Randomized Pedigree Principal Component Analysis

A pedigree can be represented as a genetic relationship matrix (GRM). Therefore, pedigrees can in principle be subjected to (and visualised by) principal component analysis (PCA). However, doing this naively is very slow for large pedigrees of, say, one million individuals. We present the Randomized Pedigree Principal Component Analysis approach, which performs rapid PCA of a pedigree GRM using randomized linear algebra.

Henderson (1975) developed an efficient way to compute the lower Cholesky factor of the inverse GRM and Colleau (2002) explicitly showed how to multiply pedigree GRM with an arbitrary vector efficiently. Our approach uses these two algorithmic ingredients to rapidly compute the principal components of pedigree GRM without forming the pedigree GRM. This is achieved via the randomized singular value decomposition (rSVD) described in Halko et al. (2011). The resulting principal components can reveal the underlying population structure of a pedigree.

Preprint

Check out our preprint on bioRxiv here.

R package

Setup

randPedPCA is on CRAN!

install.package("randPedPCA")

First steps

For a demonstration, check out

library(randPedPCA)
vignette("pedigree-pca")

Python prototype

The initial prototype was developed in Python. An example can be found in notebook/Example.ipynb, which uses the rppca module in this repository.