Multiclass classification for multidimensional functional data through deep neural networks
This addresses the problem of classifying infinite-dimensional functional data for data mining applications, representing an incremental advancement in domain-specific methods.
The paper tackled multiclass classification for multidimensional functional data by introducing a novel functional deep neural network classifier, achieving convergence rates for misclassification risk and demonstrating performance on simulated and benchmark datasets.
The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass functional deep neural network (mfDNN) classifier as an innovative data mining and classification tool. Specifically, we consider sparse deep neural network architecture with rectifier linear unit (ReLU) activation function and minimize the cross-entropy loss in the multiclass classification setup. This neural network architecture allows us to employ modern computational tools in the implementation. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. We demonstrate the performance of mfDNN on simulated data and several benchmark datasets from different application domains.