Nonlinear Functional PCA for Functional Data via Neural Networks

Music City Center 

Functional principal component analysis (FPCA) is a critical technique for dimension reduction in functional data analysis (FDA). Traditional FPCA methods assume a linear structure in the observed functional data, which may not always hold, leading to inefficiencies when the data exhibits nonlinear characteristics. In this study, we propose a novel FPCA method that accommodates nonlinear structures using neural networks. We design networks specifically for functional data and explore their universal approximation properties. We conduct a simulation study to evaluate the performance of our method and apply it to a real-world dataset to further demonstrate its effectiveness. This talk is based on joint work with Rou Zhong and Jingxiao Zhang.

Curve reconstruction

Nonlinear dimension reduction

Unsupervised learning