dkDNA (version 0.1.1)

snpgrid: Diffusion kernels on SNP genotypes

Description

This function construct a diffusion kernel on a $p$-dimensional SNP grid graph, where each genotype takes on three possible configurations, namely 0 ('aa'), 1 ('Aa'), and 2('AA'). This graph is obained by the $p$-Cartesian graph product of a path graph 0-1-2. It contains $3^p$ vertices corresponding to sequences of genotypes, and two vertices are adjacent if and only if just one SNP locus differs by 1.

Usage

snpgrid(X, theta)

Arguments

X

A genotype matrix of $n$ individuals with $p$ SNPs ($n \times p$).

theta

The rate of diffusion.

Value

Diffusion kernel matrix of size $n \times n$. This can be viewed as a covariance among individuals given the diffusion rate.

References

Kondor R and Lafferty J: (2002) Diffusion Kernels on Graphs and Other Discrete Input Spaces. ICML.

Morota G, Koyama M, Rosa GJM, Weigel KA, and Gianola D. (2013). Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data. Genetics Selection Evolution. 45:17.

See Also

snphamming

Examples

# set a seed
set.seed(4321)

# create a genotype matrix of 5 individuals with 10 SNPs
X <- matrix(sample(c(0,1,2), 50, prob=c(0.35, 0.3, 0.35), replace=TRUE),
ncol=10)

# set the rate of diffusion equal to 1
theta <- 1

# compute a SNP grid kernel 
snpgrid(X, theta)