List of Figures

1. Linear discriminant analysis
2. The difference between PCA and LDA
3. The consequences of the constant-sum constraint
4. Spurious correlation of ratios
5. The dangers of using ``traditional'' statistics on the simplex
6. Mapping compositional data from $\Delta _2$ to R²
7. Linear discriminant analysis done the wrong way
8. Linear discriminant analysis done the right way
9. Results of the linear discriminant analysis mapped back to the simplex
10. Geographical locations of the training data
11. Linear discriminant analysis of the Ti-V system of Shervais (1982)
12. Quadratic discriminant analysis of the Ti-V system
13. Linear discriminant analysis of the Ti-Zr system of Pearce and Cann (1973)
14. Quadratic discriminant analysis of the Ti-Zr system
15. Linear discriminant analysis of the Ti-Zr-Y system of Pearce and Cann (1973)
16. Quadratic discriminant analysis of the Ti-Zr-Y system
17. Linear discriminant analysis of the Zr-Y-Nb system of Meschede (1986)
18. Quadratic discriminant analysis of the Zr-Y-Nb system
19. Linear discriminant analysis of the Th-Ta-Hf system of Wood (1980)
20. Quadratic discriminant analysis of the Th-Ta-Hf system
21. Linear discriminant analysis using Ti, Zr, Y and Sr
22. Linear discriminant analysis using major element data
23. Exhaustive exploration of all bivariate linear discriminant analyses using only major elements
24. Same as Figure 23, but for quadratic discriminant analysis
25. Matrices showing the performance of all possible bivariate discriminant analyses using combinations of 45 elements
26. Same as Figure 25, but for quadratic discriminant analysis
27. Performance analysis of all possible ternary discriminant analyses using TiO$_2$ and other major element oxides
28. Same as Figure 27, but using quadratic discriminant analysis
29. Performance analysis of all possible ternary discriminant analyses using Ti and other elements
30. Same as Figure 29, but using quadratic discriminant analysis
31. Best ternary linear discriminant analysis (using Si, Ti, and Sr)
32. Linear discriminant analysis using Eu, Lu, and Sr
33. Linear discriminant analysis using Ti, V and Sc
34. Quadratic discriminant analysis using Na, Nb and Sr
35. Quadratic discriminant analysis using Ti, V and Sm
36. Illustration of the bias-variance tradeoff in a regression context
37. The test data plotted on various versions of the Ti-V diagram
38. The test data plotted on the Ti-Zr diagram
39. The test data plotted on the Ti-Zr-Y diagram
40. The test data plotted on the Nb-Zr-Y diagram
41. The test data plotted on the Th-Ta-Hf diagram
42. The test data plotted on the Si-Ti-Sr diagram
43. The test data plotted on the Eu-Lu-Sr diagram
44. The test data plotted on the Ti-V-Sc diagram
45. The test data plotted on the Na-Nb-Sr diagram
46. The test data plotted on the Ti-V-Sm diagram