Non-Mercer Kernels for SVM Object Recognition

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 efficient 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.

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