Semigroup kernels on finite sets

Marco Cuturi; Jean Philippe Vert

Semigroup kernels on finite sets

Marco Cuturi
, Jean Philippe Vert

Mines ParisTech

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 17 - Proceedings of the 2004 Conference, NIPS 2004
Publisher	Neural information processing systems foundation
ISBN (Print)	0262195348, 9780262195348
Publication status	Published - 1 Jan 2005
Externally published	Yes
Event	18th Annual Conference on Neural Information Processing Systems, NIPS 2004 - Vancouver, BC, Canada Duration: 13 Dec 2004 → 16 Dec 2004

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Conference

Conference	18th Annual Conference on Neural Information Processing Systems, NIPS 2004
Country/Territory	Canada
City	Vancouver, BC
Period	13/12/04 → 16/12/04

Cite this

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title = "Semigroup kernels on finite sets",

abstract = "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.",

author = "Marco Cuturi and Vert, \{Jean Philippe\}",

year = "2005",

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series = "Advances in Neural Information Processing Systems",

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note = "18th Annual Conference on Neural Information Processing Systems, NIPS 2004 ; Conference date: 13-12-2004 Through 16-12-2004",

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Cuturi, M & Vert, JP 2005, Semigroup kernels on finite sets. in Advances in Neural Information Processing Systems 17 - Proceedings of the 2004 Conference, NIPS 2004. Advances in Neural Information Processing Systems, Neural information processing systems foundation, 18th Annual Conference on Neural Information Processing Systems, NIPS 2004, Vancouver, BC, Canada, 13/12/04.

Semigroup kernels on finite sets. / Cuturi, Marco; Vert, Jean Philippe.
Advances in Neural Information Processing Systems 17 - Proceedings of the 2004 Conference, NIPS 2004. Neural information processing systems foundation, 2005. (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Semigroup kernels on finite sets

AU - Cuturi, Marco

AU - Vert, Jean Philippe

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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.

AB - 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.

M3 - Conference contribution

AN - SCOPUS:84899023521

SN - 0262195348

SN - 9780262195348

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 17 - Proceedings of the 2004 Conference, NIPS 2004

PB - Neural information processing systems foundation

T2 - 18th Annual Conference on Neural Information Processing Systems, NIPS 2004

Y2 - 13 December 2004 through 16 December 2004

ER -

Semigroup kernels on finite sets

Abstract

Publication series

Conference

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Cite this