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Interpretable dimension reduction for classifying functional data

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  • Tian, Tian Siva
  • James, Gareth M.

Abstract

Classification problems involving a categorical class label Y and a functional predictor X(t) are becoming increasingly common. Since X(t) is infinite dimensional, some form of dimension reduction is essential in these problems. Conventional dimension reduction techniques for functional data usually suffer from one or both of the following problems. First, they do not take the categorical response into consideration, and second, the resulting reduced subspace may have a complicated relationship with the original functional data. In this paper we propose a dimension reduction method, “Functional Adaptive Classification” (FAC), specifically designed for functional classification problems. FAC uses certain complexity constraints to ensure that the reduced subspace has an easily interpretable relationship to the original functional predictor. Extensive simulation studies and an fMRI (functional Magnetic Resonance Imaging) study show that FAC is extremely competitive in comparison to other potential approaches in terms of both classification accuracy and model interpretability.

Suggested Citation

  • Tian, Tian Siva & James, Gareth M., 2013. "Interpretable dimension reduction for classifying functional data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 282-296.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:282-296
    DOI: 10.1016/j.csda.2012.06.017
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    References listed on IDEAS

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    1. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768.
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    Cited by:

    1. Fraiman, Ricardo & Gimenez, Yanina & Svarc, Marcela, 2016. "Feature selection for functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 191-208.
    2. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    3. Mousavi, Seyed Nourollah & Sørensen, Helle, 2017. "Multinomial functional regression with wavelets and LASSO penalization," Econometrics and Statistics, Elsevier, vol. 1(C), pages 150-166.
    4. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-015-0738-3 is not listed on IDEAS

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