English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Statistical Properties of Kernel Principal Component Analysis

Zwald, L., Bousquet, O., & Blanchard, G. (2004). Statistical Properties of Kernel Principal Component Analysis. In J. Shawe-Taylor, & Y. Singer (Eds.), Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004, Banff, Canada, July 1-4 (pp. 594-608). Berlin, Germany: Springer.

Item is

Basic

show hide
Genre: Conference Paper

Files

show Files

Locators

show

Creators

show
hide
 Creators:
Zwald, L, Author
Bousquet, O1, 2, Author              
Blanchard , G, Author
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

Content

show
hide
Free keywords: -
 Abstract: We study the properties of the eigenvalues of Gram matrices in a non-asymptotic setting. Using local Rademacher averages, we provide data-dependent and tight bounds for their convergence towards eigenvalues of the corresponding kernel operator. We perform these computations in a functional analytic framework which allows to deal implicitly with reproducing kernel Hilbert spaces of infinite dimension. This can have applications to various kernel algorithms, such as Support Vector Machines (SVM). We focus on Kernel Principal Component Analysis (KPCA) and, using such techniques, we obtain sharp excess risk bounds for the reconstruction error. In these bounds, the dependence on the decay of the spectrum and on the closeness of successive eigenvalues is made explicit.

Details

show
hide
Language(s):
 Dates: 2004-07
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1007/978-3-540-27819-1_41
 Degree: -

Event

show
hide
Title: 17th Annual Conference on Learning Theory (COLT 2004)
Place of Event: Banff, Canada
Start-/End Date: 2004-07-01 - 2004-07-04

Legal Case

show

Project information

show

Source 1

show
hide
Title: Learning Theory: 17th Annual Conference on Learning Theory, COLT 2004, Banff, Canada, July 1-4
Source Genre: Proceedings
 Creator(s):
Shawe-Taylor, J, Editor
Singer, Y, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 594 - 608 Identifier: ISBN: 978-3-540-22282-8

Source 2

show
hide
Title: Lecture Notes in Computer Science
Source Genre: Series
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 3120 Sequence Number: - Start / End Page: - Identifier: -