Neuron weight dynamics in the SOM and self-organized criticality

The self-organizing map (SOM) was developed as a heuristic model of a global self-organizing process. Since then it has been used in different applications as an unsupervised learning algorithm for large scale data processing. Part of the reason for its widespread use is its robustness and ability to form ordered maps in diverse situations. The dynamics of the SOM are compared to those of a system operating in self-organized criticality (SOC). An SOC system should exhibit a robust convergence to a critical state independent of the initial conditions, and the dynamics of the system should follow power laws, with the formation of self-similar structures. It is shown that instead of considering the SOM as a learning algorithm but rather as a nonlinear dynamical system, driven by perturbations (i.e. the input to be learned), which converges to an attractor (i.e. the organized configuration), the SOM can be seen as a system operating at SOC. This approach could lead to an understanding of the organized configuration in the SOM.