Accurate Probabilistic Error Bound for Eigenvalues of Kernel Matrix

  • Lei Jia
  • Shizhong Liao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5828)


The eigenvalues of the kernel matrix play an important role in a number of kernel methods. It is well known that these eigenvalues converge as the number of samples tends to infinity. We derive a probabilistic finite sample size bound on the approximation error of an individual eigenvalue, which has the important property that the bound scales with the dominate eigenvalue under consideration, reflecting the accurate behavior of the approximation error as predicted by asymptotic results and observed in numerical simulations. Under practical conditions, the bound presented here forms a significant improvement over existing non-scaling bound. Applications of this theoretical finding in kernel matrix selection and kernel target alignment are also presented.


Kernel Method Kernel Matrix Kernel Principal Component Analysis True Alignment Machine Learn Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Lei Jia
    • 1
  • Shizhong Liao
    • 1
  1. 1.School of Computer Science and Technology, Institute of Knowledge Science and EngineeringTianjin UniversityTianjinP. R. China

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