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Asymptotic conditional singular value decomposition for high-dimensional genomic data.

ABSTRACT: High-dimensional data, such as those obtained from a gene expression microarray or second generation sequencing experiment, consist of a large number of dependent features measured on a small number of samples. One of the key problems in genomics is the identification and estimation of factors that associate with many features simultaneously. Identifying the number of factors is also important for unsupervised statistical analyses such as hierarchical clustering. A conditional factor model is the most common model for many types of genomic data, ranging from gene expression, to single nucleotide polymorphisms, to methylation. Here we show that under a conditional factor model for genomic data with a fixed sample size, the right singular vectors are asymptotically consistent for the unobserved latent factors as the number of features diverges. We also propose a consistent estimator of the dimension of the underlying conditional factor model for a finite fixed sample size and an infinite number of features based on a scaled eigen-decomposition. We propose a practical approach for selection of the number of factors in real data sets, and we illustrate the utility of these results for capturing batch and other unmodeled effects in a microarray experiment using the dependence kernel approach of Leek and Storey (2008, Proceedings of the National Academy of Sciences of the United States of America 105, 18718-18723).

SUBMITTER: Leek JT

PROVIDER: S-EPMC3165001 | biostudies-literature | 2011 Jun

REPOSITORIES: biostudies-literature

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Asymptotic conditional singular value decomposition for high-dimensional genomic data.

Leek Jeffrey T JT

Biometrics 20100616 2

High-dimensional data, such as those obtained from a gene expression microarray or second generation sequencing experiment, consist of a large number of dependent features measured on a small number of samples. One of the key problems in genomics is the identification and estimation of factors that associate with many features simultaneously. Identifying the number of factors is also important for unsupervised statistical analyses such as hierarchical clustering. A conditional factor model is th ...[more]

PMID: 20560929

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Project description:BackgroundFor marker effect models and genomic animal models, computational requirements increase with the number of loci and the number of genotyped individuals, respectively. In the latter case, the inverse genomic relationship matrix (GRM) is typically needed, which is computationally demanding to compute for large datasets. Thus, there is a great need for dimensionality-reduction methods that can analyze massive genomic data. For this purpose, we developed reduced-dimension singular value decomposition (SVD) based models for genomic prediction.MethodsFast SVD is performed by analyzing different chromosomes/genome segments in parallel and/or by restricting SVD to a limited core of genotyped individuals, producing chromosome- or segment-specific principal components (PC). Given a limited effective population size, nearly all the genetic variation can be effectively captured by a limited number of PC. Genomic prediction can then be performed either by PC ridge regression (PCRR) or by genomic animal models using an inverse GRM computed from the chosen PC (PCIG). In the latter case, computation of the inverse GRM will be feasible for any number of genotyped individuals and can be readily produced row- or element-wise.ResultsUsing simulated data, we show that PCRR and PCIG models, using chromosome-wise SVD of a core sample of individuals, are appropriate for genomic prediction in a larger population, and results in virtually identical predicted breeding values as the original full-dimension genomic model (r = 1.000). Compared with other algorithms (e.g. algorithm for proven and young animals, APY), the (chromosome-wise SVD-based) PCRR and PCIG models were more robust to size of the core sample, giving nearly identical results even down to 500 core individuals. The method was also successfully tested on a large multi-breed dataset.ConclusionsSVD can be used for dimensionality reduction of large genomic datasets. After SVD, genomic prediction using dense genomic data and many genotyped individuals can be done in a computationally efficient manner. Using this method, the resulting genomic estimated breeding values were virtually identical to those computed from a full-dimension genomic model.

Dataset Information

Asymptotic conditional singular value decomposition for high-dimensional genomic data.

Publications

Asymptotic conditional singular value decomposition for high-dimensional genomic data.

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