Abstract
This study describes the application of four adaptive differential evolution algorithms to generate oblique decision trees. A population of decision trees encoded as real-valued vectors evolves through a global search strategy. Three schemes to create the initial population of the algorithms are applied to reduce the number of redundant nodes (whose test condition does not divide the set of instances). The results obtained in the experimental study aim to establish that the four algorithms have similar statistical behavior. However, using the dipole-based start strategy, the JSO method creates trees with better accuracy. Furthermore, the Success-History based Adaptive Differential Evolution with linear population reduction (LSHADE) algorithm stands out for inducing more compact trees than those created by the other variants in the three initializations evaluated.
Mexico’s National Council of Humanities, Science, and Technology (CONAHCYT) awarded a scholarship to the first author (CVU 1100085) for graduate studies at the Laboratorio Nacional de Informática Avanzada (LANIA).
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References
Bobrowski, L.: Piecewise-linear classifiers, formal neurons and separability of the learning sets. In: Proceedings of 13th International Conference on Pattern Recognition, vol. 4, pp. 224–228 (1996)
Breiman, L., Friedman, J., Olshen, R., Stone, C.: Classification and Regression Trees. Chapman and Hall (1984)
Brest, J., Maučec, M.S., Bošković, B.: Single objective real-parameter optimization: algorithm jSO. In: CEC 2017, pp. 1311–1318 (2017)
Cantú-Paz, E., Kamath, C.: Using evolutionary algorithms to induce oblique decision trees. In: GECCO 2000, pp. 1053–1060 (2000)
Draa, A., Bouzoubia, S., Boukhalfa, I.: A sinusoidal differential evolution algorithm for numerical optimisation. Appl. Soft Comput. 27, 99–126 (2015)
Estivill-Castro, V., Gilmore, E., Hexel, R.: Constructing interpretable decision trees using parallel coordinates. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds.) ICAISC 2020. LNCS (LNAI), vol. 12416, pp. 152–164. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61534-5_14
Feoktistov, V.: Differential Evolution: In Search of Solutions. Springer, New York (2007). https://doi.org/10.1007/978-0-387-36896-2
Frank, E., Hall, M., Witten, I.: The WEKA Workbench. Online Appendix (2016). https://www.cs.waikato.ac.nz/ml/weka/Witten_et_al_2016_appendix.pdf
Freitas, A.R.R., Silva, R.C.P., Guimarães, F.G.: Differential evolution and perceptron decision trees for fault detection in power transformers. In: Snášel, V., Abraham, A., Corchado, E. (eds.) SOCO 2012. AISC, vol. 188, pp. 143–152. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-32922-7_15
García, S., Fernández, A., Luengo, J., Herrera, F.: A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft. Comput. 13, 959–977 (2009). https://doi.org/10.1007/s00500-008-0392-y
Ghosh, A., Das, S., Panigrahi, B.K., Das, A.K.: A noise resilient differential evolution with improved parameter and strategy control. In: CEC 2017, pp. 2590–2597 (2017)
Jariyavajee, C., Polvichai, J., Sirinaovakul, B.: Searching for splitting criteria in multivariate decision tree using adapted JADE optimization algorithm. In: SSCI 2019, pp. 2534–2540 (2019)
Kamath, U., Liu, J.: Explainable Artificial Intelligence: An Introduction to Interpretable Machine Learning. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-83356-5
Kelly, M., Longjohn, R., Nottingham, K.: The UCI Machine Learning Repository (2023). https://archive.ics.uci.edu
Krȩtowski, M.: An evolutionary algorithm for oblique decision tree induction. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 432–437. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24844-6_63
Kretowski, M.: Evolutionary Decision Trees in Large-Scale Data Mining. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21851-5
Liu, J., Lampinen, J.: A fuzzy adaptive differential evolution algorithm. Soft. Comput. 9, 448–462 (2005). https://doi.org/10.1007/s00500-004-0363-x
Lopes, R.A., Freitas, A.R.R., Silva, R.C.P., Guimarães, F.G.: Differential evolution and perceptron decision trees for classification tasks. In: Yin, H., Costa, J.A.F., Barreto, G. (eds.) IDEAL 2012. LNCS, vol. 7435, pp. 550–557. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32639-4_67
Murthy, S.K., Kasif, S., Salzberg, S., Beigel, R.: OC1: a randomized algorithm for building oblique decision trees. In: AAAI 1993, vol. 93, pp. 322–327 (1993)
Nebro, A.J., Durillo, J.J., Vergne, M.: Redesigning the jMetal multi-objective optimization framework. In: GECCO 2015, pp. 1093–1100 (2015)
Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31306-0
Quinlan, J.R.: Induction of decision trees. Mach. Learn. 1(1), 81–106 (1986). https://doi.org/10.1007/BF00116251
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann (1993)
Rivera-Lopez, R., Canul-Reich, J.: A global search approach for inducing oblique decision trees using differential evolution. In: Mouhoub, M., Langlais, P. (eds.) AI 2017. LNCS (LNAI), vol. 10233, pp. 27–38. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57351-9_3
Rivera-Lopez, R., Canul-Reich, J., Gámez, J.A., Puerta, J.M.: OC1-DE: a differential evolution based approach for inducing oblique decision trees. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10245, pp. 427–438. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59063-9_38
Sallam, K.M., Elsayed, S.M., Sarker, R.A., Essam, D.L.: Improved united multi-operator algorithm for solving optimization problems. In: CEC 2018, pp. 1–8 (2018)
Tanabe, R., Fukunaga, A.: Success-history based parameter adaptation for differential evolution. In: CEC 2013, pp. 71–78 (2013)
Tanabe, R., Fukunaga, A.S.: Improving the search performance of SHADE using linear population size reduction. In: CEC 2014, pp. 1658–1665 (2014)
Yeung, K., Lodge, M.: Algorithmic Regulation. Oxford University Press, Oxford (2019)
Zhang, J., Sanderson, A.C.: JADE: self-adaptive differential evolution with fast and reliable convergence performance. In: CEC 2007, pp. 2251–2258 (2007)
Zhang, Y., Tiňo, P., Leonardis, A., Tang, K.: A survey on neural network interpretability. IEEE Trans. Emerg. Top. Comput. Intell. 5(5), 726–742 (2021)
Zielinski, K., Laur, R.: Stopping criteria for differential evolution in constrained single-objective optimization. In: Chakraborty, U.K. (ed.) Advances in Differential Evolution. SCI, vol. 143, pp. 111–138. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68830-3_4
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Morales-Hernández, M.Á., Rivera-López, R., Mezura-Montes, E., Canul-Reich, J., Cruz-Chávez, M.A. (2024). Comparative Study of the Starting Stage of Adaptive Differential Evolution on the Induction of Oblique Decision Trees. In: Calvo, H., Martínez-Villaseñor, L., Ponce, H., Zatarain Cabada, R., Montes Rivera, M., Mezura-Montes, E. (eds) Advances in Computational Intelligence. MICAI 2023 International Workshops. MICAI 2023. Lecture Notes in Computer Science(), vol 14502. Springer, Cham. https://doi.org/10.1007/978-3-031-51940-6_34
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