This chapter presents data mining techniques that make use of metrics defined on the set of partitions of finite sets. Partitions are naturally associated with object attributes and major data mining problem such as classification, clustering, and data preparation benefit from an algebraic and geometric study of the metric space of partitions. The metrics we find most useful are derived from a generalization of the entropic metric. We discuss techniques that produce smaller classifiers, allow incremental clustering of categorical data and help user to better prepare training data for constructing classifiers. Finally, we discuss open problems and future research directions.
A Geometric Study of Wasserstein Spaces: An Addendum on the Boundary
