On a Connection between Kernel PCA and Metric Multidimensional Scaling

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 ‖x − y‖. 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.
Original languageEnglish
Pages (from-to)11-19
Number of pages9
JournalMachine Learning
Issue number1-3
Publication statusPublished - Jan 2002

Keywords / Materials (for Non-textual outputs)

  • metric multidimensional scaling
  • MDS
  • kernel PCA
  • eigenproblem


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