Laplacian eigenfunctions learn population structure.

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 correc...

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Autores principales:	Jun Zhang, Partha Niyogi, Mary Sara McPeek
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2009
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/236e0ddf8d7c493dbbdd105857e12881
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id	oai:doaj.org-article:236e0ddf8d7c493dbbdd105857e12881
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spelling	oai:doaj.org-article:236e0ddf8d7c493dbbdd105857e128812021-11-25T06:27:42ZLaplacian eigenfunctions learn population structure.1932-620310.1371/journal.pone.0007928https://doaj.org/article/236e0ddf8d7c493dbbdd105857e128812009-12-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/19956572/?tool=EBIhttps://doaj.org/toc/1932-6203Principal 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.Jun ZhangPartha NiyogiMary Sara McPeekPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 4, Iss 12, p e7928 (2009)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jun Zhang Partha Niyogi Mary Sara McPeek Laplacian eigenfunctions learn population structure.
description	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.
format	article
author	Jun Zhang Partha Niyogi Mary Sara McPeek
author_facet	Jun Zhang Partha Niyogi Mary Sara McPeek
author_sort	Jun Zhang
title	Laplacian eigenfunctions learn population structure.
title_short	Laplacian eigenfunctions learn population structure.
title_full	Laplacian eigenfunctions learn population structure.
title_fullStr	Laplacian eigenfunctions learn population structure.
title_full_unstemmed	Laplacian eigenfunctions learn population structure.
title_sort	laplacian eigenfunctions learn population structure.
publisher	Public Library of Science (PLoS)
publishDate	2009
url	https://doaj.org/article/236e0ddf8d7c493dbbdd105857e12881
work_keys_str_mv	AT junzhang laplacianeigenfunctionslearnpopulationstructure AT parthaniyogi laplacianeigenfunctionslearnpopulationstructure AT marysaramcpeek laplacianeigenfunctionslearnpopulationstructure
_version_	1718413668534714368

Laplacian eigenfunctions learn population structure.

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