A Method to Construct the Mapping to the Feature Space for the Dot Product Kernels

  • Degang Chen
  • Qiang He
  • Chunru Dong
  • Xizhao Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3930)


Dot product kernels are a class of important kernel in the theory of support vector machine. This paper develops a method to construct the mapping that map the original data set into the high dimensional feature space, on which the inner product is defined by a dot product kernel. Our method can also be applied to the Gaussian kernels. Via this mapping, the structure of features in the feature space is easy to be observed, and the linear separability of data sets in the feature space is studied. We obtain that any two finite sets of data with empty overlap in the original space will become linearly separable in an infinite dimensional feature space, and a sufficient and necessary condition is also developed for two infinite sets of data in the original data space being linearly separable in the feature space, this condition can be applied to examine the existences and uniqueness of the hyperplane which can separate all the possible inputs correctly.


Support Vector Machine Feature Space Gaussian Kernel Reproduce Kernel Hilbert Space Polynomial Kernel 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Degang Chen
    • 1
  • Qiang He
    • 2
  • Chunru Dong
    • 2
  • Xizhao Wang
    • 2
  1. 1.Department of Mathematics and PhysicsNorth China Electric Power UniversityBeijingP.R. China
  2. 2.Department of Mathematics and Computer ScienceHebei UniversityBaodingP.R. China

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