Discovering genetic ancestry using spectral graph theory
Open accessAbstract
As one approach to uncovering the genetic underpinnings of complex disease, individuals are measured at a large number of genetic variants (usually SNPs) across the genome and these SNP genotypes are assessed for association with disease status. We propose a new statistical method called Spectral‐GEM for the analysis of genome‐wide association studies; the goal of Spectral‐GEM is to quantify the ancestry of the sample from such genotypic data. Ignoring structure due to differential ancestry can lead to an excess of spurious findings and reduce power. Ancestry is commonly estimated using the eigenvectors derived from principal component analysis (PCA). To develop an alternative to PCA we draw on connections between multidimensional scaling and spectral graph theory. 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. Often the results from Spectral‐GEM are straightforward to interpret and therefore useful in association analysis. We illustrate the new algorithm with an analysis of the POPRES data [Nelson et al., 2008]. Genet. Epidemiol. 34:51–59, 2010. © 2009 Wiley‐Liss, Inc.
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The software SpectralGEM estimated five significant dimensions of ancestry.
“The software used was SpectralGEM (48), which estimated five significant dimensions of ancestry (Supplementary Material, Fig. S1).”
From A genome-wide scan for common alleles affecting risk for autism (2010) · cites this paper as [48]
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“PCA [4], spectral graph theory [5], structured association analysis [6,7] and genomic control [8] can detect underlying population substructure with SNP data.”
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“Compared with SA, PCA is implemented simply in GWAS [16-19], where PCA selects top components to capture the broad relatedness across individuals, and these principal components are fitted as covariates correcting the inflation due to stratification [20, 21].”
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“While a variety of statistical methods exist for determining population structure from genetic data [Li and Yu, 2008; Lee et al., 2009; Li et al., 2010], the most common approach for inferring ancestry is to conduct a principal component analysis (PCA) of genome-wide SNP data [Chen et al.”
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“Finally, because our current study focuses on unrelated samples and the PC-based adjustment for population stratification, it would be interesting to investigate the same issues with other adjustment methods [e.g., Engelhardt and Stephens, 2010; Guan et al., 2009; Lee et al., 2010; Pritchard et al., 2000; Zhu et al.,…”
Roberts, G. H. L., Paul, S., Yorgov, D., Santorico, S. A., & Spritz, R. A. (2019) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2019.06.013 · Cited by 39 · see citing works
“Genetic sub-structure for each of the three GWAS cohorts was determined by Spectral-GEM.14 We used best-guess genotypes if the genotype posterior probability wasR0.”
MethodAchkar, J.-P., Klei, L., de Bakker, P. I. W., Bellone, G., Rebert, N. A., Scott, R. J., Lu, Y., Regueiro, M. D., Brzezinski, A., Kamboh, M. I., et al. (2011) · Genes and Immunity · doi:10.1038/gene.2011.79 · Cited by 37 · see citing works
Self-citationA spectral graph approach to discovering genetic ancestry
Lee, A. B., Luca, D., & Roeder, K. (2010) · The Annals of Applied Statistics · doi:10.1214/09-aoas281 · Cited by 34 · see citing works
Self-citationPediatric to Adult Shift in Vitiligo Onset Suggests Altered Environmental Triggering
Jin, Y., Santorico, S. A., & Spritz, R. A. (2019) · Journal of Investigative Dermatology · doi:10.1016/j.jid.2019.06.131 · Cited by 32 · see citing works
Distributed Training of Graph Convolutional Networks
Scardapane, S., Spinelli, I., & Lorenzo, P. D. (2020) · IEEE Transactions on Signal and Information Processing over Networks · doi:10.1109/tsipn.2020.3046237 · Cited by 31 · see citing works
“NOWADAYS, graph-based data are pervasive, with applications ranging from social networks [1] to epidemiology [2], recommender systems [3], cyber-security [4], sensor networks [5], natural language processing [6], genomics [7], and many more.”
