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Method of Training a Kernel Tree

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Abstract

Axis-parallel decision trees perform poorly on that multidimensional sparse data that are frequently input in many tasks. A straightforward solution is to create decision trees that have oblique splits; however, most training approaches have low performance. These models can easily overfit, so they should be combined with a random ensemble. This paper proposes an algorithm to train kernel decision trees. At each stump, the algorithm optimizes a loss function with a margin rescaling approach that simultaneously optimizes the margin and impurity criteria. We performed an experimental evaluation of several tasks, such as studying the reaction of social media users and image recognition. The experimental results show that the proposed algorithm trains ensembles that outperform other oblique or kernel forests in many datasets.

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REFERENCES

  1. Breiman, L., Friedman, J., Olshen, R., and Stone, C., Classification And Regression Trees, Routledge, 2017. https://doi.org/10.1201/9781315139470

    Book  Google Scholar 

  2. Chen, T. and Guestrin, C., XGBoost: A scalable tree boosting system, Proceedings of the 22nd ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, San Francisco, 2016, New York: Association for Computing Machinery, 2016, pp. 785–794. https://doi.org/10.1145/2939672.2939785

  3. Breiman, L., Random forests, Mach. Learn., 2001, vol. 45, no. 1, pp. 5–32. https://doi.org/10.1023/a:1010933404324

    Article  Google Scholar 

  4. Golea, M., Bartlett, P., Lee, W.S., and Mason, L., Generalization in decision trees and DNF: Does size matter?, Advances in Neural Information Processing Systems, Jordan, M., Kearns, M., and Solla, S., Eds., MIT Press, 1997, vol. 10. https://proceedings.neurips.cc/paper_files/paper/1997/file/4f87658ef0de194413056248-a00ce009-Paper.pdf.

  5. Vapnik, V.N., An overview of statistical learning theory, IEEE Trans. Neural Networks, 1999, vol. 10, no. 5, pp. 988–999. https://doi.org/10.1109/72.788640

    Article  CAS  PubMed  Google Scholar 

  6. Breiman, L., Technical note: Some properties of splitting criteria, Mach. Learn., 1996, vol. 24, no. 1, pp. 41–47. https://doi.org/10.1007/bf00117831

    Article  Google Scholar 

  7. Liu, W. and Tsang, I., Sparse perceptron decision tree for millions of dimensions, Proc. AAAI Conf. Artif. Intell., 2016, vol. 30, no. 1. https://doi.org/10.1609/aaai.v30i1.10247

  8. Liu, W. and Tsang, I.W., Making decision trees feasible in ultrahigh feature and label dimensions, J. Mach. Learn. Res., 2017, vol. 18, no. 1, pp. 2814–2849. https://doi.org/10.1142/9789811205675_0011

    Article  MathSciNet  Google Scholar 

  9. Bennett, K.P. and Blue, J.A., A support vector machine approach to decision trees, 1998 IEEE Int. Joint Conf. on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence, Anchorage, Alaska, 1998, IEEE, 1998, pp. 2396–2401. https://doi.org/10.1109/ijcnn.1998.687237

  10. Menze, B.H., Kelm, B.M., Splitthoff, D.N., Koethe, U., and Hamprecht, F.A., On oblique random forests, Machine Learning and Knowledge Discovery in Databases, Gunopulos, D., Hofmann, T., Malerba, D., and Vazirgiannis, M., Eds., Lecture Notes in Computer Science, vol. 6912, Berlin: Springer, 2011, pp. 453–469. https://doi.org/10.1007/978-3-642-23783-6_29

    Book  Google Scholar 

  11. Tibshirani, R. and Hastie, T., Margin trees for highdimensional classification, J. Mach. Learn. Res., 2007, vol. 8, no. 3, pp. 637–652.

