BMVC 2004, Kingston, 7th-9th Sept, 2004

Non-Mercer Kernels for SVM Object Recognition
S. Boughorbel (INRIA, France), J.P.Tarel (ESE, LCPC, France) and F.
Fleuret (INRIA, France)

On the one hand, Support Vector Machines have met with significant success in solving
difficult pattern recognition problems with global features representation. On the
other hand, local features in images have shown to be suitable representations for effi-
cient object recognition. Therefore, it is natural to try to combine SVM approach with
local features representation to gain advantages on both sides. We study in this paper the
Mercer property of matching kernels which mimic classical matching algorithms used in
techniques based on points of interest. We introduce a new statistical approach of kernel
positiveness. We show that despite the absence of an analytical proof of the Mercer
property, we can provide bounds on the probability that the Gram matrix is actually positive
definite for kernels in large class of functions, under reasonable assumptions. A few
experiments validate those on object recognition tasks.
(pdf article)