This method (Martinetz and Schulten, 1991; Martinetz, 1993) is usually not used on its own but in conjunction with other methods (see sections 5.3 and 5.4). It is, however, instructive to study

- 1.
- Initialize the set to contain
*N*units

with reference vectors chosen randomly according to .Initialize the connection set , , to the empty set:

- 2.
- Generate at random an input signal according to .
- 3.
- Determine units and such that

and

- 4.
- If a connection between and
does not exist already, create it:

- 5.
- Continue with step 2 unless the maximum number of signals is reached.

**Figure 5.3:** *Competitive Hebbian learning* 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. Obviously, the method is
sensitive to initialization since the initial positions are always
equal to the final positions.

**Figure:** *Competitive Hebbian learning* 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