    Google Scholar 

  12. Manwani, N. and Sastry, P.S., Geometric decision tree, IEEE Trans. Syst., Man, Cybern., Part B (Cybern.), 2011, vol. 42, no. 1, pp. 181–192. https://doi.org/10.1109/tsmcb.2011.2163392

    Article  Google Scholar 

  13. Hofmann, T., Schölkopf, B., and Smola, A.J., Kernel methods in machine learning, Ann. Stat., 2008, vol. 36, no. 3, pp. 1171–1220. https://doi.org/10.1214/009053607000000677

    Article  MathSciNet  Google Scholar 

  14. Norouzi, M., Collins, M.D., Fleet, D.J., and Kohli, P., CO2 forest: Improved random forest by continuous optimization of oblique splits, 2015. https://doi.org/10.48550/arXiv.1506.06155

  15. Tsochantaridis, I., Jochims, T., Hofmann, T., and Altun, Ya., Large margin methods for structured and interdependent output variables, J. Mach. Learn. Res., 2005, vol. 6, no. 9, pp. 1453–1484.

    MathSciNet  Google Scholar 

  16. Yuille, A.L. and Rangarajan, A., The concave-convex procedure, Neural Comput., 2003, vol. 15, no. 4, pp. 915–936. https://doi.org/10.1162/08997660360581958

    Article  CAS  PubMed  Google Scholar 

  17. DeSalvo, G. and Mohri, M., Random composite forests, Proc. AAAI Conf. Artif. Intell., 2016, vol. 30, no. 1. https://doi.org/10.1609/aaai.v30i1.10203

  18. Hehn, T.M., Kooij, J.F.P., and Hamprecht, F.A., End-to-end learning of decision trees and forests, Int. J. Comput. Vision, 2020, vol. 128, no. 4, pp. 997–1011. https://doi.org/10.1007/s11263-019-01237-6

    Article  MathSciNet  Google Scholar 

  19. İrsoy, O. and Alpaydin, E., Autoencoder trees, Proc. Mach. Learn. Res., 2016, vol. 45, pp. 378–390. http://proceedings.mlr.press/v45/Irsoy15.

  20. Chai, Z. and Zhao, C., Multiclass oblique random forests with dual-incremental learning capacity, IEEE Trans. Neural Networks Learn. Syst., 2020, vol. 31, no. 12, pp. 5192–5203. https://doi.org/10.1109/tnnls.2020.2964737

    Article  Google Scholar 

  21. Hecht-Nielsen, R., Theory of the backpropagation neural network, Neural Networks for Perception: Computation, Learning, and Architectures, Wechsler, H., Ed., Academic, 1992, pp. 65–93. https://doi.org/10.1016/b978-0-12-741252-8.50010-8

    Book  Google Scholar 

  22. Yang, B., Shen, S., and Gao, W., Weighted oblique decision trees, Proc. AAAI Conf. Artif. Intell., 2019, vol. 33, no. 1, pp. 5621–5627. https://doi.org/10.1609/aaai.v33i01.33015621

  23. Carreira-Perpinán, M.A. and Tavallali, P., Alternating optimization of decision trees, with application to learning sparse oblique trees, Adv. Neural Inf. Process. Syst., 2018, vol. 31. https://proceedings.neurips.cc/paper/2018/hash/185c29dc24325934ee377cfda20e414c-Abstract.html.

  24. Kumar, M.A. and Gopal, M., A hybrid SVM based decision tree, Pattern Recognit., 2010, vol. 43, no. 12, pp. 3977–3987. https://doi.org/10.1016/j.patcog.2010.06.010

    Article  ADS  Google Scholar 

  25. Krizhevsky, A., Learning multiple layers of features from tiny images, MSc Thesis, Toronto: Univ. of Toronto, 2009.

  26. YouTube channels dataset. http://keen.isa.ru/youtube. Cited July 14, 2022.

  27. Blake, C., UCI repository of machine learning databases. http://www.ics.uci.edu/~mlearn/MLRepository.html. Cited July 14, 2022.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Correspondence to D. A. Devyatkin or O. G. Grigoriev.

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Devyatkin, D.A., Grigoriev, O.G. Method of Training a Kernel Tree. Sci. Tech. Inf. Proc. 50, 390–396 (2023). https://doi.org/10.3103/S0147688223050040

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