### 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 language | English (US) |
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Title of host publication | 2004 Sensor Array and Multichannel Signal Processing Workshop |

Pages | 52-58 |

Number of pages | 7 |

State | Published - Dec 1 2004 |

Event | 2004 Sensor Array and Multichannel Signal Processing Workshop - Barcelona, Spain Duration: Jul 18 2004 → Jul 21 2004 |

### Publication series

Name | 2004 Sensor Array and Multichannel Signal Processing Workshop |
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### Other

Other | 2004 Sensor Array and Multichannel Signal Processing Workshop |
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Country | Spain |

City | Barcelona |

Period | 7/18/04 → 7/21/04 |

### Keywords

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

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## Cite this

*2004 Sensor Array and Multichannel Signal Processing Workshop*(pp. 52-58). (2004 Sensor Array and Multichannel Signal Processing Workshop).