Functional data classification: a wavelet approach |
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Authors: | Chung Chang Yakuan Chen R. Todd Ogden |
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Affiliation: | 1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, Republic of China 2. Department of Biostatistics, Columbia University, New York, NY, USA
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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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