To overcome some of the challenges encountered in constructing a successful eigenmap of the genetic ancestry, we propose a spectral graph approach. These methods are more flexible than PCA and allow for the different ways of modeling structure and similarities in data. Our alternative approach utilizes a spectral embedding derived from the so-called normalized Laplacian of a graph. We proceed by making the connection between PCA, multidimensional scaling (MDS) and spectral graph theory. We conclude with a presentation of the new algorithm, which is illustrated via an analysis of the POPRES data [Nelson et al., 2008].
