Functional data classification: a wavelet approach (original) (raw)

Abstract

In recent years, several methods have been proposed to deal with functional data classification problems (e.g., one-dimensional curves or two- or three-dimensional images). One popular general approach is based on the kernel-based method, proposed by Ferraty and Vieu (Comput Stat Data Anal 44:161–173, 2003). The performance of this general method depends heavily on the choice of the semi-metric. Motivated by Fan and Lin (J Am Stat Assoc 93:1007–1021, 1998) and our image data, we propose a new semi-metric, based on wavelet thresholding for classifying functional data. This wavelet-thresholding semi-metric is able to adapt to the smoothness of the data and provides for particularly good classification when data features are localized and/or sparse. We conduct simulation studies to compare our proposed method with several functional classification methods and study the relative performance of the methods for classifying positron emission tomography images.

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Acknowledgments

The research was supported in part by NIH grants (5 R01 EB009744-03 and 5 R01 MH099003-02) and grants from the National Science Council of Taiwan (NSC 100-2118-M-110-004 and NSC 100-2118-M-110-004).

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Authors and Affiliations

1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, Republic of China
   Chung Chang
2. Department of Biostatistics, Columbia University, New York, NY, USA
   Yakuan Chen & R. Todd Ogden

Authors

1. Chung Chang
2. Yakuan Chen
3. R. Todd Ogden

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Correspondence toChung Chang.

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Chang, C., Chen, Y. & Ogden, R.T. Functional data classification: a wavelet approach.Comput Stat 29, 1497–1513 (2014). https://doi.org/10.1007/s00180-014-0503-4

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• Received: 01 August 2013
• Accepted: 08 May 2014
• Published: 04 June 2014
• Issue date: December 2014
• DOI: https://doi.org/10.1007/s00180-014-0503-4

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