Interpretable dimension reduction for classifying functional data
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.
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- Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
- Ferraty, Frederic & Vieu, Philippe & Viguier-Pla, Sylvie, 2007. "Factor-based comparison of groups of curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4903-4910, June.
- Jerome H. Friedman & Trevor Hastie & Rob Tibshirani, . "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, American Statistical Association, vol. 33(i01).
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
- Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
- Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
- 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.
- 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.
- 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.
- Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
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