How can I Identify the stable state of a self-organizing map during training? I need this to control my Iterations (i.e to continue or stop training when stable). I have tried looking at percentage change of topological error and also mean quantization error but these two keep changing and never gets to a stable state.
You're using the batch map algorithm, hopefully, which has more robust convergence. Have you referred to Kohonen's recent MATLAB book? It touches on this very issue in "4.2 Stable state of the learning process" and also notes a number of methods for achieving convergence in Chapter 5, such as using two training phases (coarse and fine).
Also, there is a trick that can result in a convergence to a stable state.
"... if the neighborhood function is held constant during the last iterations, whatever its width is, and the same input data are applied iteratively, the ordering process will be stabilized (converge) in a finite number of training cycles. So far we have found no exceptions to this observation." Kohonen, T. K. (2014). MATLAB Implementations and Applications of the Self-Organizing Map. http://docs.unigrafia.fi/publications/kohonen_teuvo/