A Fast Algorithm for Some Exploratory Methods in Categorical Data Problems

Two methods for categorical data problems, a discriminant analysis procedure and a procedure for the reduction of dimensionality can be summarized as an attempt to give a good forecast knowing an individuals categories on a subset of the variables for the category of a fixed variable and for the categories of the rest of the variables, respectively. The most simple algorithm checks all subsets that are to be considered and chooses the best one. This needs several re-orderings of the observed frequencies. In this paper an eager and fast algorithm is proposed that skips the cells of the contingency table in descending order of their observed frequencies and puts them into a set as long as they can be correctly forecasted together based on one of the subsets of the variables considered. Such a maximal subset of cells defines a subset of the variables that is optimal in some cases and is ‘not very bad’ at least.