Independent component analysis for multivariate functional data

TL;DR

This paper extends two independent component analysis methods to multivariate functional data, enabling extraction of important features beyond traditional functional principal component analysis, with demonstrated advantages through simulations and real data.

Contribution

It introduces two novel, Fisher consistent ICA methods for vector-valued functional data, addressing the dependency structure via finite-dimensional subspace assumptions.

Findings

Methods outperform functional PCA in simulations

Application to hand gesture data shows practical usefulness

Proposed techniques effectively extract independent components

Abstract

We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and frequently in modern applications, and extending independent component analysis to this setting allows us to distill important information from this type of data, going a step further than the functional principal component analysis. To allow the inversion of the covariance operator we make the assumption that the dependency between the component functions lies in a finite-dimensional subspace. In this subspace we define fourth cross-cumulant operators and use them to construct the two novel, Fisher consistent methods for solving the independent component problem for vector-valued functions. Both simulations and an application on a hand gesture data set show the usefulness and advantages of the proposed methods over functional principal component analysis.