Visualising error surfaces for adaptive filters and other purposes

Modern neural and adaptive systems often have complicated error performance surfaces with many local extrema. Visualising and understanding these surfaces is critical to effective tuning of these systems but almost all visualisation methods are confined to two dimensions. Here we show how to use a morphological scale-space transform to convert these multi-dimensional complex error surfaces into two-dimensional trees where the leaf nodes are local minima and other nodes represent decision points such as saddle points and points of inflection