Fig. 5

Relative and absolute normalization performance. In the top row the predicted \(\text {log}_{10}(C_{j}(t_i;\varvec{\uptheta })/C_{j}(0;\varvec{\uptheta }))\) (\(i \in \{1, ..., n_{\text {time points}}\}\), \(j \in \{1, ..., {n_{\text {metabolites}}}\}\)) are plotted as a function of the true, underlying \(\text {log}_{10}(C_{j}(t_i)/C_{j}(0))\). The bottom row shows the predicted \(V\) as a function of the true, underlying \(V\). The columns represent different normalization models (PQN, PKM\(_{\text {minimal}}\), and MIX\(_{\text {minimal}}\) from left to right). As no absolute \(V\) can be calculated from PQN the bottom left plot is omitted. To illustrate the effect of different RMSE and rRMSE sizes (which both are calculated from \(V\)), we show their mean over 100 replicates in comparison to the R\(^2\)  values calculated from the points plotted. Intuitively rRMSE is a measure of good correlation on the top row whereas RMSE is a measured of good correlation on the bottom row (high R\(^2\), low rRMSE/RMSE respectively)