BUCHI NIRCal - Manual (Page 45)

Chemometrics
NIRCal 5.5 Manual, Version A 45
The scores can be represented in two- or three-dimensional PC plots. Each number represents a
spectrum, v in its score.
Here, the scores of the spectra 1, 2 and 3 of the PCs 1 and 2 are graphically represented. Each
spectrum with "i" PCs will also have "i" scores. The closer together the points in the plot, the "more
similar" the spectra. It is now possible to break down an unknown spectrum with regard to these two
PCs, i.e. to determine the scores. If this spectrum is located, e.g. in the region of 1, it will be identified
as 1.
User-allocated properties of the spectra (e.g. quantity, good/poor quality, identity) do not have any
effect on the Principal Component Analysis.
The Mahalanobis distance
The introduction of Mahalanobis distances means an artificial scaling of the scores with the square
scores sum being normalised. At the same time this leads to a stretching or compression of the PCs,
since the product obtained from the score and PC is not changed.
A new normalisation is performed so that the scores v
in of the spectra n will retain roughly the same
magnitude as the PC index increases. Scores are variables without unit that must only be considered
relative to one another.
The purpose behind all this is to make physical or chemical properties which have only slight effects
on the spectral data and which therefore only manifest themselves in higher PCs as visible as those
clearly shown in the spectra.
The scores are normalised as follows:
Formula:
For this reason, the points in the 2-D plots are evenly distributed, i.e. the scores of all PCs have the
same average magnitude. On the other hand, individual PCs are appropriately reduced or increased.
For further evaluation, only the normalised scores are used.