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Globally optimal clusterwise regression by mixed logical-quadratic programming

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  • Carbonneau, Réal A.
  • Caporossi, Gilles
  • Hansen, Pierre

Abstract

Exact global optimization of the clusterwise regression problem is challenging and there are currently no published feasible methods for performing this clustering optimally, even though it has been over thirty years since its original proposal. This work explores global optimization of the clusterwise regression problem using mathematical programming and related issues. A mixed logical-quadratic programming formulation with implication of constraints is presented and contrasted against a quadratic formulation based on the traditional big-M, which cannot guarantee optimality because the regression line coefficients, and thus errors, may be arbitrarily large. Clusterwise regression optimization times and solution optimality for two clusters are empirically tested on twenty real datasets and three series of synthetic datasets ranging from twenty to one hundred observations and from two to ten independent variables. Additionally, a few small real datasets are clustered into three lines.

Suggested Citation

  • Carbonneau, Réal A. & Caporossi, Gilles & Hansen, Pierre, 2011. "Globally optimal clusterwise regression by mixed logical-quadratic programming," European Journal of Operational Research, Elsevier, vol. 212(1), pages 213-222, July.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:1:p:213-222
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    References listed on IDEAS

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    Cited by:

    1. Reis dos Santos, M. Isabel & Reis dos Santos, Pedro M., 2016. "Switching regression metamodels in stochastic simulation," European Journal of Operational Research, Elsevier, vol. 251(1), pages 142-147.
    2. Adil M. Bagirov & Julien Ugon & Hijran G. Mirzayeva, 2015. "Nonsmooth Optimization Algorithm for Solving Clusterwise Linear Regression Problems," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 755-780, March.
    3. 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.
    4. Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    5. Young Woong Park & Yan Jiang & Diego Klabjan & Loren Williams, 2017. "Algorithms for Generalized Clusterwise Linear Regression," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 301-317, May.
    6. Bagirov, Adil M. & Ugon, Julien & Mirzayeva, Hijran, 2013. "Nonsmooth nonconvex optimization approach to clusterwise linear regression problems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 132-142.
    7. Joki, Kaisa & Bagirov, Adil M. & Karmitsa, Napsu & Mäkelä, Marko M. & Taheri, Sona, 2020. "Clusterwise support vector linear regression," European Journal of Operational Research, Elsevier, vol. 287(1), pages 19-35.

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