Partition triples: A tool for reduction of data sets

Abstract

Data sets discussed in this paper are presented as tables with rows corresponding to examples (entities, objects) and columns to attributes. A partition triple is defined for such a table as a triple of partitions on the set of examples, the set of attributes, and the set of attribute values, respectively, preserving the structure of a table. The idea of a partition triple is an extension of the idea of a partition pair, introduced by J. Hartmanis and J. Stearns in automata theory. Results characterizing partition triples and algorithms for computing partition triples are presented. The theory is illustrated by an example of an application in machine learning from examples. © 1996 Academic Press, Inc.