Independent component analysis for multivariate functional data

Research output: Contribution to journalArticle

Researchers

  • Joni Virta
  • Bing Li
  • Klaus Nordhausen
  • Hannu Oja

Research units

  • University of Turku
  • Pennsylvania State University
  • Vienna University of Technology

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.

Details

Original languageEnglish
Article number104568
JournalJournal of Multivariate Analysis
Volume176
Publication statusPublished - 1 Mar 2020
MoE publication typeA1 Journal article-refereed

    Research areas

  • Covariance operator, Dimension reduction, Fourth order blind identification, Functional principal component analysis, Hilbert space, Joint approximate diagonalization of eigenmatrices

ID: 40653720