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 o f 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 lead s to a metric MDS algorithm where the desired configuration of points is fo und via the solution of an eigenproblem rather than through the iterative o ptimization of the stress objective function. The question of kernel choice is also discussed.