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Digital Object Identifier 10.1109/MSP.2013.2297439

Date of publication: 12 February 2015

he widespread use of multisensor technology and the emergence of big data

sets have highlighted the limitations of standard flat-view matrix models and

the necessity to move toward more versatile data analysis tools. We show that

higher-order tensors (i.e., multiway arrays) enable such a fundamental para-

digm shift toward models that are essentially polynomial, the uniqueness of

which, unlike the matrix methods, is guaranteed under very mild and natural conditions.

Benefiting from the power of multilinear algebra as their mathematical backbone, data

analysis techniques using tensor decompositions are shown to have great flexibility in the

choice of constraints which match data properties and extract more general latent compo-

nents in the data than matrix-based methods.

A comprehensive introduction to tensor decompositions is provided from a signal process-

ing perspective, starting from the algebraic foundations, via basic canonical polyadic and Tucker

models, to advanced cause-effect and multiview data analysis schemes. We show that tensor

decompositions enable natural generalizations of some commonly used signal processing para-

digms, such as canonical correlation and subspace techniques, signal separation, linear regres-

sion, feature extraction, and classification. We also cover computational aspects and point out

how ideas from compressed sensing (CS) and scientific computing may be used for addressing

the otherwise unmanageable storage and manipulation issues associated with big data sets. The

IMAGE LICENSED BY GRAPHIC STOCK

[

Andrzej Cichocki, Danilo P. Mandic,

Anh Huy Phan, Cesar F. Caiafa,

Guoxu Zhou, Qibin Zhao, and

Lieven De Lathauwer

]

[

From two-way to multiway component analysis

]

TENSOR

DECOMPOSITIONS

for Signal Processing

Applications

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