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Chung Chang

2011-12-30
15:00:00 - 16:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In recent years, lots of methods have been proposed to deal with functional data classification problems. One of the approaches is the kernel-based method, proposed by Ferraty and Vieu. The idea of their method is to define a semi- metric to compute the distance between functions and use a kernel-type estimator to estimate the conditional probability to classify each function. However, the performance of their method is largely affected by the choice of the semi-metric. Motivated by Fan and Lin (1998), we proposed a new semi-metric, based on wavelet thresholding to classify the functional data. A wavelet-thresholding semi-metric has advantages for adapting the smoothness of data and is especially powerful for classification when data are sparse. We will present some simulation results to compare different semi-metrics and explain why some of the semi-metrics do not work. A brief discussion about the relationship between the proposed semi-metric and Euclidean distance will be given. Although we are using curves as examples in this talk, the proposed method can be used for 2- or 3-dimensional images as well.