Discriminant analysis

Knowing the groups changes the question: no longer a structure but a boundary

Mind map of chapter 25: the inertia of a partitioned cloud decomposes exactly, I_T = I_B + I_W, and 72.8 % of the inertia lies in the gap between blocks. Fisher's criterion maximises the ratio of separation to dispersion; with two groups the solution is the line of centres reweighted by internal stability. Separating is not spreading: the discriminant axis correlates only at 0.86 with the first factorial axis, and the criterion that carried the latter receives the smallest coefficient here. The most useful criterion is the one that separates least on its own — because it separates differently. Hence the distinction between marginal and conditional contribution.