  Results of neural network learning are always subject to some variability,
due to the sensitivity to initial conditions, to convergence to local minima,
and, sometimes more dramatically, to sampling variability. This paper presents
a set of tools designed to assess the reliability of the results of
Self-Organizing Maps (SOM), i.e. to test on a statistical basis the confidence
we can have on the result of a specific SOM. The tools concern the quantization
error in a SOM, and the neighborhood relations (both at the level of a specific
pair of observations and globally on the map). As a by-product, these measures
also allow to assess the adequacy of the number of units chosen in a map. The
tools may also be used to measure objectively how the SOM are less sensitive to
non-linear optimization problems (local minima, convergence, etc.) than other
neural network models.
