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Analysis of population structure: a unifying framework and novel methods based on sparse factor analysis.

ABSTRACT: We consider the statistical analysis of population structure using genetic data. We show how the two most widely used approaches to modeling population structure, admixture-based models and principal components analysis (PCA), can be viewed within a single unifying framework of matrix factorization. Specifically, they can both be interpreted as approximating an observed genotype matrix by a product of two lower-rank matrices, but with different constraints or prior distributions on these lower-rank matrices. This opens the door to a large range of possible approaches to analyzing population structure, by considering other constraints or priors. In this paper, we introduce one such novel approach, based on sparse factor analysis (SFA). We investigate the effects of the different types of constraint in several real and simulated data sets. We find that SFA produces similar results to admixture-based models when the samples are descended from a few well-differentiated ancestral populations and can recapitulate the results of PCA when the population structure is more "continuous," as in isolation-by-distance models.

SUBMITTER: Engelhardt BE

PROVIDER: S-EPMC2940725 | biostudies-literature | 2010 Sep

REPOSITORIES: biostudies-literature

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Analysis of population structure: a unifying framework and novel methods based on sparse factor analysis.

Engelhardt Barbara E BE Stephens Matthew M

PLoS genetics 20100916 9

We consider the statistical analysis of population structure using genetic data. We show how the two most widely used approaches to modeling population structure, admixture-based models and principal components analysis (PCA), can be viewed within a single unifying framework of matrix factorization. Specifically, they can both be interpreted as approximating an observed genotype matrix by a product of two lower-rank matrices, but with different constraints or prior distributions on these lower-r ...[more]

PMID: 20862358

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Project description:BackgroundHigh throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account.ResultsWe propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks.ConclusionSparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform (group lasso approach) as well as structures that involve all data platforms (Elitist lasso approach).AvailabilityThe additional file contains a MATLAB implementation of the sparse simultaneous component method.

Project description:BackgroundSince the publication of the first draft of the human genome in 2000, bioinformatic data have been accumulating at an overwhelming pace. Currently, more than 3 million sequences and 35 thousand structures of proteins and nucleic acids are available in public databases. Finding correlations in and between these data to answer critical research questions is extremely challenging. This problem needs to be approached from several directions: information science to organize and search the data; information visualization to assist in recognizing correlations; mathematics to formulate statistical inferences; and biology to analyze chemical and physical properties in terms of sequence and structure changes.ResultsHere we present MultiSeq, a unified bioinformatics analysis environment that allows one to organize, display, align and analyze both sequence and structure data for proteins and nucleic acids. While special emphasis is placed on analyzing the data within the framework of evolutionary biology, the environment is also flexible enough to accommodate other usage patterns. The evolutionary approach is supported by the use of predefined metadata, adherence to standard ontological mappings, and the ability for the user to adjust these classifications using an electronic notebook. MultiSeq contains a new algorithm to generate complete evolutionary profiles that represent the topology of the molecular phylogenetic tree of a homologous group of distantly related proteins. The method, based on the multidimensional QR factorization of multiple sequence and structure alignments, removes redundancy from the alignments and orders the protein sequences by increasing linear dependence, resulting in the identification of a minimal basis set of sequences that spans the evolutionary space of the homologous group of proteins.ConclusionMultiSeq is a major extension of the Multiple Alignment tool that is provided as part of VMD, a structural visualization program for analyzing molecular dynamics simulations. Both are freely distributed by the NIH Resource for Macromolecular Modeling and Bioinformatics and MultiSeq is included with VMD starting with version 1.8.5. The MultiSeq website has details on how to download and use the software: http://www.scs.uiuc.edu/~schulten/multiseq/

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Analysis of population structure: a unifying framework and novel methods based on sparse factor analysis.

Publications

Analysis of population structure: a unifying framework and novel methods based on sparse factor analysis.

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