Semigroup Kernels on Finite Sets

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Semigroup Kernels on Finite Sets
Complex objects can often be conveniently represented by finite sets of simpler components, such as images by sets of patches or texts by bags of words. We study the class of positive definite (p.d.) kernels for two such objects that can be expressed as a function of the merger of their respective sets of components. We prove a general integral representation of such kernels and present two particular examples. One of them leads to a kernel for sets of points living in a space endowed itself with a positive definite kernel. We provide experimental results on a benchmark experiment of handwritten digits image classification which illustrate the validity of the approach.
Marco Cuturi, Jean-Philippe Vert
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where NIPS
Authors Marco Cuturi, Jean-Philippe Vert
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