This model stems from Kohonen (1982) and builds upon earlier work of Willshaw and von der Malsburg (1976). The model is similar to the (much later developed)

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
to

for a suitable initial value and a final value .
The complete *self-organizing feature map* algorithm is the following:

- Initialize the set to contain units

with reference vectors chosen randomly according to .Initialize the connection set to form a rectangular grid.

Initialize the time parameter

*t*:

- Generate at random an input signal according to .
- Determine the winner :

- Adapt each unit
*r*according to

whereby

and

- Increase the time parameter
*t*:

- If continue with step 2.

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).

Sat Apr 5 18:17:58 MET DST 1997