IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v82y2022i4d10.1007_s10898-021-01107-x.html
   My bibliography  Save this article

Graph, clique and facet of boolean logical polytope

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-021-01107-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10898-021-01107-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guo, Cui & Ryoo, Hong Seo, 2021. "On Pareto-Optimal Boolean Logical Patterns for Numerical Data," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Lejeune, Miguel & Lozin, Vadim & Lozina, Irina & Ragab, Ahmed & Yacout, Soumaya, 2019. "Recent advances in the theory and practice of Logical Analysis of Data," European Journal of Operational Research, Elsevier, vol. 275(1), pages 1-15.
    3. Kedong Yan & Dongjing Miao & Cui Guo & Chanying Huang, 2021. "Efficient feature selection for logical analysis of large-scale multi-class datasets," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 1-23, July.
    4. 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.
    5. Mohamed Elhefnawy & Ahmed Ragab & Mohamed-Salah Ouali, 2023. "Polygon generation and video-to-video translation for time-series prediction," Journal of Intelligent Manufacturing, Springer, vol. 34(1), pages 261-279, January.
    6. Riku-Pekka Nikula & Konsta Karioja & Kauko Leiviskä & Esko Juuso, 2019. "Prediction of mechanical stress in roller leveler based on vibration measurements and steel strip properties," Journal of Intelligent Manufacturing, Springer, vol. 30(4), pages 1563-1579, April.
    7. Ahmed Elsheikh & Soumaya Yacout & Mohamed-Salah Ouali & Yasser Shaban, 2020. "Failure time prediction using adaptive logical analysis of survival curves and multiple machining signals," Journal of Intelligent Manufacturing, Springer, vol. 31(2), pages 403-415, February.
    8. Hussein A. Taha & Soumaya Yacout & Yasser Shaban, 2023. "Autonomous self-healing mechanism for a CNC milling machine based on pattern recognition," Journal of Intelligent Manufacturing, Springer, vol. 34(5), pages 2185-2205, June.
    9. S. Nadarajah & I. E. Okorie, 2021. "On the maximum and minimum for classes of univariate distributions," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(2), pages 290-309, April.
    10. Jie Yang & Shaowen Lu & Liangyong Wang, 2020. "Fused magnesia manufacturing process: a survey," Journal of Intelligent Manufacturing, Springer, vol. 31(2), pages 327-350, February.
    11. Xiang Li & Wei Zhang & Qian Ding & Jian-Qiao Sun, 2020. "Intelligent rotating machinery fault diagnosis based on deep learning using data augmentation," Journal of Intelligent Manufacturing, Springer, vol. 31(2), pages 433-452, February.
    12. Hemir da Cunha Santiago & José Carlos da Silva Cavalcanti & Ricardo Bastos Cavalcante Prudêncio & Mohamed A. Mohamed & Leonie Asfora Sarubbo & Attilio Converti & Manoel Henrique da Nóbrega Marinho, 2023. "A Novel Remaining Useful Estimation Model to Assist Asset Renewal Decisions Applied to the Brazilian Electric Sector," Energies, MDPI, vol. 16(6), pages 1-24, March.
    13. Li, Xiang & Zhang, Wei & Ding, Qian, 2019. "Deep learning-based remaining useful life estimation of bearings using multi-scale feature extraction," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 208-218.
    14. Leonardo Lozano & David Bergman & J. Cole Smith, 2020. "On the Consistent Path Problem," Operations Research, INFORMS, vol. 68(6), pages 1913-1931, November.
    15. 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.
    16. Gerardo Emanuel Granados & Loïc Lacroix & Kamal Medjaher, 2020. "Condition monitoring and prediction of solution quality during a copper electroplating process," Journal of Intelligent Manufacturing, Springer, vol. 31(2), pages 285-300, February.
    17. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:82:y:2022:i:4:d:10.1007_s10898-021-01107-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.