TY - GEN

T1 - Low-rank decomposition of multi-way arrays

T2 - 2004 Sensor Array and Multichannel Signal Processing Workshop

AU - Sidiropoulos, N. D.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Canonical decomposition (CANDECOMP)

KW - Low-rank decomposition

KW - Parallel factor analysis (PARAFAC)

KW - Three-way analysis

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M3 - Conference contribution

AN - SCOPUS:28244467902

SN - 0780385454

T3 - 2004 Sensor Array and Multichannel Signal Processing Workshop

SP - 52

EP - 58

BT - 2004 Sensor Array and Multichannel Signal Processing Workshop

Y2 - 18 July 2004 through 21 July 2004

ER -