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On Pareto-Optimal Boolean Logical Patterns for Numerical Data

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  • Guo, Cui
  • Ryoo, Hong Seo

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.

Suggested Citation

  • Guo, Cui & Ryoo, Hong Seo, 2021. "On Pareto-Optimal Boolean Logical Patterns for Numerical Data," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002010
    DOI: 10.1016/j.amc.2021.126153
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    References listed on IDEAS

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    1. Kedong Yan & Hong Seo Ryoo, 2017. "Strong valid inequalities for Boolean logical pattern generation," Journal of Global Optimization, Springer, vol. 69(1), pages 183-230, September.
    2. Yasser Shaban & Mouhab Meshreki & Soumaya Yacout & Marek Balazinski & Helmi Attia, 2017. "Process control based on pattern recognition for routing carbon fiber reinforced polymer," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 165-179, January.
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    7. Sorin Alexe & Eugene Blackstone & Peter Hammer & Hemant Ishwaran & Michael Lauer & Claire Pothier Snader, 2003. "Coronary Risk Prediction by Logical Analysis of Data," Annals of Operations Research, Springer, vol. 119(1), pages 15-42, March.
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