Closed Sets for Labeled Data

Abstract

Closed sets are being successfully applied in the context of compacted data representation for association rule learning. However, their use is mainly descriptive. This paper shows that, when considering labeled data, closed sets can be adapted for prediction and discrimination purposes by conveniently contrasting covering properties on positive and negative examples. We formally justify that these sets characterize the space of relevant combinations of features for discriminating the target class. In practice, identifying relevant/irrelevant combinations of features through closed sets is useful in many applications. Here we apply it to compacting emerging patterns and essential rules and to learn descriptions for subgroup discovery.

Feature Construction Based on Closedness Properties Is Not That Simple

“…In, e.g., [1,5], the authors mine free itemsets and closed itemsets (i.e., CECs) once the class attribute has been removed from the entire database. Other proposals, e.g., [3,4], consider (closed) itemset mining from samples of each class separately.…”

“…Indeed, when considering contingency tables (See Tab. 2), for all the studied approaches, f * 1 and f * 0 are known (class distribution). However, if we consider the proposals from [3,4] based on frequent closed itemsets mined per class, we get directly the value f 11 (i.e., f req(X ∪ c, r)) and the value for f 01 can be inferred. Closure equivalence classes in [5] only inform us on f 1 * (i.e., f req(X, r)) and f 0 * .…”

“…Based on a set of original features, the idea is to compute new features that may better describe labeled samples such that the predictive accuracy of classifiers can be improved. When considering the case of 0/1 data (i.e., in most of the cases, collections of attribute-value pairs that are true or not within a sample), several authors have proposed to look at feature construction based on patterns that satisfy closedness-related constraints [1,2,3,4,5,6]. Using patterns that hold in 0/1 data as features (e.g., itemsets or association rules) is not new.…”

“…Moreover, a few researchers have considered condensed representations of frequent sets for feature construction. Garriga et al [3] have proposed to characterize a target class with a collection of relevant closed itemsets. Li et al [1] invoke MDL principle and suggest that free itemsets might be better than closed ones.…”

Difference-Based Estimates for Generalization-Aware Subgroup Discovery

“…Although other interestingness measures can be adapted accordingly, we focus on these two families of generalization-aware measures in this paper, since they are the only ones, which have been described in previous literature and applied in practical applications. We will also not argue about advantages of these functions in comparison to traditional measures or other methods that avoid redundant output, such as closed pattern [12], but focus on efficient mining for these generalization-aware measures by introducing novel, difference-based optimistic estimates.…”