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Can someone describe how the SparCC corrected correlation measure works?

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?

enter image description here

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

This is the part I don't understand: enter image description here

rna-seq chip-seq genome microbiome metagenomics
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