TY - JOUR
T1 - Deep neural network classifier for multidimensional functional data
AU - for the Alzheimer's Disease Neuroimaging Initiative
AU - Wang, Shuoyang
AU - Cao, Guanqun
AU - Shang, Zuofeng
N1 - Publisher Copyright:
© 2023 Board of the Foundation of the Scandinavian Journal of Statistics.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Minimax excess misclassification risk
KW - functional classification
KW - functional data analysis
KW - functional neural networks
KW - multidimensional functional data
UR - http://www.scopus.com/inward/record.url?scp=85160075490&partnerID=8YFLogxK
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U2 - 10.1111/sjos.12660
DO - 10.1111/sjos.12660
M3 - Article
AN - SCOPUS:85160075490
SN - 0303-6898
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
ER -