A Kernel Approach to Metric Multidimensional Scaling
- Cite this paper as:
- Webb A. (2002) A Kernel Approach to Metric Multidimensional Scaling. In: Caelli T., Amin A., Duin R.P.W., de Ridder D., Kamel M. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2002. Lecture Notes in Computer Science, vol 2396. Springer, Berlin, Heidelberg
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.
Keywordsmultidimensional scaling kernel representation nonlinear feature extraction
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