Closed Itemsets and Minimal Generators: A Comparison of Their Effects on Associative Classifiers

Abstract Associative classification (AC) is a well-established family of interpretable classifiers that combines association rule mining with supervised learning. Despite decades of research, a fundamental design choice remains largely unexamined: whether classifiers should be built from general rules, derived from minimal generators (MGs), or from more specific rules, derived from closed itemsets (CIs). While general rules are often assumed to generalize better, CI-based approaches are computationally more efficient and provide a lossless condensed representation of the rule space. However, their practical impact on classification performance has never been systematically isolated and evaluated. In this work, we present a comprehensive empirical study that disentangles rule generality from other algorithmic design choices. Across twenty public datasets with varying characteristics, we construct associative classifiers using either MG-based or CI-based rules, while keeping all other components -- rule ranking, selection strategy, and prediction mechanism -- strictly identical. Both coverage-based and lazy-based classifier construction strategies are considered, and performance is evaluated using multiple metrics, including accuracy, balanced accuracy, and F1-score. Our results show that classifiers built from MGs and CIs achieve nearly identical predictive performance and often rely on rules from the same equivalence classes, resulting in highly similar classification behavior. In contrast, CI-based approaches offer substantial computational advantages, significantly reducing rule-mining and classifier-construction costs. These findings challenge the prevailing reliance on general-purpose frequent itemset mining in AC and provide strong empirical support for adopting CI-based mining as the default strategy, without sacrificing effectiveness or interpretability.