# skernel: Stratified Kernel In KMDA: Kernel-Based Metabolite Differential Analysis

## Description

This function defines a stratified kernel for metabolite abundance level measurements.

## Usage

 `1` ```skernel(x, y, rho) ```

## Arguments

 `x` a numerical scalar or vector of metabolomic measurements. `y` a numerical scalar or vector of metabolomic measurements. `rho` a positive kernel shape parameter.

## Details

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).

## Value

A non-negative real value.

## References

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.

## Examples

 ```1 2 3 4 5 6``` ``` 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) ```

### Example output

```[1] 0
[1] 1.125352e-07
```

KMDA documentation built on May 30, 2017, 8:11 a.m.