Hilbertian metrics and positive definite kernels on probability measures
Matthias Hein and Olivier Bousquet
In: AISTATS 2005, 6-8 Jan 2005, Barbados.
We investigate the problem of defining Hilbertian metrics resp.
positive definite kernels on probability measures, continuing previous work. This type of kernels has shown very good
results in text classification and has a wide range of possible
applications. In this paper we extend the two-parameter family of
Hilbertian metrics of Topsoe such that it now includes all
commonly used Hilbertian metrics on probability measures. This
allows us to do model selection among these metrics in an elegant
and unified way. Second we investigate further our approach to
incorporate similarity information of the probability space into
the kernel. The analysis provides a better understanding of these
kernels and gives in some cases a more efficient way to compute
them. Finally we compare all proposed kernels in two text and two
image classification problems.