标题： 通过同时特征选择增强多类分类对多变量函数数据的能力 显示英文标题

标题： Empowering Multi-class Classification for Multivariate Functional Data with Simultaneous Feature Selection

摘要： 利用复杂功能数据类型进行分类任务的机会随着影像数据的日益丰富而出现。 然而，能够有效处理影像数据的工具有限，更不用说那些能够进一步利用其他一维功能数据的工具了。 受阿尔茨海默病神经影像学倡议（ADNI）提供的大量数据启发，我们引入了一种针对复杂功能数据的新分类器。 该框架中的每个观测可能与多个功能过程相关，这些过程在维度上各不相同，例如曲线和图像。 每个预测变量都是无限维函数空间中的随机元素，功能预测变量的数量p可能远大于样本量n。 在本文中，我们引入了一种称为功能BIC深度神经网络的新颖且可扩展的分类器。 通过采用稀疏深度修正线性单元网络架构并结合LassoNet算法，所提出的统一模型同时执行特征选择和分类，这与现有的功能数据分析分类器不同。 挑战来自于多个功能过程之间的复杂互相关结构，同时这些过程的分布没有任何假设。 进行了模拟研究和实际数据应用以展示其优越的性能。 显示英文摘要

摘要： The opportunity to utilize complex functional data types for conducting classification tasks is emerging with the growing availability of imaging data. However, the tools capable of effectively managing imaging data are limited, let alone those that can further leverage other one-dimensional functional data. Inspired by the extensive data provided by the Alzheimer's Disease Neuroimaging Initiative (ADNI), we introduce a novel classifier tailored for complex functional data. Each observation in this framework may be associated with numerous functional processes, varying in dimensions, such as curves and images. Each predictor is a random element in an infinite dimensional function space, and the number of functional predictors p can potentially be much greater than the sample size n. In this paper, we introduce a novel and scalable classifier termed functional BIC deep neural network. By adopting a sparse deep Rectified Linear Unit network architecture and incorporating the LassoNet algorithm, the proposed unified model performs feature selection and classification simultaneously, which is contrast to the existing functional data classifiers. The challenge arises from the complex inter-correlation structures among multiple functional processes, and at meanwhile without any assumptions on the distribution of these processes. Simulation study and real data application are carried out to demonstrate its favorable performance.