I read in many places that k-means clustering algorithm does not perform well when dealing with multidimensional binary data (so vectors whose entries are zero or one).

Intuitively, it is pretty easy to understand why: in a 1000 dimensional space, all the points have a similar distance, and k-means is a distance based method.

I am wondering if there is any study/paper that proves exactly this, or where there behavior of k-means in this setting is extensively studied.