Laplacian Eigenfunctions Learn Population Structure

• Published in: PloS one Vol. 4; no. 12; p. e7928
• Main Authors: Zhang, Jun, Niyogi, Partha, McPeek, Mary Sara
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.12.2009; Public Library of Science (PLoS)
• Subjects: Analysis; Animals; Birds; Clustering; Computer Simulation; Databases, Genetic; Ecology/Global Change Ecology; Eigenvectors; Euclidean space; Evolutionary Biology/Evolutionary Ecology; Genetic diversity; Genetics; Genetics and Genomics/Population Genetics; Genome-wide association studies; Genomes; Genomics; Genotype & phenotype; Graph theory; Methods; Migration; Outliers (statistics); Passeriformes - genetics; Population Dynamics; Population genetics; Population structure; Principal Component Analysis; Principal components analysis; Rheumatoid arthritis; Studies; United States > US; Illinois; Chicago Illinois
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0007928

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.