Tensor decompositions: Principles and application to food sciences
Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
Standard
Tensor decompositions : Principles and application to food sciences. / Cohen, Jérémy; Bro, Rasmus; Comon, Pierre.
Source Separation in Physical-Chemical Sensing. ed. / Christian Jutten; Leonardo Tomazeli Duarte; Saïd Moussaoui. Wiley, 2023. p. 255-323.Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - CHAP
T1 - Tensor decompositions
T2 - Principles and application to food sciences
AU - Cohen, Jérémy
AU - Bro, Rasmus
AU - Comon, Pierre
N1 - Publisher Copyright: © 2024 John Wiley & Sons Ltd. All rights reserved.
PY - 2023
Y1 - 2023
N2 - Tensors of order d may be seen as arrays of entries indexed by d indices. They naturally appear as data, and arrays in applications such as chemistry, food science, forensics, environmental analysis and many other fields. Extracting and visualizing the underlying features from tensors is an important source separation problem. This chapter first describes an important class of data mining methods for tensors, namely low-rank tensor approximations (CPD, Tucker3) in the case of order d=3. In such a case, striking differences already exist compared to low-rank approximations of matrices, which are tensors of order d=2. Constrained decompositions and coupled decompositions, which are important variants of tensor decompositions, are also discussed in detail, along with practical learning algorithms. Finally, tensor decompositions are illustrated as a tool for source separation in food sciences. In particular fluorescence spectroscopy, electrophoresis in gel, or chromatography especially coupled with mass spectrometry, are techniques where tensor decompositions are known to be useful. Some of the many other source separation problems that may be tackled with tensor decompositions are briefly discussed in the concluding remarks.
AB - Tensors of order d may be seen as arrays of entries indexed by d indices. They naturally appear as data, and arrays in applications such as chemistry, food science, forensics, environmental analysis and many other fields. Extracting and visualizing the underlying features from tensors is an important source separation problem. This chapter first describes an important class of data mining methods for tensors, namely low-rank tensor approximations (CPD, Tucker3) in the case of order d=3. In such a case, striking differences already exist compared to low-rank approximations of matrices, which are tensors of order d=2. Constrained decompositions and coupled decompositions, which are important variants of tensor decompositions, are also discussed in detail, along with practical learning algorithms. Finally, tensor decompositions are illustrated as a tool for source separation in food sciences. In particular fluorescence spectroscopy, electrophoresis in gel, or chromatography especially coupled with mass spectrometry, are techniques where tensor decompositions are known to be useful. Some of the many other source separation problems that may be tackled with tensor decompositions are briefly discussed in the concluding remarks.
KW - Candecomp
KW - Canonical Polyadic (CP) decomposition
KW - Chromatography
KW - Electrophoresis
KW - Fluorescence
KW - Mass spectrogram
KW - PARAFAC
KW - Polycyclic Aromatic Hydrocarbons (PAH)
KW - Tensor
KW - Tucker
U2 - 10.1002/9781119137252.ch6
DO - 10.1002/9781119137252.ch6
M3 - Book chapter
AN - SCOPUS:85175766590
SN - 9781119137221
SP - 255
EP - 323
BT - Source Separation in Physical-Chemical Sensing
A2 - Jutten, Christian
A2 - Duarte, Leonardo Tomazeli
A2 - Moussaoui, Saïd
PB - Wiley
ER -
ID: 372832751