MDS was originally developed to visualize high-dimensional data. The downside of using PCA for a quantitative analysis is that the associated metric is highly sensitive to outliers, which diminishes its ability to capture the major dimensions of ancestry. Our goal in this paper is to develop a spectral embedding scheme that is less sensitive to outliers and that is better, in many settings, at clustering observations similar in ancestry. We note that the choice of eigenmap is not unique: Any positive semi-definite matrix H defines a low-dimensional embedding and associated distance metric according to Equations 1 and 2. Hence, we will use the general framework of MDS and PC maps but introduce a different kernel for improved performance. Below we give some motivation for the modified kernel and describe its main properties from the point of view of spectral graph theory and spectral clustering.
