A new method of generalizing Sammon mapping with application to algorithm speed-up

¹ Pattern Recognition Group, Department of Applied Physics, Faculty of Applied Sciences,
Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands
² Shell International E&P, PO Box 60, 2280 AB Rijswijk, The Netherlands

Elzbieta P"ekalska¹, Dick de Ridder¹, Robert P.W. Duin¹, Martin A. Kraaijveld²

Key words and phrases: Sammon mapping, multidimensional scaling, triangulation, neural networks, distance mapping

Abstract:

Sammon mapping comes from the area of multidimensional scaling and is an important pattern recognition tool. It is a nonlinear projection method, which reveals the structure present in data. Sammon mapping has two disadvantages. Firstly, it lacks generalization, which means that new points cannot be added to the obtained map without recalculating it. Secondly, because it operates on all interpoint distances, the complexity of finding the mapping is very high. The solution to the first problem is used in improving the speed of the algorithm.

To save computation time without losing the mapping quality, we investigate three possible speed-ups. They are hybrid methods being a combination of Sammon mapping, based on a subset of points, and respectively: triangulation, neural network and our proposal, distance mapping. These approaches are verified by some experiments, showing that distance mapping performs the best.