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
{"title":"Deep neural network classifier for multidimensional functional data","authors":"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","doi":"10.1111/sjos.12660","DOIUrl":null,"url":null,"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.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"29 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scandinavian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/sjos.12660","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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.