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Statistical Properties of Kernel Principal Component Analysis




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.

Author(s): Blanchard, G. and Bousquet, O. and Zwald, L.
Journal: Machine Learning
Volume: 66
Number (issue): 2-3
Pages: 259-294
Year: 2006
Month: March
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1007/s10994-006-6895-9
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Statistical Properties of Kernel Principal Component Analysis},
  author = {Blanchard, G. and Bousquet, O. and Zwald, L.},
  journal = {Machine Learning},
  volume = {66},
  number = {2-3},
  pages = {259-294},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = mar,
  year = {2006},
  month_numeric = {3}