@. Laurent, L. Brusquet, A. Tenenhaus, and G. Lechuga, Analyse discriminante multivoie sparse, 48èmes Journées de Statistique de la SFdS (JdS), 2016.

@. Laurent, L. Brusquet, A. Tenenhaus, G. Lechuga, V. Perlbarg et al., Une pénalité de groupe pour des données multivoie de grande dimension, p.2015

L. L. @bullet-arthur-tenenhaus, G. Brusquet, and . Lechuga, Multiway regularized generalized canonical correlation analysis, 47èmes Journées de Statistique de la SFdS (JdS), 2015.

@. Laurent, L. Brusquet, G. Lechuga, and A. Tenenhaus, Régression logistique multivoie, 46èmes Journées de Statistique de la SFdS (JdS), 2014.

L. L. @bullet-gisela-lechuga, V. Brusquet, L. Perlbarg, D. Puybasset, A. Galanaud et al., Discriminant Analysis for Multiway Data, 2014.

B. Chapter, @. Gisela-lechuga, L. L. Brusquet, V. Perlbarg, and D. Galanaud, Discriminant Analysis for Multiway Data, Proceedings in Mathematics & Statistics, 2015.

G. Journals, L. L. Lechuga, V. Brusquet, L. Perlbarg, D. Puybasset et al., Discriminant Analysis for Multiway Data, p.2017

. Abdi-2007-]-hervé and . Abdi, Singular value decomposition (SVD) and generalized singular value decomposition. Encyclopedia of measurement and statistics, pp.907-912, 2007.

. Abdi-2010-]-hervé and . Abdi, Partial least squares regression and projection on latent structure regression (PLS Regression), Wiley Interdisciplinary Reviews: Computational Statistics, vol.15, issue.1, pp.97-106, 2010.
DOI : 10.1006/nimg.2002.1094

. Adachi-2016-]-kohei and . Adachi, Matrix-based introduction to multivariate data analysis, 2016.

L. Andrew, . Alexander, M. Jee-eun-lee, R. Lazar, M. B. Boudos et al., Diffusion tensor imaging of the corpus callosum in Autism, Neuroimage, vol.34, issue.1, pp.61-73, 2007.

L. Andrew, . Alexander, M. Jee-eun-lee, . Lazar, S. Aaron et al., Diffusion tensor imaging of the brain, Neurotherapeutics, vol.4, issue.3, pp.316-329, 2007.

F. Bach, R. Jenatton, J. Mairal, and G. Obozinski, Structured Sparsity through Convex Optimization, Statistical Science, vol.27, issue.4, pp.450-468, 2012.
DOI : 10.1214/12-STS394

URL : https://hal.archives-ouvertes.fr/hal-00621245

W. Brett, . Bader, G. Tamara, and . Kolda, Efficient MATLAB computations with sparse and factored tensors, SIAM Journal on Scientific Computing, vol.30, issue.1, pp.205-231, 2007.

A. Baroulier, M. Douch, P. Messinesi, L. L. Brusquet, G. Lechuga et al., Modèle de durée pour données multivoie, 49èemes Journées de Statistique de la SFdS (JdS). SFdS, p.2017, 2017.

J. Peter, C. Basser, and . Pierpaoli, Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI, Journal of magnetic resonance, vol.213, issue.2, pp.560-570, 2011.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends, Machine Learning, pp.1-122, 2011.

]. Bro, Multiway calibration. Multilinear PLS, Journal of Chemometrics, vol.10, issue.1, pp.47-61, 1996.
DOI : 10.1002/(SICI)1099-128X(199601)10:1<47::AID-CEM400>3.0.CO;2-C

]. Bro, Multiway calibration. Multilinear PLS, Journal of Chemometrics, vol.10, issue.1, pp.47-61, 1996.
DOI : 10.1002/(SICI)1099-128X(199601)10:1<47::AID-CEM400>3.0.CO;2-C

R. Bro and . Parafac, Tutorial and applications. Chemometrics and intelligent laboratory systems, pp.149-171, 1997.

]. Bro, J. J. Workman, J. Paul, R. Mobley, R. Bruce et al., Review of chemometrics applied to spectroscopy: 1985-95, part 3â??multi- way analysis, 1997.

