JADE for Tensor-Valued Observations

Joni Virta, Bing Li, Klaus Nordhausen, Hannu Oja

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely, matrices or tensors (e.g., images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth-order blind identification (FOBI) specially suited for tensor-valued observations was proposed and showed to outperform its vector version for tensor data. In this article, we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background, we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors. Supplementary material including the proofs of the theorems and the codes for running the simulations and the real data example are available online.

Original languageEnglish (US)
Pages (from-to)628-637
Number of pages10
JournalJournal of Computational and Graphical Statistics
Volume27
Issue number3
DOIs
StatePublished - Jul 3 2018

Fingerprint

Diagonalization
Tensor
Independent Component Analysis
Asymptotic Properties
Fourth Order
Data analysis
Simulation
Higher Order
Estimator
Observation
Independent component analysis
Theorem
Standards
Asymptotic properties
Usefulness
Competitors

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

Cite this

Virta, Joni ; Li, Bing ; Nordhausen, Klaus ; Oja, Hannu. / JADE for Tensor-Valued Observations. In: Journal of Computational and Graphical Statistics. 2018 ; Vol. 27, No. 3. pp. 628-637.
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JADE for Tensor-Valued Observations. / Virta, Joni; Li, Bing; Nordhausen, Klaus; Oja, Hannu.

In: Journal of Computational and Graphical Statistics, Vol. 27, No. 3, 03.07.2018, p. 628-637.

Research output: Contribution to journalArticle

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