From the practical point of view, the decompositon of information in the new coordinate system is of primary interest. The PCA decomposes the information of a set of spectra into information about the samples and into information about the variables (signals). Information about the samples is displayed in so-called scores plot. An example is shown in the top row on the right side of the figure. Samples, which are very similar, cluster, and samples which are different are separated. Information about variables is shown in so-called loadings plots. In these plots, variables, which are similar (for example various signals of the same metabolite). In the example shown in the figure, the signals in the loadings plot shown in the second column (right side), which belong to the same metabolite are color coded with the same color. For exmple, the signals of 2-oxoglutarate are colored in blue, the signals of taurine are colored in magenta, the signals of citrate are colored in red and so on. Only signals, which vary significantly in the data set are lying outside of the cloud of signals around the coordinate origin. When combining the information of the loadings plot and the scores plot, it is obvious, which signals are responsible for the separation of which samples. In the example below, high-dosed samples are colored in black, low-dosed samples are colored in red and non-dosed samples are colored in green. The three dose-groups are separated along principal component 1. Variables with high positive or negative values for principal component 1 are responsible for this separation. In this example, mainly 2-oxoglutarate (variable encircled in blue) and also citrate (red circles) are responsible for the separation. If the set of samples originate from a time series, the time information can also be shown in so-called time-trajectories (bottom right plot). In this plot it is shown, how different dose groups show different time trajectories.
Decompostion of a set of spectra (left) into information about samples (scores plot on the top right) and into information about the signals (loadings plot on the middle right). If the various samples origninat from a time series, also the time information can be decomposed (time trajectory, bottom right).