Machine Learning

, Volume 46, Issue 1, pp 11–19

On a Connection between Kernel PCA and Metric Multidimensional Scaling

  • Christopher K.I. Williams
Article

DOI: 10.1023/A:1012485807823

Cite this article as:
Williams, C.K. Machine Learning (2002) 46: 11. doi:10.1023/A:1012485807823

Abstract

In this note we show that the kernel PCA algorithm of Schölkopf, Smola, and Müller (Neural Computation, 10, 1299–1319.) can be interpreted as a form of metric multidimensional scaling (MDS) when the kernel function k(x, y) is isotropic, i.e. it depends only on ‖xy‖. This leads to a metric MDS algorithm where the desired configuration of points is found via the solution of an eigenproblem rather than through the iterative optimization of the stress objective function. The question of kernel choice is also discussed.

metric multidimensional scaling MDS kernel PCA eigenproblem 
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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Christopher K.I. Williams
    • 1
  1. 1.Division of InformaticsThe University of EdinburghEdinburghUK

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