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Supervised classification of curves via a combined use of functional data analysis and tree-based methods

Author

Listed:
  • Fabrizio Maturo

    (University of Campania Luigi Vanvitelli)

  • Rosanna Verde

    (University of Campania Luigi Vanvitelli)

Abstract

Technological advancement led to the development of tools to collect vast amounts of data usually recorded at temporal stamps or arriving over time, e.g. data from sensors. Common ways of analysing this kind of data also involve supervised classification techniques; however, despite constant improvements in the literature, learning from high-dimensional data is always a challenging task due to many issues such as, for example, dealing with the curse of dimensionality and looking for a trade-off between complexity and accuracy. Nowadays, research in functional data analysis (FDA) and statistical learning is very lively to address these drawbacks adequately. This study offers a supervised classification strategy that combines FDA and tree-based procedures. Specifically, we introduce functional classification trees, functional bagging, and functional random forest exploiting the functional principal components decomposition as a tool to extract new features and build functional classifiers. In addition, we introduce new tools to support the understanding of the classification rules, such as the functional empirical separation prototype, functional predicted separation prototype, and the leaves’ functional deviance. Furthermore, we suggest some possible solutions for choosing the number of functional principal components and functional classification trees to be implemented in the supervised classification procedure. This research aims to provide an approach to improve the accuracy of the functional classifier, serve the interpretation of the functional classification rules, and overcome the classical drawbacks due to the high-dimensionality of the data. An application on a real dataset regarding daily electrical power demand shows the functioning of the supervised classification proposal. A simulation study with nine scenarios highlights the performance of this approach and compares it with other functional classification methods. The results demonstrate that this line of research is exciting and promising; indeed, in addition to the benefits of the suggested interpretative tools, we exceed the previously established accuracy records on a dataset available online.

Suggested Citation

  • Fabrizio Maturo & Rosanna Verde, 2023. "Supervised classification of curves via a combined use of functional data analysis and tree-based methods," Computational Statistics, Springer, vol. 38(1), pages 419-459, March.
  • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01236-1
    DOI: 10.1007/s00180-022-01236-1
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    References listed on IDEAS

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    1. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    2. Bongiorno, Enea G. & Goia, Aldo, 2019. "Describing the concentration of income populations by functional principal component analysis on Lorenz curves," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 10-24.
    3. Neska Haouij & Jean-Michel Poggi & Raja Ghozi & Sylvie Sevestre-Ghalila & Mériem Jaïdane, 2019. "Random forest-based approach for physiological functional variable selection for driver’s stress level classification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 157-185, March.
    4. Gregorutti, Baptiste & Michel, Bertrand & Saint-Pierre, Philippe, 2015. "Grouped variable importance with random forests and application to multiple functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 15-35.
    5. Fabrizio Maturo & Antonio Balzanella & Tonio Di Battista, 2019. "Building Statistical Indicators of Equitable and Sustainable Well-Being in a Functional Framework," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(3), pages 449-471, December.
    6. Cristian Preda & Gilbert Saporta & Caroline Lévéder, 2007. "PLS classification of functional data," Computational Statistics, Springer, vol. 22(2), pages 223-235, July.
    7. Nerini, David & Ghattas, Badih, 2007. "Classifying densities using functional regression trees: Applications in oceanology," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4984-4993, June.
    8. Manuel Escabias & Ana Aguilera & M. Aguilera-Morillo, 2014. "Functional PCA and Base-Line Logit Models," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 296-324, October.
    9. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    10. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    11. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    12. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    13. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    14. Francisco Ocaña & Ana Aguilera & Manuel Escabias, 2007. "Computational considerations in functional principal component analysis," Computational Statistics, Springer, vol. 22(3), pages 449-465, September.
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