The aim of a factor breakdown is to describe the spectra with less data; in other words, to achieve a reduction in the data. This is done by means of wavelengths which are high-correlated in one data record being complied to one factor. In the case of NIR spectra this is very readily possible, since, for example, adjacent wavelengths are high-correlated.|
Factor breakdown compiles the wavelengths in question to a new factor, and provides the samples with high absorption values with high factor values, while the samples with low absorption values obtain low factor values.
It has already been said that there is a great deal of superfluous information contained in the NIR spectrum of the samples, because some wavelengths are high co-related, and therefore contain the same information about the samples. In mathematical terms the factors are determined in such a way that the new factors are orthogonal; in other words, there is no correlation between the factors. The data reduction which is attained by the factor breakdown therefore resolves the problem of multi co-linearity, which has been addressed earlier.
A point of approach for the calculation of the factor breakdown, in addition to the correlation between the wavelengths, is the scatter of the spectra in the data record, i.e. areas in the spectrum which clearly have scatter, are described jointly in one factor. As a result of this, the content substances which cause evident scatters in the spectrum, described in the first factors, are those which cause minor scatters in later factors. From a number of factors onwards, which is still to be determined, the remaining scatter in the spectrum is assessed as noise, and is excluded from further calculations.
The factors are set out in the factor breakdown in such a way that they are orthogonal to one another; i.e. there are no correlations between the factors. The population descriptions which are derived must therefore be symmetrical, and this should apply to every combination of the factors.