Can someone describe how the SparCC corrected correlation measure works?

Question

[jolespin]

I've been reading this paper. The first part of the algorithm makes perfect sense but I'm not sure how the Dirchlet Process plays a role and why the iterative steps are needed?

http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002687

This is the part I don't understand: