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In order to explain the results obtained with the GCQC and the associated analytical geometry indicators, each cluster has been analyzed by using the estimated density distribution of the PCA scores associated with GC-FTIR spectra.
The GCQC increases with 10% in the case of the spectra preprocessed with the w selective amplifier in comparison with the case of unprocessed spectra.
Validation of the Global Clustering Quality Coefficient (GCQC).
The correct classification rates confirm the ranking provided by GCQC for the spectra preprocessing functions and their positive effect on the quality of the clusters in comparison with the case of unprocessed spectra (see Tables 5 and 7).
The increased predictive power indicated by the GCQC in the case of the w selective amplifier is validated by an improved correct classification rate.
The GCQC has indicated a slightly lower predictive power for the models generated by spectra preprocessing with the [w.sup.2] selective amplifier.
Finally, the GCQC has forecasted that the best results may be obtained with the spectra preprocessed with the [(w - 1).sup.2] amplifying selector.
In order to obtain an objective ranking, we have defined a GCQC that allows the quantitative overall assessment of the efficiency of the PCA based screening systems.
The hierarchy indicated by the GCQC has been explained by analyzing the dynamics of the cumulated explained variance, the associated number of PCs, and the estimated density distributions determined for the PC1 and PC2 scores associated with stimulant amphetamines, hallucinogenic amphetamines, and negative compounds.
In conclusion, GCQC maybe used to compare score plots provided by this nonhierarchical clustering technique in the same way as the cophenetic correlation coefficient may be used for ranking different algorithms generating hierarchical classification trees (dendrograms).
Last but not least, we would like to emphasize that the use of quantitative (analytical geometry and GCQC) indicators presents the major advantage of allowing the automatic evaluation of the cluster relative position and dispersion, as well as of the overall predictive power of the models.
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