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Graph, clique and facet of boolean logical polytope

Author

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  • Kedong Yan

    (Nanjing University of Science and Technology)

  • Hong Seo Ryoo

    (Korea University)

Abstract

Logical analysis of data (LAD) discovers useful knowledge from a set of data in the form of a Boolean pattern for classifying future data. Generating a pattern has been shown to be equivalent to solving a 0–1 multilinear program (MP). Thus, the success of LAD is tightly related to how efficiently practical instances of pattern generation MP’s can be solved. For a polyhedral relaxation of LAD pattern generation MP, this paper introduces a new notion of similarity among data that allows for simultaneously relaxing multiple terms of the objective function of MP into a single valid inequality for the Boolean MP polytope. Specifically, we present a framework for constructing three types of strong valid inequalities from cliques in multiple graph representations of data that collectively yield a tight polyhedral relaxation of MP. Furthermore, we specify conditions under which each type of the new inequalities defines a facet of the MP polytope. In comparison with methods from the literature, benefits of the new inequalities are validated through classification experiments with 8 public machine learning datasets.

Suggested Citation

  • Kedong Yan & Hong Seo Ryoo, 2022. "Graph, clique and facet of boolean logical polytope," Journal of Global Optimization, Springer, vol. 82(4), pages 1015-1052, April.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:4:d:10.1007_s10898-021-01107-x
    DOI: 10.1007/s10898-021-01107-x
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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.
    3. Alberto Del Pia & Aida Khajavirad, 2017. "A Polyhedral Study of Binary Polynomial Programs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 389-410, May.
    4. Ahmed Ragab & Mohamed-Salah Ouali & Soumaya Yacout & Hany Osman, 2016. "Remaining useful life prediction using prognostic methodology based on logical analysis of data and Kaplan–Meier estimation," Journal of Intelligent Manufacturing, Springer, vol. 27(5), pages 943-958, October.
    5. Jocelyn, Sabrina & Chinniah, Yuvin & Ouali, Mohamed-Salah & Yacout, Soumaya, 2017. "Application of logical analysis of data to machinery-related accident prevention based on scarce data," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 223-236.
    6. M. W. Brauner & N. Brauner & P. L. Hammer & I. Lozina & D. Valeyre, 2007. "Logical Analysis of Computed Tomography Data to Differentiate Entities of Idiopathic Interstitial Pneumonias," Springer Optimization and Its Applications, in: Panos M. Pardalos & Vladimir L. Boginski & Alkis Vazacopoulos (ed.), Data Mining in Biomedicine, pages 193-208, Springer.
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    Cited by:

    1. Camur, Mustafa C. & Sharkey, Thomas C. & Vogiatzis, Chrysafis, 2023. "The stochastic pseudo-star degree centrality problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 525-539.
    2. Hoai An Le Thi & Tao Pham Dinh & Yaroslav D. Sergeyev, 2022. "Preface to the special issue dedicated to the 6th World Congress on Global Optimization held in Metz, France, July 8–10, 2019," Journal of Global Optimization, Springer, vol. 82(4), pages 655-657, April.

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