Alloco 2007 looked at random locations of single nucleotide polymorphisms(SNPs) and found that, using random SNPs, you still get very good correspondence between self-identification and best fit genetic cluster. Using as few as 100 randomly selected SNPs, they found a roughly 97% correspondence between self-reported ancestry and best-fit genetic cluster.
https://pubmed.ncbi.nlm.nih.gov/17349058/