Local PSOMs and Chebyshev PSOMs -Improving the Parametrised Self-Organizing Maps
Jörg Andreas Walter, Helge Joachim Ritter · 1995
We report on two new improvements for the "Parameterised Self-Organizing Map" (PSOM). Both achieve a significant increase in mapping accuracy and computational efficiency. For a growing number of training points the use of higher order polynomials to construct the PSOM "mapping manifold" in [7] can suffer from the increasing tendency to oscillate between the support points. We propose here to confine the algorithm to a subset of the training knots, resulting in what we call the "local-PSOM" algorithm. This allows to avoid the use of high-degree polynomials without sacrificing accuracy. At the same time, the new approach offers a significant saving in required computations. A second way to improve the mapping preciseness makes use of the superior approximation properties of Chebyshev polynomials for the PSOM mapping manifold. The benefits of the two new approaches are demonstrated with two benchmark problems: (i) approximating a Gaussian bell function and (ii) learning of the (forward a...