Suppose that we train a self-organising map (SOM) with a given dataset. Would it make sense to cluster the neurons of the SOM instead of the original datapoints? This doubt came to me after reading this paper, in which the following is stated:
The most important benefit of this procedure is that computational load decreases considerably, making it possible to cluster large data sets and to consider several different preprocessing strategies in a limited time. Naturally, the approach is valid only if the clusters found using the SOM are similar to those of the original data.
In this answer it is clearly stated that SOMs don't include clustering, but some clustering procedure can be made on the SOM after it has been trained. I thought that this meant the clustering was done on the neurons of the SOM, which are in some sense a mapping of the original data, but I'm not sure about this. So, what I want to know is:
Yes, the usual approach seems to be either hierarchical or k-means (you'll need to dig this up how it was originally done - as seen in the paper you linked, many variants including two-level approaches have been explored later) on the neurons. If you consider SOMs to be a quantization and projection technique, all of these approaches are valid to use.
It's cheaper because they are just 2 dimensional, Euclidean, and much fewer points. So that is well in line with the source that you have.
Note that a SOM neuron may be empty, it it is inbetween of two extremely well separated clusters.