While often successful in describing the structure in data, PCA has some notable weaknesses, as illustrated in our exploration of POPRES [Nelson et al., 2008]. Part of the challenge faced by PCA from POPRES is the disproportionate representation of individuals of European ancestry combined with individuals from multiple continents. To obtain results more in keeping with knowledge about population demographics, Nelson et al. [2008] supplement POPRES with 207 unrelated subjects from the four core HapMap samples. In addition, to overcome problems due to the dominant number of samples of European descent, they remove 889 and 175 individuals from the Swiss and the UK samples, respectively. Because PCA is sensitive to outliers, it performs a careful search for outliers, exploring various subsets of the data iteratively. After making these adjustments they obtain an excellent description of the ancestry of those individuals in the remaining sample. From this analysis we see that with careful handling, PCA successfully reveals ancestry. Likewise, when analysis is restricted to individuals of European ancestry, PCA again works very well [Novembre et al., 2008]. Less nuanced application of the approach leads to much less useful insights as we showed above.
