Fast tensorial JADE

Joni Virta, Niko Lietzén, Pauliina Ilmonen, Klaus Nordhausen

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Abstract

We propose a novel method for tensorial‐independent component analysis. Our approach is based on TJADE and k‐JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of k‐JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large‐scale video data, for which neither TJADE nor k‐JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters. Supplementary material including the R‐code for running the examples and the proofs of the theoretical results is available online.
Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalScandinavian Journal of Statistics
DOIs
Publication statusE-pub ahead of print - 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • independent component analysis
  • joint diagonalization
  • Kronecker structure
  • limiting normality
  • tensorial-independent component analysis

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