for color
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.