Figure 23 shows an example of such a visualization
for all bivariate LDAs using the major oxides. Of the 756 training
data, not all had been analysed for all major elements. The upper
right triangular part of the matrices in this figure show the number
of analyses for which both elements were measured. Using the same
color-code but a different scale, the lower left triangular parts of
the matrices show the resubstitution errors of the 55 possible
bivariate LDAs. For example, the lower left triangular matrices of
Figure 23 show that only 13.5% of IABs, 15.2% of
MORBs and 7.4% of OIBs were misclassified by an LDA using TiO
and
KO. The overall resubstitution error is 12%. The upper right
triangular parts of the same figure show that 229 out of 256 IABs, 230
out of 241 MORBs and 203 out of 259 OIBs were used for the
construction of the LDA, accounting for a total of 662 out of 756
training data. Figure 24 shows the same thing for
QDA.
Figure 25 visualizes the results of all possible
bivariate LDAs for the complete dataset of 45 elements. On the whole,
Ti jumps out as the apparently best overall discriminator. One might
think that the Tm-Sc diagram performs very well, considering that the
overall error (shown in the upper right triangle of the lower right
matrix of Figure 25) is only 7.7%. 12% of the IABs,
8.8% of the OIBs and only 2.4% of the MORBs in the training data
were misclassified. However, the upper right triangular matrices of
the same figure show that only 101 of 756 training data were used for
the classification. Only 25/256 of the IABs, 42/241 of the MORBs and
34/259 of the OIBs were analysed for both Tm and Sc, thereby greatly
reducing the reliability of the classification. Figure
25 shows the results of all possible bivariate QDAs
for the database of 45 elements. The strikingly different colors of
the lower triangular matrices on this figure illustrate the
difficulties in classifying IABs. Both MORBs and IABs are relatively
easy to separate, but the geochemical variability of IABs is much
larger, for reasons discussed before.