The choice of weight matrix W is also open for further investigation. We selected a simple kernel derived from the traditional kernel employed in PCA analysis; however any matrix that measures the non-negative genetic similarity between pairs of individuals is a candidate. A natural choice with roots in both genetics [Purcell et al., 2007] and spectral graph theory is based on IBS sharing. For individuals i and j, let sij be the fraction of alleles shared by the pair identical by state across the panel of SNPs. Define the corresponding weight as wij = exp{−(1 − sij)/ε}. In this formulation ε is a tuning parameter. Preliminary investigation suggests this kernel has good properties, but further study is required to develop a data-dependent choice of the tuning parameter.