D. Carroll, Generalization of canonical correlation analysis to three or more sets of variables, Proceedings of the 76th annual convention of the American Psychological Association, pp.227-228, 1968.
DOI : 10.1037/e473742008-115

B. D. De-lathauwer-lieven-de-lathauwer, J. Moor, and . Vandewalle, A Multilinear Singular Value Decomposition, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1253-1278, 2000.
DOI : 10.1137/S0895479896305696

. De-leeuw-de-leeuw, W. Forrest, Y. Young, and . Takane, Additive structure in qualitative data: An alternating least squares method with optimal scaling features, Psychometrika, vol.41, issue.4, pp.471-503, 1976.
DOI : 10.1007/BF02296971

D. Leeuw and D. Leeuw, Block-relaxation Algorithms in Statistics, Information systems and data analysis, pp.308-324, 1994.
DOI : 10.1007/978-3-642-46808-7_28

D. Leeuw and D. Leeuw, Applications of convex analysis to multidimensional scaling, Department of Statistics, 2005.

T. Bradley-efron, I. Hastie, R. Johnstone, and . Tibshirani, Least angle regression. The Annals of statistics, pp.407-499, 2004.

A. Ronald and . Fisher, The use of multiple measurements in taxonomic problems, Annals of eugenics, vol.7, issue.2, pp.179-188, 1936.

D. Galanaud, V. Perlbarg, R. Gupta, D. Robert, P. Stevens et al., Assessment of White Matter Injury and Outcome in Severe Brain TraumaA Prospective Multicenter Cohort, The Journal of the American Society of Anesthesiologists, vol.117, issue.86, pp.1300-1310, 2012.

P. Geladi, H. Isaksson, L. Lindqvist, S. Wold, and K. Esbensen, Principal component analysis of multivariate images, Chemometrics and Intelligent Laboratory Systems, vol.5, issue.3, pp.209-220, 1989.
DOI : 10.1016/0169-7439(89)80049-8

A. Grubb, P. Walsh, N. Lambe, T. Murrells, and S. Robinson, Survey of British clinicians' views on management of patients in persistent vegetative state, The Lancet, vol.348, issue.9019, pp.35-40, 1996.
DOI : 10.1016/S0140-6736(96)02030-2

M. Hanafi, A. Henk, and . Kiers, Analysis of K sets of data, with differential emphasis on agreement between and within sets, Computational Statistics & Data Analysis, vol.51, issue.3, pp.1491-1508, 2006.
DOI : 10.1016/j.csda.2006.04.020

A. Richard and . Harshman, Foundations of the PARAFAC procedure: Models and conditions for an" explanatory" multi-modal factor analysis, 1970.

R. Hastie-2009-]-trevor-hastie, J. Tibshirani, J. Friedman, and . Franklin, The elements of statistical learning: data mining, inference and prediction, The Mathematical Intelligencer, vol.27, issue.58, pp.83-85, 2009.

L. Frank and . Hitchcock, The Expression of a Tensor or a Polyadic as a Sum of Products, Journal of Mathematics and Physics, vol.6, issue.4, pp.164-189, 1927.

E. Arthur, . Hoerl, W. Robert, and . Kennard, Ridge regression: applications to nonorthogonal problems, Technometrics, vol.12, issue.1, pp.69-82, 1970.

A. Roger and . Horn, The hadamard product, Proc. Symp. Appl. Math, pp.87-169, 1990.

A. Roger, R. Horn, and . Mathias, Block-matrix generalizations of Schur's basic theorems on Hadamard products, Linear Algebra and its Applications, vol.172, pp.337-346, 1992.

A. Roger, . Horn, R. Charles, and . Johnson, Matrix analysis, 2012.

]. Horst, Relations amongm sets of measures, Psychometrika, vol.10, issue.2, pp.129-149, 1961.
DOI : 10.1007/BF02289710

R. David, K. Hunter, and . Lange, A tutorial on MM algorithms, The American Statistician, vol.58, issue.1, pp.30-37, 2004.

R. Jenatton, A. Gramfort, V. Michel, G. Obozinski, E. Eger et al., Multiscale Mining of fMRI Data with Hierarchical Structured Sparsity, SIAM Journal on Imaging Sciences, vol.5, issue.3, pp.835-856, 2012.
DOI : 10.1137/110832380

URL : https://hal.archives-ouvertes.fr/inria-00589785

]. S. Keerthi, K. B. Duan, S. K. Shevade, and A. N. Poo, A Fast Dual Algorithm for Kernel Logistic Regression, Machine Learning, vol.20, issue.3, pp.151-165, 2005.
DOI : 10.1109/34.735807

R. Jon and . Kettenring, Canonical analysis of several sets of variables, Biometrika, pp.433-451, 1971.

C. Khatri and . Rao, Solutions to some functional equations and their applications to characterization of probability distributions. Sankhy¯ a: The Indian Journal of Statistics, Series A, pp.167-180, 1968.

