Table 1.

Listing of most commonly used data scaling methods in metabolic fingerprinting multivariate analyses.¹

Method	Equation	Goal	Advantage	Disadvantage
Centering	$${\stackrel{\sim }{x}}_{\mathit{\text{ik}}}=x_{\mathit{\text{ik}}}-{\overline{x}}_k$$	Focus on differences, not similarities	Removes offset from the data	Unsuitable for heteroscedastic data
UV	$${\stackrel{\sim }{x}}_{\mathit{\text{ik}}}=\frac{x_{\mathit{\text{ik}}}-{\overline{x}}_k}{s_k}$$	Compare metabolites based on correlation	All metabolites equally important	Inflation of measurement errors
Range	$${\stackrel{\sim }{x}}_{\mathit{\text{ik}}}=\frac{x_{\mathit{\text{ik}}}-{\overline{x}}_k}{x_{k,max}-x_{k,min}}$$	Compare metabolites relative to biological response range	All metabolites equally important. Biologically related scaling	Inflation of measurement errors, sensitive to outliers
Pareto	$${\stackrel{\sim }{x}}_{\mathit{\text{ik}}}=\frac{x_{\mathit{\text{ik}}}-{\overline{x}}_k}{\sqrt{s_k}}$$	Reduce relative importance of large values, partially preserve data structure	Stays closer to original measurement than UV	Sensitive to large fold changes
Vast	$${\stackrel{\sim }{x}}_{\mathit{\text{ik}}}=\frac{x_{\mathit{\text{ik}}}-{\overline{x}}_k}{s_k}C\frac{{\overline{x}}_k}{s_k}$$	Focus on small fluctuations	Aims for robustness, uses prior group knowledge	Not suited for large induced variation without group structure
Level	$${\stackrel{\sim }{x}}_{\mathit{\text{ik}}}=\frac{x_{\mathit{\text{ik}}}-{\overline{x}}_k}{{\overline{x}}_k}$$	Focus on relative response	Suited for biomarker identification	Inflation of measurement errors

¹Variable subscripts reflect conventions shown in Figure 1, with the mean of the k -th variable in X represented by x̄_k and its deviation represented by s_k, the sample standard deviation. Reprinted with permission from reference [82], (Copyright 2006 van den Berg et. al.).