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Statistical Consistency of Kernel Canonical Correlation Analysis




While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates of the associated functions to their population counterparts has not yet been established. This paper gives a mathematical proof of the statistical convergence of kernel CCA, providing a theoretical justification for the method. The proof uses covariance operators defined on reproducing kernel Hilbert spaces, and analyzes the convergence of their empirical estimates of finite rank to their population counterparts, which can have infinite rank. The result also gives a sufficient condition for convergence on the regularization coefficient involved in kernel CCA: this should decrease as n^{-1/3}, where n is the number of data.

Author(s): Fukumizu, K. and Bach, FR. and Gretton, A.
Journal: Journal of Machine Learning Research
Volume: 8
Pages: 361-383
Year: 2007
Month: February
Day: 0

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

Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Statistical Consistency of Kernel Canonical Correlation Analysis},
  author = {Fukumizu, K. and Bach, FR. and Gretton, A.},
  journal = {Journal of Machine Learning Research},
  volume = {8},
  pages = {361-383},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = feb,
  year = {2007},
  month_numeric = {2}