BackgroundA Genome Wide Association Study for Longevity in Cattle
Mészáros, G., Eaglen, S., Waldmann, P., & Sölkner, J. (2014) · Open Journal of Genetics · doi:10.4236/ojgen.2014.41007 · Cited by 31 · see citing works
“Population stratification due to differences in ancestry was taken into account using 103 eigenvectors computed by the Gem Tools function [22], which relies on eigenmaps constructed by spectral clustering techniques [23], an approach that is closely related to principal component analysis [24].”
MethodKiryluk, K., Bomback, A. S., Cheng, Y.-L., Xu, K. H., Cámara, P. G., Rabadán, R., Sims, P. A., & Barasch, J. M. (2017) · Seminars in Nephrology · doi:10.1016/j.semnephrol.2017.09.006 · Cited by 29 · see citing works
Prediction of biogeographical ancestry from genotype: a comparison of classifiers
Cheung, E. Y. Y., Gahan, M. E., & McNevin, D. B. (2016) · International Journal of Legal Medicine · doi:10.1007/s00414-016-1504-3 · Cited by 30 · see citing works
Enhanced Localization of Genetic Samples through Linkage-Disequilibrium Correction
Baran, Y., Quintela, I., Carracedo, Á., Paşaniuc, B., & Halperin, E. (2013) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2013.04.023 · Cited by 29 · see citing works
Retrospective Binary-Trait Association Test Elucidates Genetic Architecture of Crohn Disease
Jiang, D., Zhong, S., & McPeek, M. S. (2016) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2015.12.012 · Cited by 29 · see citing works
Laplacian Eigenfunctions Learn Population Structure
Zhang, J., Niyogi, P., & McPeek, M. S. (2009) · PLoS ONE · doi:10.1371/journal.pone.0007928 · Cited by 27 · see citing works
“[20] simply take wjk~ ffiffiffiffiffi cjk p if cjkw0, otherwise wjk~0: Generally there is room for different choices of weights which may give close performance, and the optimal weight is worth further investigation.”
BackgroundMethodGenetics in psychiatry: common variant association studies
Buxbaum, J. D., Baron‐Cohen, S., & Devlin, B. (2010) · Molecular Autism · doi:10.1186/2040-2392-1-6 · Cited by 26 · see citing works
“In general, case-control studies should include matching based on ancestry using standard approaches [12-14]; and with the reduced cost of genotyping, this is now an expectation in all well-designed studies.”
Self-citationZhang, Y., Shen, X., & Pan, W. (2013) · Genetic Epidemiology · doi:10.1002/gepi.21764 · Cited by 24 · see citing works
“Lee et al. [2009] proposed a spectral clustering method, called SDR here.”
MethodDetecting individual ancestry in the human genome
Wollstein, A., & Lao, Ó. (2015) · Investigative Genetics · doi:10.1186/s13323-015-0019-x · Cited by 24 · see citing works
“Usually, investigators apply both model-free (for example, PCA or MDS) and model-based methods (for example, ADMIXTURE, FRAPPE, or STRUCTURE) to the same dataset [45,46].”
BackgroundInfluentialFang, H., & Pan, W. (2010) · Genetic Epidemiology · doi:10.1002/gepi.20529 · Cited by 23 · see citing works
Allen, A. S., & Satten, G. A. (2011) · American Journal of Epidemiology · doi:10.1093/aje/kwq406 · Cited by 22 · see citing works
“We found that 3 linear combinations of SNP genotypes were adequate (14) to describe the genome-wide correlations due to the admixture of European and African ancestries in this population (see Web Appendix for additional details).”
BackgroundPattern analysis of genetics and genomics: a survey of the state-of-art
Chaki, J., & Dey, N. (2019) · Multimedia Tools and Applications · doi:10.1007/s11042-019-7181-8 · Cited by 21 · see citing works
Epstein, M. P., Duncan, R., Broadaway, K. A., He, M., Allen, A. S., & Satten, G. A. (2012) · Genetic Epidemiology · doi:10.1002/gepi.21611 · Cited by 21 · see citing works
“, 2006] and also used SpectralGEM to identify significant eigenvectors derived from spectral-graph theory [Lee et al., 2009].”
