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 -