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Title: Functional data analysis using deep neural networks
Abstract Functional data analysis is an evolving field focused on analyzing data that reveals insights into curves, surfaces, or entities within a continuous domain. This type of data is typically distinguished by the inherent dependence and smoothness observed within each data curve. Traditional functional data analysis approaches have predominantly relied on linear models, which, while foundational, often fall short in capturing the intricate, nonlinear relationships within the data. This paper seeks to bridge this gap by reviewing the integration of deep neural networks into functional data analysis. Deep neural networks present a transformative approach to navigating these complexities, excelling particularly in high‐dimensional spaces and demonstrating unparalleled flexibility in managing diverse data constructs. This review aims to advance functional data regression, classification, and representation by integrating deep neural networks with functional data analysis, fostering a harmonious and synergistic union between these two fields. The remarkable ability of deep neural networks to adeptly navigate the intricate functional data highlights a wealth of opportunities for ongoing exploration and research across various interdisciplinary areas. This article is categorized under:Data: Types and Structure > Time Series, Stochastic Processes, and Functional DataStatistical Learning and Exploratory Methods of the Data Sciences > Deep LearningStatistical Learning and Exploratory Methods of the Data Sciences > Neural Networks  more » « less
Award ID(s):
2319342
PAR ID:
10656816
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
Wiley WIREs Computational Statistics
Date Published:
Journal Name:
WIREs Computational Statistics
Volume:
16
Issue:
4
ISSN:
1939-5108
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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