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The intrinsically infinite-dimensional features of the functionalobservations over multidimensional domains render the standard classificationmethods effectively inapplicable. To address this problem, we introduce a novelmulticlass functional deep neural network (mfDNN) classifier as an innovativedata mining and classification tool. Specifically, we consider sparse deepneural network architecture with rectifier linear unit (ReLU) activationfunction and minimize the cross-entropy loss in the multiclass classificationsetup. This neural network architecture allows us to employ moderncomputational tools in the implementation. The convergence rates of themisclassification risk functions are also derived for both fully observed anddiscretely observed multidimensional functional data. We demonstrate theperformance of mfDNN on simulated data and several benchmark datasets fromdifferent application domains.

Multiclass classification for multidimensional functional data through deep neural networks