A Kernel Approach to Metric Multidimensional Scaling

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The solution for the parameters of a nonlinear mapping in a metric multidimensional scaling by transformation, in which a stress criterion is optimised, satisfies a nonlinear eigenvector equation, which may be solved iteratively. This can be cast in a kernel-based framework in which the configuration of training samples in the transformation space may be found iteratively by successive linear projections, without the need for gradient calculations. A new data sample can be projected using knowledge of the kernel and the final configuration of data points.