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Kernels, Associated Structures and Generalizations


Technical Report


This paper gives a survey of results in the mathematical literature on positive definite kernels and their associated structures. We concentrate on properties which seem potentially relevant for Machine Learning and try to clarify some results that have been misused in the literature. Moreover we consider different lines of generalizations of positive definite kernels. Namely we deal with operator-valued kernels and present the general framework of Hilbertian subspaces of Schwartz which we use to introduce kernels which are distributions. Finally indefinite kernels and their associated reproducing kernel spaces are considered.

Author(s): Hein, M. and Bousquet, O.
Number (issue): 127
Year: 2004
Month: July
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: Max Planck Institute for Biological Cybernetics, Tübingen, Germany

Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Kernels, Associated Structures and Generalizations},
  author = {Hein, M. and Bousquet, O.},
  number = {127},
  organization = {Max-Planck-Gesellschaft},
  institution = {Max Planck Institute for Biological Cybernetics, T{\"u}bingen, Germany},
  school = {Biologische Kybernetik},
  month = jul,
  year = {2004},
  month_numeric = {7}