On a connection between kernel PCA and metric multidimensional scaling. (English) Zbl 1052.68118
Summary: We show that the kernel PCA algorithm of B. Schölkopf, A. Smola, and K. R. Müller [Neural Comput. 10, 1299–1319 (1998)] 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.
MSC:
68T05 | Learning and adaptive systems in artificial intelligence |