Figure 3

Two-dimensional SOM performance in the unstable case. (A) Feed-forward weights (white discs) as they have failed to organize into a topographic map after 7000 epochs. The input in this case is a two-dimensional rectangular uniform distribution (black dots). (B) \(\delta x - \delta y\) representation (black cloud), mean of δx (red line), and the linear regression of the \(\delta x - \delta y\) representation (magenta line). The fact that the cloud looks diffused indicates that the topographic map is not well organized, as confirmed by a high value of \(\mathcal{P}=0.41\). (C) Distortion indicates that the loss of information during the learning process never drops (converges to an equilibrium) instead it oscillates. This means that the mapping of the input data to a two-dimensional map has failed. (D) Temporal evolution of norm-2 of feed-forward weights of three neurons placed at \(r^{\ast }=(0.25, 0.25)\), \((0.1, 0.225)\), and \((0.35, 0.075)\)). Condition (15) is violated, and accordingly the weights do not converge to an equilibrium