Rather than using traditional PCA, we utilize a variant of this approach that arises from spectral graph theory [12]. The basic idea is to represent the population as a weighted graph, where the weights reflect the degree of similarity between pairs of subjects. As with PCA, the graph is then embedded to a lower dimensional space using the top eigenvectors of a function of the weight matrix. Lee et al. [12] show that the spectral graph analysis (SGA) leads to more meaningful clusters than ancestry estimated via PCA. Eigenvectors calculated based upon PCA are strongly affected by uneven sampling of populations [32]. While somewhat susceptible to this bias, the SGA is more robust to cluster size [33]. Moreover, SGA also identifies eigenvectors that successfully separate the data into homogeneous clusters that frequently correspond to demographic labels [12].
