Skip to main content
Log in

Unbiased recursive decision tree for supervised functional data classification with applying on electrocardiogram signals

  • Regular Paper
  • Published:
International Journal of Data Science and Analytics Aims and scope Submit manuscript

Abstract

Tree-structured methods are considered one of the most powerful tools in classification and regression. Nowadays, Machine Learning for functional data is gaining great attention in different fields. Tree-based models for functional variables are limited; and therefore, there are in a need to propose an efficient classifier in this active area. The current study focuses on the supervised classification of functional data considering functional covariates and multiclass responses. The traditional binary tree approach is extended into a functional framework combining functional tree-based classification (FCT). Two data-driven approaches, including Fourier transformation and functional derivation, are conformed to process data. The conditional recursive partitioning and functional permutation test are employed to search the independence structure between functional inputs. The Bonferroni P-value adjustment and some hyperparameters are utilized to determine the optimal splitting and control tree growth. The obtained results from comprehensive simulation studies implementation are compared favorably with existing methods and showed a good performance in both of computational time and classification accuracy. Additionally, the applied electrocardiogram dataset demonstrates the usefulness and advantage of the proposed FCT method. The current study findings confirm that the proposed method is more reliable and give a high correct classification rate. Generally, this research line is promising and makes the analysis understandable and informative in the medical data classification context.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Breiman, L., Friedman, J., Olshen, R., Stone, C.: Classification and Regression Trees. Wadsworth International Group, California (1984). https://zbmath.org/0541.62042

  2. Schlosser, L., Hothorn, T., Torsten, A.: The Power of Unbiased Recursive Partitioning: A Unifying View of CTree, MOB, and GUIDE. arXiv Preprint arXiv:1906.10179 (2019)

  3. Hothorn, T., Hornik, K., Zeileis, A.: Unbiased recursive partitioning: a conditional inference framework. J. Comput. Graph. Stat. 15(3), 651–674 (2006). https://doi.org/10.1198/106186006X133933

    Article  MathSciNet  Google Scholar 

  4. Zeileis, A., Hothorn, T., Hornik, K.: Model-based recursive partitioning. J. Comput. Graph. Stat. 17(2), 492–514 (2008)

    Article  MathSciNet  Google Scholar 

  5. Strasser, H., Weber, C.: On the asymptotic theory of permutation statistics. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business (1999)

  6. Ghattas, B., Michel, P., Boyer, L.: Clustering nominal data using unsupervised binary decision trees: comparisons with the state of the art methods. Pattern Recognit. 67, 177–185 (2017)

    Article  Google Scholar 

  7. Nespoli, G.: Classification and Regression Energy Tree with Net-work Predictors. Sapienza Università di Roma (2019)

    Google Scholar 

  8. Ramsay, J.O., Silverman, B.W.: Functional Data Analysis. Springer Series in Statistics, Springer, New York (2005)

    Book  MATH  Google Scholar 

  9. Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics, Springer, New York (2006)

    MATH  Google Scholar 

  10. Febrero-bande, M., Oviedo, M.: Statistical computing in functional data analysis: the R package fda.usc. J. Stat. Softw. (2012). https://doi.org/10.18637/jss.v051.i04

    Article  Google Scholar 

  11. Balakrishnan, S., Madigan, D.: Decision trees for functional variables. In: Sixth International Conference on Data Mining (ICDM’06). IEEE, pp. 798–802 (2006). https://doi.org/10.1109/ICDM.2006.49

  12. Nerini, D., Ghattas, B.: Classifying densities using functional regression trees: applications in oceanology. Comput. Stat. Data Anal. 51(10), 4984–4993 (2007). https://doi.org/10.1016/j.csda.2006.09.028

    Article  MathSciNet  MATH  Google Scholar 

  13. Brandi, M.: Classification and Regression Energy Tree for Functional Data. Sapienza Università di Roma (2018)

    Google Scholar 

  14. Belli, E., Vantini, S.: Measure inducing classification and regression trees for functional data. Stat. Anal. Data Min. (2021). https://doi.org/10.1002/sam.11569

