On Pareto-Optimal Boolean Logical Patterns for Numerical Data

Abstract

This paper clarifies the difference between intrinsically 0-1 data and binarized numerical data for Boolean logical patterns and strengthens mathematical results and methods from the literature on Pareto-optimal LAD patterns. Toward this end, we select suitable pattern definitions from the literature and adapt them with attention given to unique characteristics of individual patterns and the disparate natures of Boolean and numerical data. Next, we propose a set of revised criteria and definitions by which useful LAD patterns are clearly characterized for both 0-1 and real-valued data. Furthermore, we fortify recent pattern generation optimization models and demonstrate how earlier results on Pareto-optimal patterns can be adapted in accordance with revised pattern definitions. A numerical study validates practical benefits of the results of this paper through optimization-based pattern generation experiments. (C) 2021 Elsevier Inc. All rights reserved.