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Strong valid inequalities for Boolean logical pattern generation

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  • Kedong Yan

    (Korea University)

  • Hong Seo Ryoo

    (Korea University)

Abstract

0–1 multilinear programming (MP) captures the essence of pattern generation in logical analysis of data (LAD). This paper utilizes graph theoretic analysis of data to discover useful neighborhood properties among data for data reduction and multi-term linearization of the common constraint of an MP pattern generation model in a small number of stronger valid inequalities. This means that, with a systematic way to more efficiently generating Boolean logical patterns, LAD can be used for more effective analysis of data in practice. Mathematical properties and the utility of the new valid inequalities are illustrated on small examples and demonstrated through extensive experiments on 12 real-life data mining datasets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:1:d:10.1007_s10898-017-0512-2
    DOI: 10.1007/s10898-017-0512-2
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    References listed on IDEAS

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    1. Gabriela Alexe & Sorin Alexe & Peter Hammer & Bela Vizvari, 2006. "Pattern-based feature selection in genomics and proteomics," Annals of Operations Research, Springer, vol. 148(1), pages 189-201, November.
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    Cited by:

    1. 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.
    2. Guo, Cui & Ryoo, Hong Seo, 2021. "On Pareto-Optimal Boolean Logical Patterns for Numerical Data," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Kedong Yan & Hong Seo Ryoo, 2019. "A multi-term, polyhedral relaxation of a 0–1 multilinear function for Boolean logical pattern generation," Journal of Global Optimization, Springer, vol. 74(4), pages 705-735, August.

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