Fig. 1

Dimensionality analysis for the PPM training set. Top panels show the results obtained by the Principal Component Analysis (PCA) ran on 175 × 5 matrix, [E S A B V], of Abraham solute descriptors for the training set of the Zhang Model in the form of a Scree Plot of eigenvalues (i.e., the amount of variation retained by each principal component), and b the correlation circle showing the relationship and quality of representation, square cosine (cos2), of variables in first two dimensions. Lower panels show c the distribution of quality of representation, Cos2, into 8 dimensions and d the correlogram of the correlation matrix, obtained respectively by the PCA and Pearson correlation analysis of 175 × 8 matrix, [E S A B V log \(K_{ow}\) log \(K_{aw}\) \(log K_{p}\)]. In b, the length of arrowed line from the origin shows the quality of representation of variable. Angles between the arrowed lines show the degree of correlations: Descriptor A is almost orthogonal to E, S, B and V descriptors, which are mutually positively correlated. In c, color intensity and size of the circle are proportional to the quality of presentation of a variable. In d, blue and red color respectively show positive and negative correlations between the pair. The value of correlation coefficient for each pair of variables is shown in each square. All correlations, shown here, were statistically significant (p < 0.05). In b, c, Dim. stands for the dimension