On a Connection between Kernel PCA and Metric Multidimensional Scaling

Authors:
Christopher K. I. Williams
Affiliations:
Division of Informatics, The University of Edinburgh, 5 Forrest Hill, Edinburgh EH1 2QL, UK. c.k.i.williams@ed.ac.uk
Venue:
Machine Learning
Year:
2002

Citing 3
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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 ‖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.