Tensor Decomposition for Signal Processing and Machine Learning

Tensors or multiway arrays are functions of three or more indices (i, j, k, . . . )-similar to matrices (two-way arrays), which are functions of two indices (r, c) for (row, column). Tensors have a rich history, stretching over almost a century, and touching upon numerous disciplines; but they have...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 65; H. 13; S. 3551 - 3582
Hauptverfasser: Sidiropoulos, Nicholas D., De Lathauwer, Lieven, Xiao Fu, Kejun Huang, Papalexakis, Evangelos E., Faloutsos, Christos
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.07.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
alternating direction method of multipliers
alternating optimization
Arrays
canonical polyadic decomposition (CPD)
classification
collaborative filtering
communications
Cramér–Rao bound
Data analysis
Data mining
Decomposition
Gauss–Newton
gradient descent
harmonic retrieval
higher-order singular value decomposition (HOSVD)
Machine learning
Matrix algebra
Matrix decomposition
mixture modeling
multilinear singular value decomposition (MLSVD)
NP-hard problems
Optimization
parallel factor analysis (PARAFAC)
rank
Signal processing
Signal processing algorithms
source separation
speech separation
Statistical analysis
stochastic gradient
subspace learning
Tensile stress
Tensor decomposition
tensor factorization
Tensors
topic modeling
Tucker model
Tutorials
uniqueness
ISSN:1053-587X, 1941-0476
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Zusammenfassung:Tensors or multiway arrays are functions of three or more indices (i, j, k, . . . )-similar to matrices (two-way arrays), which are functions of two indices (r, c) for (row, column). Tensors have a rich history, stretching over almost a century, and touching upon numerous disciplines; but they have only recently become ubiquitous in signal and data analytics at the confluence of signal processing, statistics, data mining, and machine learning. This overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors. As such, it focuses on fundamentals and motivation (using various application examples), aiming to strike an appropriate balance of breadth and depth that will enable someone having taken first graduate courses in matrix algebra and probability to get started doing research and/or developing tensor algorithms and software. Some background in applied optimization is useful but not strictly required. The material covered includes tensor rank and rank decomposition; basic tensor factorization models and their relationships and properties (including fairly good coverage of identifiability); broad coverage of algorithms ranging from alternating optimization to stochastic gradient; statistical performance analysis; and applications ranging from source separation to collaborative filtering, mixture and topic modeling, classification, and multilinear subspace learning.
Bibliographie:ObjectType-Article-1
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2690524