Shape comparisons using least-squares

Correlation coefficients ranged from 0.6 or lower to 0.7, depending on the reference compound that was used. With only a few exceptions, similar results were obtained for the other descriptors. Since the biodata and the shape descriptors in this study are both multivariate, canonical correlation analysis was selected to provide a single overall measure of correlation between molecular shape and biological activity, for comparison of the various shape descriptors. In canonical correlation analysis, the combination of the predictor variables is found, which correlates highest with any possible combination of the response variables (23). A similar approach is taken in Partial Least Squares (PLS) analysis (24). 

Third, comparisons of the shape were carried out among the substructures with a least square fitting method (19). All the analyses described above were done by using the ACACS (Advanced Computer Aided Chemistry System), which has been developed through the joint cooperation of this company, Sumitomo Pharmaceuticals, and NEC (20). 

Fig. 14.9 Comparison of the measured J°values ( ) of sample C with those calculated (+) using the s values obtained from the Jp(f) line-shape analyses and the curve calculated from the empirical functional form log( J°) = a - - b/x + cjx djx x being the temperature in °C) best fitted to the calculated values. Note As the Jp(t) curve at 134.1°C is not available for analysis to obtain the s value, the J° value at 134.1°C used in the least-squares fitting is the experimental value itself.

See Klingenberg and Montiero (2005) for a CVA variant that circumvents this problem to some extent experiments with partial least squares comparisons of CVA scores to shape data suggest this approach may also be used to obtain heuristic linear models of the CVA space. 

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