MethodA Method to Exploit the Structure of Genetic Ancestry Space to Enhance Case-Control Studies
Bodea, C. A., Neale, B. M., Ripke, S., Daly, M. J., Devlin, B., Roeder, K., Barclay, M. L., Peyrin‐Biroulet, L., Chamaillard, M., Colombel, J.-F., et al. (2016) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2016.02.025 · Cited by 20 · see citing works
Self-citationGemTools: A fast and efficient approach to estimating genetic ancestryPreprint
Klei, L., Kent, B. P., Melhem, N., Devlin, B., & Roeder, K. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1104.1162 · Cited by 19 · see citing works
“In GemTools, eigenmaps are constructed using a spectral clustering techniques (Lee et al., 2010), an approach that is closely related to principal component analysis (Price et al., 2006).”
MethodSelf-citationCrossett, A., Kent, B. P., Klei, L., Ringquist, S., Trucco, M., Roeder, K., & Devlin, B. (2010) · Statistics in Medicine · doi:10.1002/sim.4057 · Cited by 15 · see citing works
“Analysis was performed separately for each continent using SpectralGEM.”
BackgroundMethodInfluentialSelf-citationManifold Learning for Human Population Structure Studies
Siu, H., Li, J., & Xiong, M. (2012) · PLoS ONE · doi:10.1371/journal.pone.0029901 · Cited by 16 · see citing works
“More seriously, PCA is sensitive to data noises and missing values [11].”
BackgroundTeyssèdre, S., Elsen, J.-M., & Ricard, A. (2012) · Genetics Selection Evolution · doi:10.1186/1297-9686-44-32 · Cited by 15 · see citing works
“Pca-based approaches ([26], eigenstrat; [51], pca-based logistic regression; [52], lapstruct (which makes use of spectral graph theory to build principal components) were compared in [53] to the genomic control described by Devlin and Roeder [24] and to roadtrips.”
ResultGraphlet Laplacians for topology-function and topology-disease relationships
Windels, S. F. L., Malod‐Dognin, N., & Pržulj, N. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz455 · Cited by 15 · see citing works
“Applications of spectral embedding include visualizing genetic ancestry (Lee et al., 2010) and pseudo-temporal ordering of single-cell RNA-seq profiles (Campbell et al., 2015).”
BackgroundCorrecting for Population Stratification in Genomewide Association Studies
Lin, D. Y., & Zeng, D. (2011) · Journal of the American Statistical Association · doi:10.1198/jasa.2011.tm10294 · Cited by 14 · see citing works
Chen, G. K., Millikan, R. C., John, E. M., Ambrosone, C. B., Bernstein, L., Zheng, W., Hu, J. J., Chanock, S. J., Ziegler, R. G., Bandera, E. V., et al. (2010) · PLoS Genetics · doi:10.1371/journal.pgen.1001096 · Cited by 12 · see citing works
“If there is overlap due to ancestry for cases and controls then tests like the Bourgain test, principal components, multidimensional scaling [22], and genomic matching [23,24] have a much greater likelihood of success than in the previous examples.”
Principal Component Analyses in Anthropological Genetics
Chen, X., Chen, C., & Li, J. (2011) · Advances in Anthropology · doi:10.4236/aa.2011.12002 · Cited by 11 · see citing works
“Related approaches, such as multidimensional scaling (MDS) and genetic matching, have also proven useful (Lee et al., 2010; Luca et al., 2008) and can be carried out using the PLINK software (Purcell et al., 2007).”
MethodAdvances on Methodologies for Genome-wide Association Studies in Plants
Feng, J., Wen, Y.-J., Zhang, J., & ZHANG, Y.-M. (2016) · ACTA AGRONOMICA SINICA · doi:10.3724/sp.j.1006.2016.00945 · Cited by 11 · see citing works
Genetic Analysis of Mitochondrial Ribosomal Proteins and Cognitive Aging in Postmenopausal Women
Mozhui, K., Snively, B. M., Rapp, S. R., Wallace, R. B., Williams, R. W., & Johnson, K. (2017) · Frontiers in Genetics · doi:10.3389/fgene.2017.00127 · Cited by 11 · see citing works
“The GECCO group maintains a standard list of SNPs for genetic ancestry analysis that were selected according to recommendations by Lee et al. (2010).”
