Seminar Details
Date 
18112005 
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 wellknown measures: the
chi2measure, the Hellinger distance, the JensenShannon 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.



