  Mapping human genetic variation is fundamentally interesting in fields such
as anthropology and forensic inference. At the same time patterns of genetic
diversity confound efforts to determine the genetic basis of complex disease.
Due to technological advances it is now possible to measure hundreds of
thousands of genetic variants per individual across the genome. Principal
component analysis (PCA) is routinely used to summarize the genetic similarity
between subjects. The eigenvectors are interpreted as dimensions of ancestry.
We build on this idea using a spectral graph approach. In the process we draw
on connections between multidimensional scaling and spectral kernel methods.
Our approach, based on a spectral embedding derived from the normalized
Laplacian of a graph, can produce more meaningful delineation of ancestry than
by using PCA. The method is stable to outliers and can more easily incorporate
different similarity measures of genetic data than PCA. We illustrate a new
algorithm for genetic clustering and association analysis on a large,
genetically heterogeneous sample.
