Maximal predictive classification

Consider n point populations characterised by v dichotomous variables, constant within populations. For any classification into k classes, a list of valtues (class predictors) can be constructed for the variables of each class, and used to predict the properties of any individual belonging to that class. The maximal predictive criterion selects that partition of the n populations into k classes which maximises the inuimber, Wk, of correct predictions. The average number, Bk, of properties correctly predicted for members of each class using the class predictors of the other k 1 classes, measures the separation between classes. The best choice of k is related to maximising Wk Bk . A general method is given for defining optimal hierarchical classification using any optimal k-class criterion, not necessarily depending on taxonomic distance. Maximal predictive classes have an optimal identification property and other properties, useful for constructing search algorithms, are given. An example illustrates the results. Multilevel qualitative variables and differing probabilities of occurrence for each population are acceptable, but random variation within populations needs further consideration.