Independent component analysis for tensor-valued data

Joni Virta, Bing Li, Klaus Nordhausen, Hannu Oja

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

In preprocessing tensor-valued data, e.g., images and videos, a common procedure is to vectorize the observations and subject the resulting vectors to one of the many methods used for independent component analysis (ICA). However, the tensor structure of the original data is lost in the vectorization and, as a more suitable alternative, we propose the matrix- and tensor fourth order blind identification (MFOBI and TFOBI). In these tensorial extensions of the classic fourth order blind identification (FOBI) we assume a Kronecker structure for the mixing and perform FOBI simultaneously on each direction of the observed tensors. We discuss the theory and assumptions behind MFOBI and TFOBI and provide two different algorithms and related estimates of the unmixing matrices along with their asymptotic properties. Finally, simulations are used to compare the method's performance with that of classical FOBI for vectorized data and we end with a real data clustering example.

Original languageEnglish (US)
Pages (from-to)172-192
Number of pages21
JournalJournal of Multivariate Analysis
Volume162
DOIs
StatePublished - Nov 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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