A. Henk, J. Kiers, . Mf-ten, R. Berge, and . Bro, PARAFAC2-Part I. A direct fitting algorithm for the PARAFAC2 model, Journal of Chemometrics, vol.13, issue.3-4, pp.275-294, 1999.

A. Henk and . Kiers, Towards a standardized notation and terminology in multiway analysis, Journal of chemometrics, vol.14, issue.3 8, pp.105-122, 2000.

G. Tamara and . Kolda, Orthogonal tensor decompositions, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, pp.243-255, 2001.

G. Tamara, . Kolda, W. Brett, and . Bader, Tensor decompositions and applications, SIAM review, vol.51, issue.3, pp.455-500, 2009.

N. Krämer, Analysis of High Dimensional Data with Partial Least Squares and Boosting, 2007.

]. Krishnan, L. J. Williams, A. R. Mcintosh, and H. Abdi, Partial Least Squares (PLS) methods for neuroimaging: A tutorial and review, NeuroImage, vol.56, issue.2, pp.455-475, 2011.
DOI : 10.1016/j.neuroimage.2010.07.034

M. Pieter, J. D. Kroonenberg, and . Leeuw, Principal component analysis of three-mode data by means of alternating least squares algorithms, Psychometrika, vol.45, issue.1, pp.69-97, 1980.

M. Pieter and . Kroonenberg, Three-mode principal component analysis: Theory and applications, 1983.

B. Joseph and . Kruskal, Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear algebra and its applications, pp.95-138, 1977.

K. Lange and . Lange, Numerical analysis for statisticians, 2010.
DOI : 10.1007/978-1-4419-5945-4

G. Henry and . Law, Research methods for multimode data analysis, 1984.

L. Brusquet, 2. Brusquet, G. Lechuga, and A. Tenenhaus, Régression logistique multivoie, 46èemes Journées de Statistique de la SFdS (JdS). SFdS, p.2014

L. Brusquet, 2. Brusquet, G. Lechuga, V. Perlbarg, L. Puy-basset et al., Une pénalité de groupe pour des données multivoie de grande dimension, 47èemes Journées de Statistique de la SFdS (JdS). SFdS, p.2015

L. Brusquet, 2. Brusquet, A. Tenenhaus, and G. Lechuga, Analyse discriminante multivoie sparse, 48èemes Journées de Statistique de la SFdS (JdS). SFdS, p.2016
URL : https://hal.archives-ouvertes.fr/hal-01376457

]. Lechuga, L. L. Brusquet, V. Perlbarg, L. Puy-basset, D. Galanaud et al., Discriminant Analysis for Multiway Data, PLS and Related methods. PLS, p.2014, 2014.
DOI : 10.1093/brain/awm294

URL : https://hal.archives-ouvertes.fr/hal-01235812

]. Lechuga, L. L. Brusquet, V. Perlbarg, L. Puy-basset, D. Galanaud et al., Discriminant Analysis for Multiway Data, p.2015, 2015.
DOI : 10.1093/brain/awm294

URL : https://hal.archives-ouvertes.fr/hal-01235812

J. Walter-lindberg, S. Persson, and . Wold, Partial least-squares method for spectrofluorimetric analysis of mixtures of humic acid and lignin sulfonate, Analytical Chemistry, vol.55, issue.4, pp.643-648, 1983.
DOI : 10.1021/ac00255a014

Z. Liu, F. Jiang, G. Tian, S. Wang, F. Sato et al., Sparse Logistic Regression with Lp Penalty for Biomarker Identification, Statistical Applications in Genetics and Molecular Biology, vol.6, issue.1, 2007.
DOI : 10.2202/1544-6115.1248

]. Liu, G. Trenkler, . Hadamard, and . Khatri-rao, Kronecker and other matrix products, Int. J. Inf. Syst. Sci, vol.4, issue.1, pp.160-177, 2008.

F. John, C. Macgregor, C. Jaeckle, M. Kiparissides, and . Koutoudi, Process monitoring and diagnosis by multiblock PLS methods, AIChE Journal, vol.40, issue.5, pp.826-838, 1994.

P. A. Montes, F. Valdés-sosa, . Miwakeichi, I. Robin, . Goldman et al., Concurrent EEG/fMRI analysis by multiway Partial Least Squares, NeuroImage, vol.22, issue.3, pp.1023-1034, 2004.
DOI : 10.1016/j.neuroimage.2004.03.038

P. Roderick and . Mcdonald, A simple comprehensive model for the analysis of covariance structures: Some remarks on applications, British Journal of Mathematical and Statistical Psychology, vol.33, issue.2, pp.161-183, 1980.

