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Abstract:
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We propose the estimation procedures for nonlinear support vector machine (SVM) where the predictor is a vector of random functions and the response is labels. The relation between the response and predictor can be nonlinear and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads to a construction of two functional spaces: the first representing the functional data, assumed to be a Hilbert space, and the second characterizing nonlinear- ity, assumed to be a reproducing kernel Hilbert space. A particularly attractive feature of our construction is that the two spaces are nested, in the sense that the kernel for the second space is determined by the inner product of the first. We propose multiple estimators of varying complexities with respective effectiveness in differing situations. We apply this method to data sets on electroencephalogram (EEG) measurements for potentially alcoholic patients and on functional magnetic resonance imaging (fMRI) measurements for potentially attention deficit hyperactivity disorder (ADHD) patients.
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