Generalized principal curves are capable of representing complex
data structures as they may have branching points or may consist of
disconnected parts. For their construction using an unsupervised learning
algorithm the templates need to be structurally adaptive. The present
algorithm meets this goal by a combination of a competitive Hebbian
learning scheme and a self-organizing map algorithm. Whereas the Hebbian
scheme captures the main topological features of the data, in the
map the neighborhood widths are automatically adjusted in order to suppress
the noisy dimensions. It is noteworthy that the procedure which is
natural in prestructured Kohonen nets could be carried over to a neural
gas algorithm which does not use an initial connectivity. The principal
curve is then given by an averaging procedure over the critical
uctuations of the map exploiting noise-induced phase transitions in the neural
gas