D. Carl and . Meyer, Matrix analysis and applied linear algebra, Siam, vol.2, 2000.

G. Sebastian-mika, J. Ratsch, B. Weston, K. Scholkopf, and . Muller, Fisher Discriminant Analysis with Kernels, IEEE Conference on Neural Networks for Signal Processing IX, pp.41-48, 1999.

P. Kevin and . Murphy, Machine learning: a probabilistic perspective, 2012.

T. Ian and . Nabney, Efficient training of RBF networks for classification, International Journal of Neural Systems, vol.14, issue.03, pp.201-208, 2004.

Y. Andrew and . Ng, Feature selection, L 1 vs. L 2 regularization, and rotational invariance, Proceedings of the twenty-first international conference on Machine learning, p.78, 2004.

D. Yael, A. Reijmer, . Leemans, M. Sophie, I. Heringa et al., Improved sensitivity to cerebral white matter abnormalities in Alzheimer's disease with spherical deconvolution based tractography, PloS one, vol.7, issue.8, pp.44074-2012, 2012.

R. Rosipal and N. Krämer, Overview and Recent Advances in Partial Least Squares, Subspace, latent structure and feature selection, pp.34-51, 2006.
DOI : 10.1002/(SICI)1097-0193(1997)5:4<254::AID-HBM9>3.0.CO;2-2

E. Sanchez, R. Bruce, and . Kowalski, Tensorial calibration: I. First-order calibration, Journal of Chemometrics, vol.31, issue.4, pp.247-263, 1988.
DOI : 10.1080/00032717508059038

E. Sanchez, R. Bruce, and . Kowalski, Tensorial calibration: II. Second-order calibration, Journal of Chemometrics, vol.41, issue.4, pp.265-280, 1988.
DOI : 10.1002/cem.1180020405

W. Forrest and . Young, Component models for three-way data: An alternating least squares algorithm with optimal scaling features, Psychometrika, vol.45, issue.1, pp.39-67, 1980.

J. Alexander and . Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond, 2001.

S. Shalev-shwartz-2014-]-shai-shalev-shwartz and . Ben-david, Understanding machine learning: From theory to algorithms, p.2014
DOI : 10.1017/CBO9781107298019

. Shawe-taylor, John Shawe-Taylor and Nello Cristianini. Kernel methods for pattern analysis, 2004.

A. Sidaros, W. Aase, K. Engberg, . Sidaros, G. Matthew et al., Diffusion tensor imaging during recovery from severe traumatic brain injury and relation to clinical outcome: a longitudinal study, Brain, vol.131, issue.2, pp.559-572, 2008.
DOI : 10.1093/brain/awm294

D. Nicholas, R. Sidiropoulos, . Bro, B. Georgios, and . Giannakis, Parallel factor analysis in sensor array processing, IEEE transactions on Signal Processing, vol.48, issue.8, pp.2377-2388, 2000.

K. Age, P. Smilde, . Hein-van-der-graaf, A. Durk, T. Doornbos et al., Multivariate calibration of reversed-phase chromatographic systems. Some designs based on three-way data analysis, Analytica Chimica Acta, vol.235, pp.41-51, 1990.

K. Age, . Smilde, A. Durk, and . Doornbos, Three-way methods for the calibration of chromatographic systems: Comparing PARAFAC and three-way PLS, Journal of Chemometrics, vol.5, issue.4, pp.345-360, 1991.

K. Age, J. A. Smilde, . Westerhuis, and J. Sijmen-de, A framework for sequential multiblock component methods, Journal of chemometrics, vol.17, issue.6, pp.323-337, 2003.

I. Lindsay and . Smith, A tutorial on principal components analysis, p.52, 2002.

S. Song, S. Sun, J. Michael, C. Ramsbottom, J. Chang et al., Dysmyelination Revealed through MRI as Increased Radial (but Unchanged Axial) Diffusion of Water, NeuroImage, vol.17, issue.3, pp.1429-1436, 2002.
DOI : 10.1006/nimg.2002.1267

J. Spinnato, M. Roubaud, B. Burle, and B. Torrésani, Finding EEG space-time-scale localized features using Matrix-based penalized discriminant analysis, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.6004-6008, 2014.
DOI : 10.1109/ICASSP.2014.6854756

URL : https://hal.archives-ouvertes.fr/hal-00989928

A. Tenenhaus and L. L. Brusquet, Analyse Factorielle Discriminante Multi-voie, 45èmes Journée de Statistique de la SFdS, p.2013, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00862329

C. Arthur-tenenhaus, V. Philippe, K. Guillemot, J. Cao, V. Grill et al., Variable selection for generalized canonical correlation analysis, Biostatistics, pp.1-2014, 2014.

