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Supervised classification for functional data: A weighted distance approach

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  • Alonso, Andrés M.
  • Casado, David
  • Romo, Juan
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    Abstract

    A natural methodology for discriminating functional data is based on the distances from the observation or its derivatives to group representative functions (usually the mean) or their derivatives. It is proposed to use a combination of these distances for supervised classification. Simulation studies show that this procedure performs very well, resulting in smaller testing classification errors. Applications to real data show that this technique behaves as well as–and in some cases better than–existing supervised classification methods for functions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 7 ()
    Pages: 2334-2346

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2334-2346

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Supervised classification; Discriminant analysis; Functional data; Weighted distances;

    References

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    1. Chiou, Jeng-Min & Li, Pai-Ling, 2008. "Correlation-Based Functional Clustering via Subspace Projection," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1684-1692.
    2. C. Abraham & P. A. Cornillon & E. Matzner-Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B-Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595.
    3. Zhang, Zhen & Müller, Hans-Georg, 2011. "Functional density synchronization," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2234-2249, July.
    4. López-Pintado, Sara & Romo, Juan, 2011. "A half-region depth for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1679-1695, April.
    5. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    6. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 10(2), pages 419-440, December.
    7. James G.M. & Sugar C.A., 2003. "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 397-408, January.
    8. Cuesta-Albertos, Juan Antonio & Fraiman, Ricardo, 2007. "Impartial trimmed k-means for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4864-4877, June.
    9. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    10. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    11. Li, Bin & Yu, Qingzhao, 2008. "Classification of functional data: A segmentation approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4790-4800, June.
    12. 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.
    13. Jeng-Min Chiou & Pai-Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699.
    14. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
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    Cited by:
    1. Ramón Jesús Flores Díaz & Rosa E. Lillo & Juan Romo, 2014. "Homogeneity test for functional data based on depth measures," Statistics and Econometrics Working Papers ws140101, Universidad Carlos III, Departamento de Estadística y Econometría.
    2. Esdras Joseph & Pedro Galeano & Rosa E. Lillo, 2013. "The Mahalanobis distance for functional data with applications to classification," Statistics and Econometrics Working Papers ws131312, Universidad Carlos III, Departamento de Estadística y Econometría.
    3. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.

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