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Nonsmooth Optimization Algorithm for Solving Clusterwise Linear Regression Problems

Author

Listed:
  • Adil M. Bagirov

    (Federation University Australia)

  • Julien Ugon

    (Federation University Australia)

  • Hijran G. Mirzayeva

    (Federation University Australia)

Abstract

Clusterwise linear regression consists of finding a number of linear regression functions each approximating a subset of the data. In this paper, the clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem and an algorithm based on an incremental approach and on the discrete gradient method of nonsmooth optimization is designed to solve it. This algorithm incrementally divides the whole dataset into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate good starting points for solving global optimization problems at each iteration of the incremental algorithm. The algorithm is compared with the multi-start Späth and the incremental algorithms on several publicly available datasets for regression analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-014-0566-y
    DOI: 10.1007/s10957-014-0566-y
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    References listed on IDEAS

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    1. Preda, C. & Saporta, G., 2005. "Clusterwise PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 99-108, April.
    2. 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.
    3. Preda, C. & Saporta, G., 2005. "PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 149-158, January.
    4. 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.
    5. A. M. Bagirov & B. Karasözen & M. Sezer, 2008. "Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 317-334, May.
    6. Wayne DeSarbo & Richard Oliver & Arvind Rangaswamy, 1989. "A simulated annealing methodology for clusterwise linear regression," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 707-736, September.
    7. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
    8. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
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    Cited by:

    1. M. Golestani & H. Sadeghi & Y. Tavan, 2018. "Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 896-916, December.
    2. Shutong Chen & Weijun Xie, 2022. "On Cluster-Aware Supervised Learning: Frameworks, Convergent Algorithms, and Applications," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 481-502, January.
    3. Napsu Karmitsa, 2016. "Testing Different Nonsmooth Formulations of the Lennard–Jones Potential in Atomic Clustering Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 316-335, October.
    4. 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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