Send to

Choose Destination
See comment in PubMed Commons below
PLoS One. 2009 Dec 1;4(12):e7928. doi: 10.1371/journal.pone.0007928.

Laplacian eigenfunctions learn population structure.

Author information

Department of Radiology, The University of Chicago, Chicago, Illinois, United States of America.


Principal components analysis has been used for decades to summarize genetic variation across geographic regions and to infer population migration history. More recently, with the advent of genome-wide association studies of complex traits, it has become a commonly-used tool for detection and correction of confounding due to population structure. However, principal components are generally sensitive to outliers. Recently there has also been concern about its interpretation. Motivated from geometric learning, we describe a method based on spectral graph theory. Regarding each study subject as a node with suitably defined weights for its edges to close neighbors, one can form a weighted graph. We suggest using the spectrum of the associated graph Laplacian operator, namely, Laplacian eigenfunctions, to infer population structure. In simulations and real data on a ring species of birds, Laplacian eigenfunctions reveal more meaningful and less noisy structure of the underlying population, compared with principal components. The proposed approach is simple and computationally fast. It is expected to become a promising and basic method for population genetics and disease association studies.

[Indexed for MEDLINE]
Free PMC Article
PubMed Commons home

PubMed Commons

How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for Public Library of Science Icon for PubMed Central
    Loading ...
    Support Center