Adaptive algorithms to track the PARAFAC decomposition of a third-order tensor

Dimitr Nion, Nicholas D. Sidiropoulos

Research output: Contribution to journalArticlepeer-review

175 Scopus citations


The PARAFAC decomposition of a higher-order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode - both serious drawbacks for on-line applications. When the data are serially acquired, or the underlying model changes with time, adaptive PARAFAC algorithms that can track the sought decomposition at low complexity would be highly desirable. This is a challenging task that has not been addressed in the literature, and the topic of this paper. Given an estimate of the PARAFAC decomposition of a tensor at instant t, we propose two adaptive algorithms to update the decomposition at instant t + 1, the new tensor being obtained from the old one after appending a new slice in the 'time' dimension. The proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state-of-art batch algorithms, at orders of magnitude lower complexity. The effectiveness of the proposed algorithms is illustrated using a MIMO radar application (tracking of directions of arrival and directions of departure) as an example.

Original languageEnglish (US)
Pages (from-to)2299-2310
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number6
StatePublished - 2009
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received September 24, 2008; accepted January 30, 2009. First published March 10, 2009; current version published May 15, 2009. The associate editor coordinating the review of this paper and approving it for publication was Dr. Zhengyuan (Daniel) Xu. The work of D. Nion was supported by a Postdoctoral Grant from the Délégation Générale pour l’Armement (DGA) via ETIS Lab., UMR 8051 (ENSEA, CNRS, Univ. Cergy-Pontoise), France.


  • Estimation
  • Generalized class
  • Polynomial phase


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