论文标题
多维功能数据的深神经网络分类器
Deep Neural Network Classifier for Multi-dimensional Functional Data
论文作者
论文摘要
我们提出了一种新方法，称为功能性深神经网络（FDNN），用于对多维功能数据进行分类。具体而言，根据培训数据的原理组成部分对深度神经网络进行了训练，该数据应用于预测未来数据功能的类标签。与依赖于高斯假设的流行功能判别分析方法不同，所提出的FDNN方法适用于一般的非高斯多维功能数据。此外，当对数密度比具有局部连接的功能模块化结构时，我们表明FDNN实现了最小值的最佳性。通过模拟和现实世界数据集证明了我们方法的优势。
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall be used to predict the class label of a future data function. Unlike the popular functional discriminant analysis approaches which rely on Gaussian assumption, the proposed FDNN approach applies to general non-Gaussian multi-dimensional functional data. Moreover, when the log density ratio possesses a locally connected functional modular structure, we show that FDNN achieves minimax optimality. The superiority of our approach is demonstrated through both simulated and real-world datasets.
