Classification of Functional Data by Detecting the Discrepancy of Second Moment Structure of Scaled functions
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This article presents a new classification method for functional data. We consider the case where different groups of functions have similar means so that it is difficult to classify them using only the mean function. To overcome this limitation, we propose the second moment-based functional classifier (SMFC). Here, we demonstrate that the new method is sensitive to divergence in the second moment structure and thus produces lower rate of misclassification compared to competitor methods. Our method uses the Hilbert-Schmidt norm to measure the divergence of second moment structure. One important innovation of our classification procedure lies in the dimension reduction step, where the SMFC method data-adaptively determines the basis functions that account for the difference of second moment structure rather than the functional principal component of each individual group, and good performance can be achieved as unnecessary variability is removed so that the classification accuracy is improved. Consistency properties of the classification procedure and the relevant estimators are established. Simulation study and real data analysis on phoneme and rat brain activity trajectories empirically validates the superiority of the proposed method.
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