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.
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