Efficient genomewide selection of PCA-correlated tSNPs for genotype imputation

Exploring genomic structure differences and similarities between the Greek and European HapMap populations: implications for association studies

Studies of the genomic structure of the Greek population and Southeastern Europe are limited, despite the central position of the area as a gateway for human migrations into Europe. HapMap has provided a unique tool for the analysis of human genetic variation. Europe is represented by the CEU (Northwestern Europe) and the TSI populations (Tuscan Italians from Southern Europe), which serve as reference for the design of genetic association studies. Furthermore, genetic association findings are often transferred to unstudied populations. Although initial studies support the fact that the CEU can, in general, be used as reference for the selection of tagging SNPs in European populations, this has not been extensively studied across Europe. We set out to explore the genomic structure of the Greek population (56 individuals) and compare it to the HapMap TSI and CEU populations. We studied 1112 SNPs (27 regions, 13 chromosomes). Although the HapMap European populations are, in general, a good reference for the Greek population, regions of population differentiation do exist and results should not be light-heartedly generalized. We conclude that, perhaps due to the individual evolutionary history of each genomic region, geographic proximity is not always a perfect guide for selecting a reference population for an unstudied population.

rCUR: an R package for CUR matrix decomposition

Background

Many methods for dimensionality reduction of large data sets such as those generated in microarray studies boil down to the Singular Value Decomposition (SVD). Although singular vectors associated with the largest singular values have strong optimality properties and can often be quite useful as a tool to summarize the data, they are linear combinations of up to all of the data points, and thus it is typically quite hard to interpret those vectors in terms of the application domain from which the data are drawn. Recently, an alternative dimensionality reduction paradigm, CUR matrix decompositions, has been proposed to address this problem and has been applied to genetic and internet data. CUR decompositions are low-rank matrix decompositions that are explicitly expressed in terms of a small number of actual columns and/or actual rows of the data matrix. Since they are constructed from actual data elements, CUR decompositions are interpretable by practitioners of the field from which the data are drawn.

Results

We present an implementation to perform CUR matrix decompositions, in the form of a freely available, open source R-package called rCUR. This package will help users to perform CUR-based analysis on large-scale data, such as those obtained from different high-throughput technologies, in an interactive and exploratory manner. We show two examples that illustrate how CUR-based techniques make it possible to reduce significantly the number of probes, while at the same time maintaining major trends in data and keeping the same classification accuracy.

Conclusions

The package rCUR provides functions for the users to perform CUR-based matrix decompositions in the R environment. In gene expression studies, it gives an additional way of analysis of differential expression and discriminant gene selection based on the use of statistical leverage scores. These scores, which have been used historically in diagnostic regression analysis to identify outliers, can be used by rCUR to identify the most informative data points with respect to which to express the remaining data points.