Kernel-based Infinite-dimensional Dimension Reduction for Functional Data

We propose a novel dimension reduction approach (Kernel-based Infinite-dimensional Dimension Reduction, KIDR) for approximating the infinite-dimensional functional data with kernel dimension reduction, originally designed for supervised problems, to unsupervised dimensionality reduction. This paper uses kernel-based independence measures to derive low-dimensional representations that maximally capture information from functional data and minimize the redundancy among the chosen features. We demonstrate that whenever the coefficients of functional data exhibit a linear or nonlinear relationship, our method achieves better results for FPCA. Moreover, our method outperforms FPCA even when the functional data is more complex.