The variance diagram VARDIA technique

In Section 34.2 we explained that factor analysis consists of a rotation of the principal components of the data matrix under certain constraints. When the objects in the data matrix are ordered, i.e. the compounds are present in certain row-windows, then the rotation matrix can be calculated in a straightforward way. For non-ordered spectra with three or less components, solution bands for the pure factors are obtained by curve resolution, which starts with looking for the purest spectra (i.e. rows) in the data matrix. In this section we discuss the VARDIA [27,28] technique which yields clusters of pure variables (columns), for a certain pure factor. 

In order to decide on the purity of the factor f as a whole, the purity of the loadings of all variables should be checked. At 30 degrees, where f = 0.866v, + 0.5v2, the variables 2 and 12 (see Table 34.3) fulfil the purity criterion. The sum of squares of all variable loadings fulfilling the purity criterion are plotted in a so-called variance diagram. At 30 degrees, this is the value /12 30 )  

The variance diagram obtained for the example discussed before is quite simple. Clusters of pure variables are found at 30 degrees (var = 0.5853) and at 300 degrees (var = 0.4868) (see Fig. 34.36). The distance from the centre of the diagram to each point is proportional to the variance value. Neighbouring points are connected by solid lines. All values were scaled in such a way that the highest variance is full scale. As can be seen from Fig. 34.36, two clusters of pure variables are found. The 

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The resulting Py-LVMS spectra were subjected to factor analysis after spectrum calibration. The variance diagram (VARDIA) technique (13) was used to determine the major components showing different time profiles. The major chemical components were visualized in the form of so-called factor spectra using the procedure described by Windig et al (14). 

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