## 8 Homo- and Heteronuclear Two-Dimensional (2D) NMR Analysis of Human Saliva
### Data Normalization, Transformation, Scaling, and Dimensionality Reduction
However, as surmised above, it does lend itself to facilitate distinction between biomolecules that have proportionately increased in concentration because of dehydration, or those that are inversely related to SFR, from'real' biomarkers responding to the effects induced by a particular disease process. Indeed, in such cases, disease-induced changes in the salivary levels of genuine biomarkers, either up- or downregulations, would be expected to differ significantly from non-etiological modifications in salivary volume. Hence, CSN is sometimes particularly applicable to selected salivary metabolomics analysis experiments, since it at least partially circumvents the requirement to correct salivary metabolite concentration data for variable SFRs or indeed explore their relationships with this parameter, assuming that it can be accurately determined. An additional normalization approach is product quotient normalization (PQN). PQN transforms 1H NMR profiles arising in metabolomics experiments in accordance with an overall estimate of the most likely 'dilution' effect [37]. This normalization approach usually involves the subtraction of a mean or median column-bucketed reference spectral profile from those of either all study samples, or a sub-set of them, usually those of the healthy control group only; this reference spectrum may represent the overall average spectrum of the control group, and all samples are normalized to this irrespective of what group they belong to, i.e., disease or control. It may also be a pre-established spectrum obtained from a reputable reference database, a single study one, or a reference model spectrum of all biomolecules detectable and present at relevant, recommended concentrations in aqueous solution at the known average biofluid pH, ionic strength (I), and viscosity parameters. Selection of the mean or median values of predictor (metabolite) variables in the reference spectrum is generally perfunctory, although use of a median spectrum appears to provide the most robust reference profile for experiments involving only small numbers of participants. It is also recommended that a CSN is performed before PQN in order to primarily scale column metabolite variables to the same absolute magnitude. Reportedly, the PQN algorithm is significantly more accurate and robust than both the CSN and vector length normalization strategies [37]. It is also highly recommended to use the now well-known autoscaling procedure to appropriately scale data. This involves the mean-centering of each metabolite column predictor variable's data-point followed by division by its estimated sample standard deviation so that the mean and variance of each one become 0 and 1, respectively (and also unit standard deviation for the latter value). This process permits each metabolite determination to be considered to be on equivalent scales, irrespective of their pre-autoscaling magnitudes; indeed, the \({}^{1}\)H NMR spectra of healthy human saliva contain some biomolecule resonances that, between-participants, are reproducibly of a much greater intensity than those of others (for example, propionate has a much higher salivary concentration than those of all methylamine species). Furthermore, in this context, any 'between-metabolite' heteroscedasticity (variance heterogeneity) problems with the complete datasets of all included metabolite variables are overcome. Although this scaling process does not prove to protect against 'between-classification-within-metabolite variable' heteroscedasticities, which remains a critical assumption for all parametric statistical tests for comparing mean values [135], we therefore further recommend that all MV datasets are further transformed using logarithmic or generalized logarithmic (glog), square root or cubed root, or even inverse transformations.