So let me get this right? they got a bunch of {1,2,3,4}^2 points and they applied k-means one (1) time with the standard l_2 metric, found 4 random ass centroids, published it, and now you're calling into question their methodology?
edit: The problem with k means is that it converges to local minima, so depending on the starting point (in this case the 4 'typologies') each run gives different results. So any typologies found are gonna be interpreted with the ideological slant of the authors. Also a heat map would have been better for representing the data: it's on a 2d grid.
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