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One-Dimensional Kohonen's Lvq Nets for Multidimensional Patterns Recognition

Skubalska-Rafajłowicz E.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 4

767-778

A new neural network based pattern recognition algorithm is proposed. The method consists in preprocessing the multidimensional data, using a space-filling curve based transformation into the unit interval, and employing Kohonen's vector quantization algorithms (of SOM and LVQ types) in one dimension. The space-filling based transformation preserves the theoretical Bayes risk. Experiments show that such an approach can produce good or even better error rates than the classical LVQ performed in a multidimensional space.

Searching for optimal experimental designs using space-filling curves

Skubalska-Rafajłowicz E., Rafajłowicz E.

Applied Mathematics and Computer Science

1998

Vol. 8, no 3

647-656

A new approach to the standard problem of searching for optimal experimental designs is considered. It consists in replacing a multidimensional search for global maxima by a one-dimensional global search. The points found in this way are then transformed to the multivariate design domain by using a space-filling curve. It is shown that this approach leads to the optimal design, provided that the one-dimensional global search is reliable. An additional advantage of the proposed approach is the possibility of visualization of the model variance surface. The results are presented for the D-optimality criterion, but their extension to other criteria is not difficult.