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Abstract A fundamental problem in functional data analysis is to classify a functional observation based on training data. The application of functional data classification has gained immense popularity and utility across a wide array of disciplines, encompassing biology, engineering, environmental science, medical science, neurology, social science, and beyond. The phenomenal growth of the application of functional data classification indicates the urgent need for a systematic approach to develop efficient classification methods and scalable algorithmic implementations. Therefore, we here conduct a comprehensive review of classification methods for functional data. The review aims to bridge the gap between the functional data analysis community and the machine learning community, and to intrigue new principles for functional data classification. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and ClassificationStatistical Models > Classification ModelsData: Types and Structure > Time Series, Stochastic Processes, and Functional Data 

In this work, we propose a deep neural networks‐based method to perform non‐parametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with rectifier linear unit (ReLU) activation function. We provide the convergence rate of the proposed deep neural networks estimator in terms of the empirical norm. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyse positron emission tomography images of patients with Alzheimer's disease obtained from the Alzheimer Disease Neuroimaging Initiative database.