Are clusters in social sciences globular? Many clustering algorithms require globular (gaussian) clusters. Main example is k-means. If clusters are not globular, these methods can bring wrong results.
In social sciences, data is often clustered by these algorithms (market segmentation is very common example). My question then is whether there are some reasons why we should regard clusters from social surveys as globular (and therefore appropriate for methods like k-means).
An example of social data that could be clustered is mentioned in my previous question. I asked my students to rate selected interest (1-5 scale) and the task then could be to cluster students according to similar interests.
 A: Technically, the clusters in k-means are not globular, but Voronoi cells. It's repeated over and over in books; and indeed there are good reasons why k-means works best when the clusters are spherical and of the same extend.
But: does the clustering actually need to be perfect?
In many use cases, there is no such thing as a "correct" clustering. Most often anything better than random will do.
k-means is then very convenient, because it not only partitions your data into a guaranteed low number of clusters (i.e. k) much better than random. But also these clusters are convex (i.e. of relatively simple shape), exhaustive (all objects are clustered, not "outliers" remain), don't overlap (more advanced techniques may produce overlapping clusters or hierarchies of clusters) and - which probably is most important to many users - are represented by a simple, data-like representative: the cluster mean.
So if you just want to have a heuristic to reduce your data set to k representative objects, k-means is a really good heuristic.
