Non-redundant Subgroup Discovery Using a Closure System

Abstract

Abstract. Subgroup discovery is a local pattern discovery task, in which descriptions of subpopulations of a database are evaluated against some quality function. As standard quality functions are functions of the described subpopulation, we propose to search for equivalence classes of descriptions with respect to their extension in the database rather than individual descriptions. These equivalence classes have unique maximal representatives forming a closure system. We show that minimum cardinality representatives of each equivalence class can be found during the enumeration process of that closure system without additional cost, while finding a minimum representative of a single equivalence class is NP-hard. With several real-world datasets we demonstrate that search space and output are significantly reduced by considering equivalence classes instead of individual descriptions and that the minimum representatives constitute a family of subgroup descriptions that is of same or better expressive power than those generated by traditional methods.

An enhanced relevance criterion for more concise supervised pattern discovery

“…In [3] it has already been shown that closed subgroups very much reduce the number of patterns in comparison to all possible patterns, while in [7] it has been shown that going from closed pattern to relevant patterns again very much reduces the amount of patterns found. Hence, it suffices to show that going from relevant patterns, i.e.…”

“…Every ∆-relevant pattern is closed on the positives, meaning that the ∆-relevant patterns is a subset of the well-known closed patterns [6,3]. Compared to heuristic approaches for redundancy avoidance, like weighted covering [13] or beam selection strategies [22], ∆-relevance is a principled approach that provides formal guarantees on the quality of the result.…”

Subgroup Discovery Algorithms: A Survey and Empirical Evaluation

“…A number of popular methods [11][12][13] implement this pruning technique. Some subgroup discovery methods [20][21] implement the optimistic estimate as a pruning criterion which has been defined in [18] as follows Definition 1 (Optimistic Estimate). An optimistic estimate oe(s) for a given quality function q is a function that satisfies the following: ∀ subgroups s, s ′ .…”

Efficiently Discovering Locally Exceptional Yet Globally Representative Subgroups

“…Whereas subgroup discovery [17] is well-studied in general [2], [4], [8], [12], [19], [24], to the best of our knowledge i end ← min{π * 1 , n 1 (Q)}; 10 for i from i beg to i end do…”