The distance on this grid is used to determine how strongly a unit is adapted when the unit is the winner.
The distance measure is the -norm (a.k.a. ``Manhattan distance''):
Ritter et al. (1991) propose to use the following function to
define the relative strength of adaptation for an arbitrary unit r in the
network (given that s is the winner):
Thereby, the standard deviation of the Gaussian is varied according
for a suitable initial value and a final value . The complete self-organizing feature map algorithm is the following:
Initialize the connection set to form a rectangular grid.
Initialize the time parameter t:
Figure 6.1 shows some stages of a simulation for a simple ring-shaped data distribution. Figure 6.2 displays the final results after 40000 adaptation steps for three other distribution. The parameters were and .
Figure 6.1: Self-organizing feature map simulation sequence for a ring-shaped uniform probability distribution. a) Initial state. b-f) Intermediate states. g) Final state. h) Voronoi tessellation corresponding to the final state. Large adaptation rates in the beginning as well as a large neighborhood range cause strong initial adaptations which decrease towards the end.
Figure: Self-organizing feature map simulation results after 40000 input signals for three different probability distributions (described in the caption of figure 4.4).