dkDNA (version 0.1.1)

hypercube: Diffusion kernels on bi-allelic genotypes

Description

This function construct a diffusion kernel on a $p$-dimensional hypercube, where each genotype takes on two possible configurations. This graph is obained by the $p$-Cartesian graph product of a complete graph $K_2$. It contains $2^p$ vertices corresponding to sequences of genotypes, and two vertices are adjacent if and only if just one SNP locus differs.

Usage

hypercube(X, theta)

Arguments

X

A genotype matrix of $n$ individuals with $p$ bi-allelic genotypes ($n \times p$).

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.

Examples

# set a seed
set.seed(4321)

# create a genotype matrix of 5 individuals with 10 bi-allelic genotypes
X <- matrix(sample(c(0,1), 50, prob=c(0.6,0.4), replace=TRUE), ncol=10)

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

# compute a hypercube kernel 
hypercube(X, theta)