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Figure 2 | The Journal of Mathematical Neuroscience

Figure 2

From: Stability analysis of a neural field self-organizing map

Figure 2

Two-dimensional SOM performance in the stable case. (A) Feed-forward weights (white discs) as they have been organized 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 is aligned around the red line indicates that the topographic map is well organized, as confirmed by a good index performance \(\mathcal{P}=0.01\). (C) Distortion indicates that the loss of information during the learning process decreases, and the mapping of the input data to a two-dimensional self-organizing map respects the structure of the neighborhoods. (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 fulfilled, and therefore the weights converge to an equilibrium giving rise to a well-formed topographic map

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