I have a a data set containing of non-negative integer data for N subjects. In other words, each subject is represented by a vector of non negative integers (the vector length may vary from subject to subject, but is typically ~ 1000) and there are N such subjects. It is believed (hypothesized) that the distributions of the non negative values vary from subject to subject and the distributions are significantly different across an unknown number of groups (clusters) of subjects. My goal is to discover the hidden clusters and to learn the histogram bins that best distinguish the distributions across the clusters.
This seems to me to be a general problem that may have been well studied and solved in several fields. I'd appreciate if people could point me to relevant literature that shows how people have formulated and solved this problem. Thanks!