Chapter

Uncertainty in Geometric Computations

Volume 704 of the series The Springer International Series in Engineering and Computer Science pp 131-141

B

  • T. PoggioAffiliated withMcGovern Institute and Center for Biological and Computational Learning Center for Genome Research, Whitehead Institute Massachusetts Institute of Technology
  • , S. MukherjeeAffiliated withMcGovern Institute and Center for Biological and Computational Learning Center for Genome Research, Whitehead Institute Massachusetts Institute of Technology
  • , R. RifkinAffiliated withMcGovern Institute and Center for Biological and Computational Learning Center for Genome Research, Whitehead Institute Massachusetts Institute of Technology
  • , A. RaklinAffiliated withMcGovern Institute and Center for Biological and Computational Learning Center for Genome Research, Whitehead Institute Massachusetts Institute of Technology
  • , A. VerriAffiliated withINFM - DISI, Universita di Genova

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Abstract

In this chapter we summarize density properties of Reproducing Kernel Hilbert Spaces induced by different classes of kernels. They are important to characterize the power of the associated hypothesis spaces. In the process we characterize the role of b, which is the constant in the standard form of the solution provided by the Support Vector Machine technique \(f(x) = \sum\nolimits_{i = 1}^\ell {\alpha _i } K\left( {x,\:x_i } \right) + b,\) which is a special case of Regularization Machines.

Keywords

RKHS regularization density