The Nature and Limits of Discriminative Patterns

Abstract

Discriminative pattern mining seeks patterns that are more prevalent in one class than another and provide good classification accuracy for the objects in which the patterns occur. A number of approaches have been proposed for finding such patterns, which are also known under a variety of names, e.g., contrast sets and emerging patterns. However, fundamental questions about the nature and limits of such patterns remain unanswered. For instance, a discriminative pattern is only interesting if it provides better discriminative power than any of its subpatterns, but it is not obvious, for example, how much additional discriminative power can be provided by a pattern over and above the discriminative power of its subpatterns. Also, what do the patterns that provide the most additional discrimination look like? And, what is the relationship of different measures for discrimination (e.g., mutual information and DiffSup, the difference of the supports in the two classes). In previous work, we made an initial attempt at analyzing the first two questions. In this paper we present several new developments. Specifically, we present a more elegant and efficient formulation of the problem of determining the best discriminative pattern that can be obtained for a particular number of variables. We also explore for the first time the limits of patterns that go beyond the 'and' logic of traditional pattern mining, e.g., patterns based on the logic of 'or', 'n of k' or 'majority wins'. We show that the discriminative advantage of 'and' based patterns over their subpatterns is more limited than that of some of the other patterns, and hence, these patterns may represent a potential area for future development of discriminative pattern mining. Finally, we explore the relationship of various measures of discriminative pattern mining. We show that our results, although based on one of the measures (DiffSup) have implications for mutual information. More generally, we identify a potential avenue of exploration, which although challenging, may offer the opportunity for making a more definitive and general statement about a certain class of discriminative measures.