Closed Sets for Labeled Data

TLDR

Closed sets have proven effective for compacted data representation in association rule learning, yet they have largely been applied only descriptively to unlabeled data. The paper adapts closed sets for classification and discrimination on labeled data by contrasting covering properties on positive and negative examples. The authors formally prove that closed sets characterize the space of relevant feature combinations for discriminating the target class. Closed sets effectively identify relevant and irrelevant feature combinations, reducing rule counts in classification and enabling efficient subgroup discovery, as shown in high‑dimensional microarray experiments.

Abstract

Closed sets have been proven successful in the context of compacted data representation for association rule learning. However, their use is mainly descriptive, dealing only with unlabeled data. This paper shows that when considering labeled data, closed sets can be adapted for classification and discrimination purposes by conveniently contrasting covering properties on positive and negative examples. We formally prove 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: to compact emerging patterns of typical descriptive mining applications, to reduce the number of essential rules in classification, and to efficiently learn subgroup descriptions, as demonstrated in real-life subgroup discovery experiments on a high dimensional microarray data set.