Stratified Kernel
This function defines a stratified kernel for metabolite abundance level measurements.
skernel(x, y, rho)
x |
a numerical scalar or vector of metabolomic measurements. |
y |
a numerical scalar or vector of metabolomic measurements. |
rho |
a positive kernel shape parameter. |
This function calculates a stratified kernel function skernel between two metabolomic measurements x and y. Suppose the metabolite-set contains p metabolites. Then measurements x and y have p components. Let x_i be the ith component of x. If x_i=0, then the ith metabolite in the metabolite-set is absent. If x_i>0, then the ith metabolite is present and x_i measures the abundance level of the ith metabolite. Measurements x and y are said to from the same stratum if they have the same set of metabolites being absent (present). If x and y are from the same stratum, then skernel(x,y,ρ) is assigned a Gaussian kernel with kernel parameter ρ. Otherwise skernel(x,y,ρ) is defined to be 0. More details can be found in Zhan et al. (2015).
A non-negative real value.
Zhan, X., Patterson, A. D., & Ghosh, D. (2015). Kernel approaches for differential expression analysis of mass spectrometry-based metabolomics data. BMC Bioinformatics, 16(1), 77.
x=c(0,0,1,2) y=c(0,1,2,0) z=c(0,0,3,4) ## x and z are from the same stratum while x and y are not. skernel(x,y,1) skernel(x,z,1)
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