Regularization with Dot-product kernels

Alex J. Smola; Zoltán L. Óvári; Robert C. Williamson

Regularization with Dot-product kernels

Alex J. Smola
, Zoltán L. Óvári
, Robert C. Williamson

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

47 Citations (Scopus)

Abstract

In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x,y) = k(x · y) satisfy Mercer's condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000
Publisher	Neural Information Processing Systems Foundation
ISBN (Print)	0262122413, 9780262122412
Publication status	Published - 2001
Event	14th Annual Neural Information Processing Systems Conference, NIPS 2000 - Denver, CO, United States Duration: 27 Nov 2000 → 2 Dec 2000

Publication series

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

Conference

Conference	14th Annual Neural Information Processing Systems Conference, NIPS 2000
Country/Territory	United States
City	Denver, CO
Period	27/11/00 → 2/12/00

Cite this

@inproceedings{b5f539abeb9d430c97606132983e2169,

title = "Regularization with Dot-product kernels",

abstract = "In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x,y) = k(x · y) satisfy Mercer's condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.",

author = "Smola, \{Alex J.\} and {\'O}v{\'a}ri, \{Zolt{\'a}n L.\} and Williamson, \{Robert C.\}",

year = "2001",

language = "English",

isbn = "0262122413",

series = "Advances in Neural Information Processing Systems",

publisher = "Neural Information Processing Systems Foundation",

booktitle = "Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000",

note = "14th Annual Neural Information Processing Systems Conference, NIPS 2000 ; Conference date: 27-11-2000 Through 02-12-2000",

}

Smola, AJ, Óvári, ZL & Williamson, RC 2001, Regularization with Dot-product kernels. in Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000. Advances in Neural Information Processing Systems, Neural Information Processing Systems Foundation, 14th Annual Neural Information Processing Systems Conference, NIPS 2000, Denver, CO, United States, 27/11/00.

Regularization with Dot-product kernels. / Smola, Alex J.; Óvári, Zoltán L.; Williamson, Robert C.
Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000. Neural Information Processing Systems Foundation, 2001. (Advances in Neural Information Processing Systems).

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

TY - GEN

T1 - Regularization with Dot-product kernels

AU - Smola, Alex J.

AU - Óvári, Zoltán L.

AU - Williamson, Robert C.

PY - 2001

Y1 - 2001

N2 - In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x,y) = k(x · y) satisfy Mercer's condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.

AB - In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x,y) = k(x · y) satisfy Mercer's condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonnegative. We give an explicit functional form for the feature map by calculating its eigenfunctions and eigenvalues.

UR - https://www.scopus.com/pages/publications/84898955546

M3 - Conference Paper

SN - 0262122413

SN - 9780262122412

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 13 - Proceedings of the 2000 Conference, NIPS 2000

PB - Neural Information Processing Systems Foundation

T2 - 14th Annual Neural Information Processing Systems Conference, NIPS 2000

Y2 - 27 November 2000 through 2 December 2000

ER -

Regularization with Dot-product kernels

Abstract

Publication series

Conference

Other files and links

Fingerprint

Cite this