PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Semigroup kernels on finite sets
Marco Cuturi and Jean-Philippe Vert
In: Advances in Neural Information Processing Systems (2005) MIT Press , Cambridge, MA , pp. 329-336.


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 epresentation 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.

PDF - Requires Adobe Acrobat Reader or other PDF viewer.
EPrint Type:Book Section
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1404
Deposited By:Jean-Philippe Vert
Deposited On:28 November 2005