Metabolite Distance Metric
This function calculates a distance metric between two metabolomic measurements. These measurements can be either scalers or vectors.
mdist(x, y)
x |
a numerical scalar or vector of metabolomic measurements. |
y |
a numerical scalar or vector of metabolomic measurements. |
If x and y are of different dimensions, function mdist returns a value of -1, which indicates the mdist(x,y) is not defined in this scenario. When x and y have the same dimension, suppose they have p components. If p=1, then x or y is the abundance level measurement of a single metabolite, which is a non-negative real number. If p>1, then x or y is measurements of a metebolite-set with multiple metabolites. In this case, let x_i be the ith component of x, which is non-negative and denotes the abundance level measurement of the ith metabolite in the metabolite-set. The distance between x and y is defined as:
mdist(x,y)= √ { ∑_i I[δ_{x_i} \neq δ_{y_i}]+ ∑_i (x_i-y_i)^2 },
where δ_{x_i}=0 if x_i=0, elsewise, δ_{x_i}=1, and I[\cdot] is the indicator function.
This function returns a non-negative value if x and y are of the same dimension. Otherwise it returns -1.
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(0,1,2) y=c(1,0,3) z=c(0,1,2,3) mdist(x,y) mdist(x,z)
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