A. Tenenhaus, L. L. Brusquet, and G. Lechuga, Multiway regularized generalized canonical correlation analysis, 47èemes Journées de Statistique de la SFdS (JdS). SFdS, p.2015, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01235979

]. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological), pp.267-288, 1996.

. Tikhonov, . Andre?, and . Tikhonov, Solutions of ill-posed problems

S. Derrick, . Tracy, G. Kankanam, and . Jinadasa, Partitioned Kronecker products of matrices and applications, Canadian Journal of Statistics, vol.17, issue.1, pp.107-120, 1989.

R. Ledyard and . Tucker, An inter-battery method of factor analysis, Psychometrika, vol.23, issue.30, pp.111-136, 1958.

R. Ledyard and . Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika, vol.31, issue.3, pp.279-311, 1966.

P. John and . Van-de-geer, Linear relations amongk sets of variables, Psychometrika, vol.49, issue.1, pp.79-94, 1984.

L. Arnold, . Van-den, and . Wollenberg, Redundancy analysis an alternative for canonical correlation analysis, Psychometrika, vol.42, issue.30, pp.207-219, 1977.

F. Charles and . Van-loan, The ubiquitous Kronecker product, Journal of computational and applied mathematics, vol.123, issue.1, pp.85-100, 2000.

A. O. Vasilescu and D. Terzopoulos, Multilinear Analysis of Image Ensembles: TensorFaces, European Conference on Computer Vision, pp.447-460, 2002.
DOI : 10.1007/3-540-47969-4_30

A. O. Vasilescu and D. Terzopoulos, TensorTextures, ACM Transactions on Graphics, vol.23, issue.3, pp.336-342, 2004.
DOI : 10.1145/1015706.1015725

A. O. Vasilescu and D. Terzopoulos, Multilinear Independent Components Analysis, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), pp.547-553, 2005.
DOI : 10.1109/CVPR.2005.240

A. Vilanova, S. Zhang, G. Kindlmann, and D. Laidlaw, An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications, Visualization and Processing of Tensor Fields, pp.121-153, 2006.
DOI : 10.1007/3-540-31272-2_7

]. Welling, Fisher linear discriminant analysis, pp.1-4, 2005.

A. Johan, T. Westerhuis, . Kourti, F. John, and . Macgregor, Analysis of multiblock and hierarchical PCA and PLS models, Journal of chemometrics, vol.12, issue.5, pp.301-321, 1998.

A. Johan, T. Westerhuis, J. F. Kourti, and . Macgregor, Analysis of multiblock and hierarchical PCA and PLS models, Journal of Chemometrics, vol.12, issue.5, pp.301-321, 1998.

W. Claudia, A. Wheeler-kingshott, and M. Cercignani, About axial and radial diffusivities, Magnetic Resonance in Medicine, vol.61, issue.5, pp.1255-1260, 2009.

M. Barry, . Wise, B. Neal, E. B. Gallagher, and . Martin, Application of PARAFAC2 to fault detection and diagnosis in semiconductor etch, Journal of chemometrics, vol.15, issue.4, pp.285-298, 2001.

]. Zhao, C. F. Caiafa, P. Danilo, L. Mandic, T. Zhang et al., Multilinear Subspace Regression: An Orthogonal Tensor Decomposition Approach, NIPS, pp.1269-1277, 2011.

]. Zhao, L. Philip, S. Shi, and . Li, Separable linear discriminant analysis, Computational Statistics & Data Analysis, vol.56, issue.12, pp.4290-4300, 2012.
DOI : 10.1016/j.csda.2012.04.003

H. Zou and T. Hastie, Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.5, issue.2, pp.301-320, 2005.
DOI : 10.1073/pnas.201162998

]. Zou, The Adaptive Lasso and Its Oracle Properties, Journal of the American Statistical Association, vol.101, issue.476, pp.1418-1429, 2006.
DOI : 10.1198/016214506000000735

]. Zou, T. Hastie, and R. Tibshirani, Sparse Principal Component Analysis, Journal of Computational and Graphical Statistics, vol.15, issue.2, pp.265-286, 2006.
DOI : 10.1198/106186006X113430