In many settings the proposed spectral graph approach, Spectral-GEM, is more robust and flexible than PCA. It determines eigenvectors that separate the data into meaningful clusters. In contrast, smartpca sometimes finds a large number of significant dimensions. For instance in a study of nearly 6,000 individuals of European ancestry smartpca identified 110 significant dimensions with two dominant axes [Heath et al., 2008]. Spectral-GEM’s embedding is not notably affected by outliers (e.g., Scenario 1 of Results). It can detect fine ancestral structure even in very heterogeneous data (Scenarios 2 and 3 of Results). Finally in a large sample of complicated ancestry, such as Scenario 3, it can successfully delineate the relatively discrete and relatively continuous ancestral components. Axes of ancestry can be used to control for structure following any of the standard epidemiological approaches: regressing out the effects of ancestry [Price et al., 2006]; matching cases and controls of similar ancestry [Luca et al., 2008]; or analyzing the homogeneous clusters using the Cochran-Mantel-Haenszel test. For most situations these approaches are likely to lead to similar results. Successfully finding the hidden structure
