Clustering Categorical Data: An Approach Based on Dynamical Systems

We describe a novel approach for clustering col-lections of sets, and its application to the analysis and mining of categorical data. By “categorical data, ” we mean tables with fields that cannot be naturally ordered by a metric- e.g., the names of producers of automobiles, or the names of prod-ucts offered by a manufacturer. Our approach is based on an iterative method for assigning and propagating weights on the categorical values in a table; this facilitates a type of similarity mea-sure arising from the co-occurrence of values in the dataset. Our techniques can be studied an-alytically in terms of certain types of non-linear dynamical systems. We discuss experiments on a variety of tables of synthetic and real data; we find that our iterative methods converge quickly to prominently correlated values of various cate-gorical fields.