The base sample, consisting of subject i =1, ...,n corresponding to the centered and scaled allele count vectors x1, ...,xn, defines X and determines the eigenmap. To project a new individual with scaled allele count vector z onto this basis we use the Nystrom approximation. The weight associated with an edge between z and x is w(z,x)={ztxifztx≥0,0otherwise.} The degree associated with z is d(z)=∑i=1nw(z,xi)+w(z,z). Finally, L(z,xi)=[d(z)di]−1∕2w(z,xi). The eigenvector coordinates for dimensions k =1, ..., S for z are ∇uk(z)=λk−1∑i=1nL(z,xi)uk(xi). Using these eigenvector coordinates we can map new individuals into an existing eigenmap using (1).
