Why SOM shows the best accuracy at 11x11? I have started working on Human Action recognition using depth images. I found this article. 
In the experiment section, they have told that they have experimented SOM of different size and for the SOM of size 11x11 they have achieved high accuracy. 
What would be the possible reason(s) in getting high accuracy at 11x11?  
 A: I feel that it is difficult to conclude from that paper that 11x11 is better than the other sizes. There's no reporting of p-values that could show that the differences are significant, so it could be possible that it's anomalous. I feel that what the paper shows is that SOM is a reasonable approach to learning actions (assuming there are quite a lot of actions that comprise an action sequence, and the neurons are learning those actions). 
I'm not really clear on why SOM would be the best choice for this task. If they are interested in improving classification performance, they should use a supervised tuning technique such as LVQ to better separate the classes. For example, we see that "walk" and "run" contributed a lot of the confusion. By using LVQ, the classifier can use the class information to help to disambiguate the similar classes. It seems intuitive that SOM will place frames showing "run" and "walk" close together on the map because it does not take into account that they are from different activities, but this will cause decreased performance.
One difficulty I see in the paper is the small size of the training set. There are only 90 videos. To know that the SOM is really learning actions, I would look at the patterns that are encoded by each neuron. Possibly there is overtraining, that the SOM is learning something instead of actions. Do the representations at each neuron really look like actions? The research also used a fixed 2000 iterations for every map, but I believe that Kohonen suggests (as a rule of thumb) to use a number of iterations that depends on the size of the map. It could be that the worse performance for 12x12 reflects undertraining, so to improve it, just increase the number of iterations. On the other hand, did the researchers use batch training or sequential? If it's batch training, then it seems that the number of iterations may have been much higher than necessary; sequential, much lower. 
Anyway, as we can see from this followup paper from the same authors, they have identified that recognition accuracy and map size does correspond with the number of iterations. I've read that it's sometimes possible to see further improvement by stopping the SOM early and then applying a smoothing operation. http://link.springer.com/article/10.1007/s00138-014-0639-9
Kohonen covers many of the ways to select the SOM parameters in the book, MATLAB Implementations and Applications of the Self-Organizing Map.
