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Bi-criteria optimization of decision trees with applications to data analysis

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  • Chikalov, Igor
  • Hussain, Shahid
  • Moshkov, Mikhail

Abstract

This paper is devoted to the study of bi-criteria optimization problems for decision trees. We consider different cost functions such as depth, average depth, and number of nodes. We design algorithms that allow us to construct the set of Pareto optimal points (POPs) for a given decision table and the corresponding bi-criteria optimization problem. These algorithms are suitable for investigation of medium-sized decision tables. We discuss three examples of applications of the created tools: the study of relationships among depth, average depth and number of nodes for decision trees for corner point detection (such trees are used in computer vision for object tracking), study of systems of decision rules derived from decision trees, and comparison of different greedy algorithms for decision tree construction as single- and bi-criteria optimization algorithms.

Suggested Citation

  • Chikalov, Igor & Hussain, Shahid & Moshkov, Mikhail, 2018. "Bi-criteria optimization of decision trees with applications to data analysis," European Journal of Operational Research, Elsevier, vol. 266(2), pages 689-701.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:689-701
    DOI: 10.1016/j.ejor.2017.10.021
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    1. Frini, Anissa & Guitouni, Adel & Martel, Jean-Marc, 2012. "A general decomposition approach for multi-criteria decision trees," European Journal of Operational Research, Elsevier, vol. 220(2), pages 452-460.
    2. Abellán, Joaquín & Masegosa, Andrés R., 2010. "An ensemble method using credal decision trees," European Journal of Operational Research, Elsevier, vol. 205(1), pages 218-226, August.
    3. Pawlak, Zdzisaw & Sowinski, Roman, 1994. "Rough set approach to multi-attribute decision analysis," European Journal of Operational Research, Elsevier, vol. 72(3), pages 443-459, February.
    4. Muller, Wolfgang & Wiederhold, Eckhard, 2002. "Applying decision tree methodology for rules extraction under cognitive constraints," European Journal of Operational Research, Elsevier, vol. 136(2), pages 282-289, January.
    5. Jose Pangilinan & Gerrit Janssens, 2011. "Pareto-optimality of oblique decision trees from evolutionary algorithms," Journal of Global Optimization, Springer, vol. 51(2), pages 301-311, October.
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    Cited by:

    1. Blanquero, Rafael & Carrizosa, Emilio & Molero-Río, Cristina & Morales, Dolores Romero, 2022. "On sparse optimal regression trees," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1045-1054.
    2. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.

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