MethodLacour, A., Schüller, V., Drichel, D., Herold, C., Jessen, F., Leber, M., Maier, W., Nöthen, M. M., Ramı́rez, A., Vaitsiakhovich, T., et al. (2015) · BMC Bioinformatics · doi:10.1186/s12859-015-0521-4 · Cited by 9 · see citing works
“PCs are widely accepted and employed, but may also have drawbacks: the decomposition is sensitive to outlying individuals [23,24] and genome-wide data are required.”
BackgroundStatistical Association Mapping of Population-Structured Genetic Data
Najafi, A., Janghorbani, S., Motahari, S. A., & Fatemizadeh, E. (2017) · IEEE Transactions on Computational Biology and Bioinformatics · doi:10.1109/tcbb.2017.2786239 · Cited by 9 · see citing works
Network-adjusted covariates for community detection
Hu, Y. H., & Wang, W. (2024) · Biometrika · doi:10.1093/biomet/asae011 · Cited by 8 · see citing works
“To examine the effects using only the covariate matrix, the last method is the spectral clustering method on XX ′ in [29].”
MethodLao, Ó., Liu, F., Wollstein, A., & Kayser, M. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003480 · Cited by 9 · see citing works
“The third analysis was performed with the clusterGem algorithm implemented in the GemTools package which uses spectral graph theory to propose clusters of individuals [52].”
MethodSNPs in CAST are associated with Parkinson disease: A confirmation study
Allen, A. S., & Satten, G. A. (2010) · American Journal of Medical Genetics Part B Neuropsychiatric Genetics · doi:10.1002/ajmg.b.31061 · Cited by 8 · see citing works
Zhang, A. J. (2010) · PLoS ONE · doi:10.1371/journal.pone.0013734 · Cited by 11 · see citing works
“Further comprehensive comparison of PCA and Laplacian eigenfunctions is available in the literature [16,18,23].”
BackgroundMethodJiang, D., & Wang, M. (2018) · Biostatistics & Epidemiology · doi:10.1080/24709360.2018.1529346 · Cited by 6 · see citing works
“Examples of other methods in this category include a model-based clustering tool for detecting population structure [96], methods related to PCA [15,144,150], and various other methods [4,59,143].”
MethodZhang, L.-X., Yan, H., Liu, Y., Xu, J., Song, J., & Yu, D. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.1c01403 · Cited by 6 · see citing works
Hereditary variants of unknown significance in African American women with breast cancer
McDonald, J. T., & Ricks‐Santi, L. J. (2022) · PLoS ONE · doi:10.1371/journal.pone.0273835 · Cited by 6 · see citing works
“PCA was performed on the study population and 26 populations from the 1000 Genomes project by plotting the principle eigenvalue components to visualize clustering of similar ancestries [30, 31].”
MethodIterative PCA for population structure analysis
Limpiti, T., Intarapanich, A., Assawamakin, A., Wangkumhang, P., & Tongsima, S. (2011) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2011.5946474 · Cited by 4 · see citing works
“We are inspired to develop EigenDev from the Eigenvalue Grads heuristic in [6] and the EigenGap method in [7].”
MethodStatistical Methods for studying Genetic Variation in Populations
Shringarpure, S. (2012) · doi:10.1184/r1/6723164 · Cited by 4 · see citing works
Stepanyan, I. V., & Lednev, M. Y. (2022) · Symmetry · doi:10.3390/sym14050844 · Cited by 4 · see citing works
“In [2], the authors used connections between multidimensional scaling and spectral graph theory to propose an alternative to PCA.”
