Low-rank decomposition of multi-way arrays: A signal processing perspective

Nikolaos Sidiropoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations

Abstract

In many signal processing applications of linear algebra tools, the signal part of a postulated model lies in a so-called signal sub-space, while the parameters of interest are in one-to-one correspondence with a certain basis of this subspace. The signal sub-space can often be reliably estimated from measured data, but the particular basis of interest cannot be identified without additional problem-specific structure. This is a manifestation of rotational indeterminacy, i.e., non-uniqueness of low-rank matrix decomposition. The situation is very different for three- or higher-way arrays, i.e., arrays indexed by three or more independent variables, for which low-rank decomposition is unique under mild conditions. This has fundamental implications for DSP problems which deal with such data. This paper provides a brief tour of the basic elements of this theory, along with many examples of application in problems of current interest in the signal processing community.

Original languageEnglish (US)
Title of host publication2004 Sensor Array and Multichannel Signal Processing Workshop
Pages52-58
Number of pages7
StatePublished - Dec 1 2004
Event2004 Sensor Array and Multichannel Signal Processing Workshop - Barcelona, Spain
Duration: Jul 18 2004Jul 21 2004

Publication series

Name2004 Sensor Array and Multichannel Signal Processing Workshop

Other

Other2004 Sensor Array and Multichannel Signal Processing Workshop
CountrySpain
CityBarcelona
Period7/18/047/21/04

Keywords

  • Canonical decomposition (CANDECOMP)
  • Low-rank decomposition
  • Parallel factor analysis (PARAFAC)
  • Three-way analysis

Fingerprint Dive into the research topics of 'Low-rank decomposition of multi-way arrays: A signal processing perspective'. Together they form a unique fingerprint.

  • Cite this

    Sidiropoulos, N. (2004). Low-rank decomposition of multi-way arrays: A signal processing perspective. In 2004 Sensor Array and Multichannel Signal Processing Workshop (pp. 52-58). (2004 Sensor Array and Multichannel Signal Processing Workshop).