On a connection between kernel PCA and metric multidimensional scaling

In this note we show that the kernel PCA algorithm of Scholkopf, Smola, and Muller (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 parallel tox - y parallel to. 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.