MethodLean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear SolverPreprint
Livne, O. E., & Brandt, A. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1108.0123 · Cited by 4 · see citing works
Determining population structure from k-mer frequencies
Hrytsenko, Y., Daniels, N. M., & Schwartz, R. S. (2025) · PeerJ · doi:10.7717/peerj.18939 · Cited by 3 · see citing works
Genome‐Wide Association Studies
McCauley, J. L., Veturi, Y., Verma, S. S., & Ritchie, M. D. (2021) · Wiley eBooks · doi:10.1002/9781119104100.ch9 · Cited by 3 · see citing works
Windels, S. F. L., Malod‐Dognin, N., & Pržulj, N. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/460964 · Cited by 2 · see citing works
“Applications of spectral embedding include visualizing genetic ancestry (Lee et al., 2010) and pseudo-temporal ordering of single-cell RNA-seq profiles (Campbell et al., 2015).”
BackgroundRevealing the range of maximum likelihood estimates in the admixture modelPreprint
Heinzel, C. S., Baumdicker, F., & Pfaffelhuber, P. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.10.18.619150 · Cited by 2 · see citing works
“Model-free methods use for example Principal Component Analysis or Spectral Graph Theory (Klei et al., 2011; Lee et al., 2010; Jombart et al., 2010) for inferring the IA.”
Shemirani, R., Belbin, G. M., Cullina, S., Caggiano, C., Gignoux, C. R., Zaitlen, N., & Kenny, E. E. (2025) · medRxiv · doi:10.1101/2025.06.04.25328990 · Cited by 2 · see citing works
Genome-Wide Association Study Heterogeneous Cohort Homogenization via Subject Weight Knock-Down
Valente, A. X. C. N., Zischkau, J., Shin, J. H., Gao, Y., & Sarkar, A. (2012) · PLoS ONE · doi:10.1371/journal.pone.0048653 · Cited by 1 · see citing works
“Two implementations of this approach are Spectral-GEM [25] and LAPSTRUCT [26].”
MethodThe Application of the Graph Laplacian in Network Forensics
McGee, C., Guo, J., & Wang, Z. (2021) · IEEE Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON) · doi:10.1109/iemcon53756.2021.9623073 · Cited by 1 · see citing works
Determining population structure from k-mer frequencies.Preprint
Hrytsenko, Y., Daniels, N. M., & Schwartz, R. S. (2023) · Research Square · doi:10.21203/rs.3.rs-1689838/v2 · Cited by 1 · see citing works
NAC: Network-Adjusted Covariates for Community Detection
Hu, Y., & Wang, W. (2023) · doi:10.32614/cran.package.nac · Cited by 1 · see citing works
Spectral clustering for multiclass Erdös-Rényi graphs
Belabbas, M.-A. (2010) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2010.5494932
Zhang, Y. (2013) · University of Minnesota Digital Conservancy (University of Minnesota)
- Authors
- Lee, A. B., Luca, D., Klei, L., Devlin, B., & Roeder, K.
- Affiliations
- Carnegie Mellon University (US)
- University of Pittsburgh (US)
- Corresponding author
- Roeder, Kathryn
- Venue
- Genetic Epidemiology
- Publisher
- Wiley
- Published
- 2009-05-19
- Volume
- 34
- Issue
- 1
- Pages
- 51-59
- ISSN
- 0741-0395 (ISSN-L)
- 1098-2272
- PMC
- PMC4610359
- OpenAlex
- W2000231790
- Cited by
- 108
- References
- 27
- Citations by year
- 2025: 2 · 2024: 2 · 2023: 3 · 2022: 6 · 2021: 6 · 2020: 2 · 2019: 6 · 2018: 3 · 2017: 6 · 2016: 7 · 2015: 6 · 2014: 5 · 2013: 6 · 2012: 13
- FWCI
- 9.30
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Genetic Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of Mental Health (R37MH057881, R01MH057881, MH057881)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Forensic and Genetic Research
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic diversity and population structure
- Keywords
- genetic ancestry estimation, spectral graph theory, genome-wide association study, normalized Laplacian, spectral embedding, multidimensional scaling, principal component analysis, population structure, complex disease genetics
- MeSH terms
- Algorithms, Genetics, Population, Humans, Models, Statistical, Cluster Analysis, Principal Component Analysis, Databases, Genetic, Genome-Wide Association Study
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