On Cluster Analysis Based on Contingency Tables

In _ Zytkow and Zembowicz (1993), a system for cluster analysis, based on two-way contingency tables, has been proposed. In its original form, the system is con ned to categorical and discrete multivariate data. The aim is to build a classi cation tree when, at each level of the tree, only binary splits are allowed. Within a one-level taxonomy formation, a systematic search is performed for pairs of variables whose association is \strong enough" in some sense (in the original algorithm, measures based on the 2 statistic are used). If such pairs are found, one of them is selected on a rather heuristic basis to guide a split. Due to its algorithmic simplicity, the system can be considered suitable for data mining applications. In the talk, the methodology proposed, including some re nements, will be presented. In particular, (i) simple and admitting clear interpretation measures of association, introduced by Goodman and Kruskal, will be used in lieu of -like statistics; (ii) instead of using some heuristics, the choice of the pair to guide a split will be based on maximization of the socalled category utility (as suggested, e.g., in Fisher and Hapanyengwi (1993) and based either on entropy or on the Gini index); (iii) discretization of, and hence permitting, continuous variables will be proposed. The search for pairs of variables conductive to one-level taxonomy is mostly based on the classical measure. The strength of association within such a pair is then increased by suitably aggregating the values of the two variables. If an (approximate) equivalence relationship between the aggregated variables is thus obtained, it can be used to guide the split (both aggregation and the split can be aided by correspondence analysis of the contingency table involved).