There are specific research for de-anonymization attempt for CoinJoin and mixing service, even though i couldn't find any. Besides, there are few popular chain analysis services such as https://www.chainalysis.com/.
What will be the impact of this analysis with the rise of LN, sidechains and other anonymity solutions?
Maybe more people will have privacy/anonymity (even though Bitcoin is only pseudonymous) concern and they might support on-chain anonymity & scaling solutions such as Schnorr Siganture and MAST.