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.

翻译：多维域上函数型观测数据固有的无限维特征使得标准分类方法难以有效应用。针对该问题，本文提出一种创新的数据挖掘与分类工具——多元函数深度神经网络（mfDNN）分类器。具体而言，我们采用修正线性单元（ReLU）激活函数的稀疏深度神经网络架构，并在多元分类框架下最小化交叉熵损失。该神经网络架构使现代计算工具的应用成为可能。同时推导了完全观测与离散观测两类多维函数数据下误分类风险函数的收敛速率。通过模拟数据及来自不同应用领域的多个基准数据集验证了mfDNN的性能。