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A new column generation algorithm for Logical Analysis of Data

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  • Pierre Hansen
  • Christophe Meyer

Abstract

We present a new column generation algorithm for the determination of a classifier in the two classes LAD (Logical Analysis of Data) model. Unlike existing algorithms who seek a classifier that at the same time maximizes the margin of correctly classified observations and minimizes the amount of violations of incorrectly classified observations, we fix the margin to a difficult-to-achieve target and minimize a piecewise convex linear function of the violation of incorrectly classified observations. Moreover a part of the training set, called control set, is reserved to select, among all feasible classifiers found by the algorithm, the one with highest performance on that set. One advantage of the proposed algorithm is that it essentially does not require any calibration. Computational results are presented that show the effectiveness of this approach. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Pierre Hansen & Christophe Meyer, 2011. "A new column generation algorithm for Logical Analysis of Data," Annals of Operations Research, Springer, vol. 188(1), pages 215-249, August.
    • Handle: RePEc:spr:annopr:v:188:y:2011:i:1:p:215-249:10.1007/s10479-011-0850-2
    DOI: 10.1007/s10479-011-0850-2
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    References listed on IDEAS

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    1. Emilio Carrizosa & Belen Martin-Barragan & Dolores Romero Morales, 2010. "Binarized Support Vector Machines," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 154-167, February.
    2. Peter Hammer & Tibérius Bonates, 2006. "Logical analysis of data—An overview: From combinatorial optimization to medical applications," Annals of Operations Research, Springer, vol. 148(1), pages 203-225, November.
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    Cited by:

    1. 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.
    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. Maurizio Boccia & Antonio Sforza & Claudio Sterle, 2020. "Simple Pattern Minimality Problems: Integer Linear Programming Formulations and Covering-Based Heuristic Solving Approaches," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1049-1060, October.
    4. Chun-An Chou & Tibérius O. Bonates & Chungmok Lee & Wanpracha Art Chaovalitwongse, 2017. "Multi-pattern generation framework for logical analysis of data," Annals of Operations Research, Springer, vol. 249(1), pages 329-349, February.
    5. Réal Carbonneau & Gilles Caporossi & Pierre Hansen, 2014. "Globally Optimal Clusterwise Regression By Column Generation Enhanced with Heuristics, Sequencing and Ending Subset Optimization," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 219-241, July.
    6. 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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