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Nonlinear functional principal component analysis using neural networks
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DOI：10.1016/j.jmva.2025.105526.png)
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Abstract
En 中文
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo & egrave;ve expansion, which assumes a linear structure of the observed functional data. However, the assumption may not always be satisfied, and the FPCA method can become inefficient when the data deviates from the linear assumption. In this paper, we propose a novel FPCA method that is suitable for data with a nonlinear structure with the use of neural networks. We construct networks that can be applied to functional data and explore the corresponding universal approximation property. The main use of our proposed nonlinear FPCA method is curve reconstruction. We conduct a simulation study to evaluate the performance of our method. The proposed method is also applied to a real-world data set to further demonstrate its superiority.
Keywords:
Curve reconstruction
Functional principal component analysis
Neural network
Nonlinear dimension reduction
Journal
J
IF:
1.7
Papers:
99
Citations:
5.8K
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ShareSaveUNIFORM CONVERGENCE RATES FOR NONPARAMETRIC REGRESSION AND PRINCIPAL COMPONENT ANALYSIS IN FUNCTIONAL/LONGITUDINAL DATA.png)
ANNALS OF STATISTICS
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ANNALS OF STATISTICSIF3.7
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