    Article  Google Scholar 

  15. Golovkine, S., Klutchnikoff, N., Patilea, V.: Clustering multivariate functional data using unsupervised binary trees. Comput. Stat. Data Anal. 168, 1–38 (2022). https://doi.org/10.1016/j.csda.2021.107376

    Article  MathSciNet  MATH  Google Scholar 

  16. Maturo, F., Verde, R.: Pooling random forest and functional data analysis for biomedical signals supervised classification: theory and application to electrocardiogram data. Stat. Med. (2022). https://doi.org/10.1002/sim.9353

    Article  MathSciNet  Google Scholar 

  17. Hael, M.A., Ma, H., Al-kuhali, H.A.: Unsupervised classification of wind speed directions based on functional discriminative latent mixture model. In: 2021 12th International Symposium on Parallel Architectures, Algorithms and Programming, pp. 110–118 (2021). https://doi.org/10.1109/PAAP54281.2021.9720313

  18. Ramsay, J.O., Silverman, B.W.: The Roughness Penalty Approach. Springer Series in Statistics, Springer, New York (1997)

    Book  Google Scholar 

  19. Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215–223 (1979). https://doi.org/10.1080/00401706.1979.10489751

    Article  MathSciNet  MATH  Google Scholar 

  20. Ramsay, J.O., Wickham, H., Graves, S.: fda: functional data analysis. https://cran.r-project.org/package=fda (2021)

  21. Oviedo, M., Fuente, D., Galeano, P., Nieto, A., Garcia-portugues, E.: “Package ‘fda.usc,’” Art. No. R package version 2.0.2. https://cran.r-project.org/package=fda.usc (2020)

  22. Hothorn, T., Hornik, K., Strobl, C., Zeileis, A.: party: a toolkit for recursive partitioning (2021). https://doi.org/10.1198/106186006X133933

  23. Hothorn, T., Seibold, H., Zeileis, A.: partykit: a toolkit for recursive partytioning. http://partykit.r-forge.r-project.org/partykit/ (2021)

  24. Hothorn, T., Zeileis, A.: partykit: a modular toolkit for recursive partytioning in R. J. Mach. Learn. Res. 16, 3905–3909 (2015)

    MathSciNet  MATH  Google Scholar 

  25. Oviedo, M., Febrero-Bander, M.: fda.tsc: functional data sets for time series classification. https://github.com/moviedo5/fda.tsc/ (2019)

  26. Schmutz, J., Bouveyron, C., Jacques, J.: Package ‘funHDDC.’ https://cran.r-project.org/package=funHDDC (2021)

  27. Schmutz, A., Jacques, J., Bouveyron, C., Chèze, L., Martin, P.: Clustering multivariate functional data in group-specific functional subspaces. Comput. Stat. 35(3), 1101–1131 (2020). https://doi.org/10.1007/s00180-020-00958-4

    Article  MathSciNet  MATH  Google Scholar 

  28. Olszewski, R.: Generalized Feature Extraction for Structural Pattern Recognition in Time-Series Data. Carnegie Mellon University, Pittsburgh (2001)

    Google Scholar 

  29. Bagnall, A., Jason, L., William, V., Eamonn, K.: The UEA & UCR time series classification repository. http://www.timeseriesclassification.com/ (2021)

  30. Baragilly, M., Gabr, H., Willis, B.H.: Clustering functional data using forward search based on functional spatial ranks with medical applications. Stat. Methods Med. Res. 31(1), 47–61 (2022). https://doi.org/10.1177/09622802211002865

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohanned Abduljabbar Hael.

Ethics declarations

Conflict of interest

The author declares no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hael, M.A. Unbiased recursive decision tree for supervised functional data classification with applying on electrocardiogram signals. Int J Data Sci Anal 16, 441–454 (2023). https://doi.org/10.1007/s41060-023-00410-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41060-023-00410-y

Keywords

Navigation