Deep neural network classifier for multidimensional functional data

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY
Shuoyang Wang, Guanqun Cao, Zuofeng Shang, Michael W. Weiner, Paul Aisen, Ronald Petersen, Michael W. Weiner, Paul Aisen, Ronald Petersen, Clifford R. Jack, William Jagust, John Q. Trojanowki, Arthur W. Toga, Laurel Beckett, Robert C. Green, Andrew J. Saykin, John C. Morris, Richard J. Perrin, Leslie M. Shaw, Zaven Khachaturian, Maria Carrillo, William Potter, Lisa Barnes, Marie Bernard, Hector González, Carole Ho, John K. Hsiao, Jonathan Jackson, Eliezer Masliah, Donna Masterman, Ozioma Okonkwo, Richard Perrin, Laurie Ryan, Nina Silverberg, Adam Fleisher, Michael W. Weiner, Diana Truran Sacrey, Juliet Fockler, Cat Conti, Dallas Veitch, John Neuhaus, Chengshi Jin, Rachel Nosheny, Miriam Ashford, Derek Flenniken, Adrienne Kormos, Robert C. Green, Tom Montine, Cat Conti, Ronald Petersen, Paul Aisen, Michael Rafii, Rema Raman, Gustavo Jimenez, Michael Donohue, Devon Gessert, Jennifer Salazar, Caileigh Zimmerman, Yuliana Cabrera, Sarah Walter, Garrett Miller, Godfrey Coker, Taylor Clanton, Lindsey Hergesheimer, Stephanie Smith, Olusegun Adegoke, Payam Mahboubi, Shelley Moore, Jeremy Pizzola, Elizabeth Shaffer, Brittany Sloan, Laurel Beckett, Danielle Harvey, Michael Donohue, Clifford R. Jack, Arvin Forghanian‐Arani, Bret Borowski, Chad Ward, Christopher Schwarz, David Jones, Jeff Gunter, Kejal Kantarci, Matthew Senjem, Prashanthi Vemuri, Robert Reid, Nick C. Fox, Ian Malone, Paul Thompson, Sophia I. Thomopoulos, Talia M. Nir, Neda Jahanshad, Charles DeCarli, Alexander Knaack, Evan Fletcher, Danielle Harvey, Duygu Tosun‐Turgut, Stephanie Rossi Chen, Mark Choe, Karen Crawford, Paul A. Yushkevich
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引用次数: 4

Abstract

Abstract We propose a new approach, called as functional deep neural network (FDNN), for classifying multidimensional functional data. Specifically, a deep neural network is trained based on the principal 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 only work for one‐dimensional functional data, the proposed FDNN approach applies to general non‐Gaussian multidimensional 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.
多维函数数据的深度神经网络分类器
摘要:本文提出了一种新的方法,称为功能深度神经网络(FDNN),用于多维功能数据的分类。具体来说,深度神经网络是基于训练数据的主成分来训练的,这些主成分将被用来预测未来数据函数的类标签。与仅适用于一维泛函数据的流行泛函判别分析方法不同,本文提出的FDNN方法适用于一般的非高斯多维泛函数据。此外,当对数密度比具有局部连接的功能模块结构时,我们证明了FDNN实现了极小极大最优性。通过模拟和真实世界的数据集证明了我们方法的优越性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Scandinavian Journal of Statistics
Scandinavian Journal of Statistics 数学-统计学与概率论
CiteScore
1.80
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia. It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications. The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems. The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.
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