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Abstract:
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In this paper, we propose a novel supervised classifier for functional data by applying multivariate functional depth. To classify functional data that have a group structure, we assume each group of the functional data is distributed from an underlying functional random variable that is m-times differential over a compact domain. To best capture the shape, amplitude and phase variations between groups of the functional data, we augment the original functional data by taking derivatives up to the m^th order. Our proposed classifier calculates, for each observation, the multivariate depth in which each element is its multivariate functional depth in each group. Assuming the multivariate depth follows a Gaussian distribution, we can predict the posterior probability of group membership for the new functional observation. The optimal order of the function derivatives to achieve the minimum misclassification rate is selected via cross-validation. We present a simulation study and some benchmark data examples to show the robust performance of our proposed supervised classifier.
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