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：多维域上函数观测数据固有的无限维特征导致传统分类方法在实际应用中失效。针对这一问题，我们提出了一种新型多分类函数深度神经网络分类器（mfDNN），作为创新的数据挖掘与分类工具。具体而言，我们采用带修正线性单元（ReLU）激活函数的稀疏深度神经网络架构，并在多分类框架下最小化交叉熵损失。该神经网络架构使我们能够应用现代计算工具进行实现。同时推导了全观测与离散观测两类多维函数数据场景下误分类风险函数的收敛速率。我们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。