A. Arash, M. Amini, and . Wainwright, High-dimensional analysis of semidefinite relaxations for sparse principal components, IEEE International Symposium on, pp.2454-2458, 2008.

D. Bertsimas, C. Pawlowski, and Y. D. Zhuo, From predictive methods to missing data imputation: An optimization approach, Journal of Machine Learning Research, vol.18, issue.196, pp.1-39, 2018.

S. Bougeard, C. El-mostafa-qannari, M. Lupo, and . Hanafi, From multiblock partial least squares to multiblock redundancy analysis. a continuum approach, Informatica, vol.22, issue.1, pp.11-26, 2011.

K. S-van-buuren and . Groothuis-oudshoorn, mice: Multivariate imputation by chained equations in r, Journal of statistical software, pp.1-68, 2010.

T. Cai and W. Liu, Adaptive thresholding for sparse covariance matrix estimation, Journal of the American Statistical Association, vol.106, issue.494, pp.672-684, 2011.

H. Chun and S. Kele?, Sparse partial least squares regression for simultaneous dimension reduction and variable selection, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.72, issue.1, pp.3-25, 2010.

L. Clemmensen, T. Hastie, D. Witten, and B. Ersbøll, Sparse discriminant analysis, Technometrics, vol.53, issue.4, pp.406-413, 2011.

A. , &. Aspremont, L. E. Ghaoui, M. I. Jordan, and G. R. Lanckriet, A direct formulation for sparse pca using semidefinite programming, Advances in neural information processing systems, pp.41-48, 2005.

E. Acar, T. G. Kolda, and D. M. Dunlavy, All-at-once Optimization for Coupled Matrix and Tensor Factorizations, 2011.

E. Acar, M. A. Rasmussen, F. Savorani, T. Naes, and R. Bro, Understanding data fusion within the framework of coupled matrix and tensor factorizations. Chemometrics and Intelligent Laboratory Systems, vol.129, pp.53-63, 2013.

S. Bakin, Adaptive regression and model selection in data mining problems, 1999.

M. Barker and W. Rayens, Partial least squares for discrimination, Journal of Chemometrics: A Journal of the Chemometrics Society, vol.17, issue.3, pp.166-173, 2003.

P. R. Bushel, R. D. Wolfinger, and G. Gibson, Simultaneous clustering of gene expression data with clinical chemistry and pathological evaluations reveals phenotypic prototypes, BMC Systems Biology, vol.1, issue.1, p.15, 2007.

L. Clemmensen, T. Hastie, D. Witten, and B. Ersbøll, Sparse discriminant analysis, Technometrics, vol.53, issue.4, pp.406-413, 2011.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B (Methodological), vol.39, issue.1, pp.1-22, 1977.

M. Ellies-oury, H. Lorenzo, C. Denoyelle, J. Saracco, and B. Picard, An original methodology for the selection of biomarkers of tenderness in five different muscles, vol.8, p.206, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02429282

T. Hastie and R. Mazumder, softImpute: Matrix Completion via Iterative Soft-Thresholded SVD. R package version, vol.1, 2015.

J. Josse and F. Husson, Handling missing values in exploratory multivariate data analysis methods, Journal de la Société Française de Statistique, vol.153, issue.2, pp.79-99, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00811888

J. Josse and F. Husson, missMDA: A Package for Handling Missing Values in Multivariate Data Analysis, Journal of Statistical Software, vol.70, issue.1, pp.1-31, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01314945

J. Josse, F. Husson, and J. Pagès, Gestion des données manquantes en analyse en composantes principales, Journal de la Société Française de Statistique, vol.150, issue.2, pp.28-51, 2009.

J. F. Kenney and E. Keeping, Linear regression and correlation, Mathematics of statistics, vol.1, pp.252-285, 1962.

K. Cao, D. Rossouw, C. Robert-granié, and P. Besse, A Sparse PLS for Variable Selection when Integrating Omics data, Statistical applications in genetics and molecular biology, vol.7, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00300204

B. Liquet, P. L. De-micheaux, B. P. Hejblum, and R. Thiébaut, Group and sparse group partial least square approaches applied in genomics context, Bioinformatics, vol.32, issue.1, pp.35-42, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01288891

H. Lorenzo, R. Misbah, J. Odeber, P. Morange, J. Saracco et al., Highdimensional multi-block analysis of factors associated with thrombin generation potential, 2019 IEEE 32nd International Symposium on Computer-Based Medical Systems (CBMS), pp.453-458, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02429302

H. Lorenzo, J. Saracco, and R. Thiébaut, Supervised learning for multi-block incomplete data, 2019.

R. Mazumder, T. Hastie, and R. Tibshirani, Spectral regularization algorithms for learning large incomplete matrices, Journal of machine learning research, vol.11, pp.2287-2322, 2010.

M. Planitz, Inconsistent systems of linear equations. The Mathematical Gazette, vol.63, pp.181-185, 1979.

, The R Journal, vol.20

P. Robert and Y. Escoufier, A Unifying Tool for Linear Multivariate Statistical Methods: The RV-Coefficient, Journal of the Royal Statistical Society: Series C (Applied Statistics), vol.25, issue.3, pp.257-265, 1976.

D. B. Rubin, Inference and missing data, Biometrika, vol.63, issue.3, pp.581-592, 1976.

J. L. Schafer and J. W. Graham, Missing data: our view of the state of the art, Psychological methods, vol.7, issue.2, p.147, 2002.

N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, A Sparse-Group Lasso, Journal of Computational and Graphical Statistics, vol.22, issue.2, pp.231-245, 2013.

D. J. Stekhoven and P. Bühlmann, MissForest--non-parametric missing value imputation for mixedtype data, Bioinformatics, vol.28, issue.1, pp.112-118, 2011.

A. Tenenhaus and M. Tenenhaus, Regularized generalized canonical correlation analysis, Psychometrika, vol.76, issue.2, p.257, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00554101

A. Tenenhaus, C. Philippe, V. Guillemot, K. Cao, J. Grill et al., Variable selection for generalized canonical correlation analysis, Biostatistics, vol.15, issue.3, pp.569-583, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01071432

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

L. Wangen and B. Kowalski, A multiblock partial least squares algorithm for investigating complex chemical systems, Journal of chemometrics, vol.3, issue.1, pp.3-20, 1989.

J. H. Ward, Hierarchical grouping to optimize an objective function, Journal of the American statistical association, vol.58, issue.301, pp.236-244, 1963.

R. A. Willoughby, Solutions of ill-posed problems (an tikhonov and vy arsenin), SIAM Review, vol.21, issue.2, p.266, 1979.

A. Rocanin-arjo, W. Cohen, L. Carcaillon, C. Frère, N. Saut et al., A meta-analysis of genome-wide association studies identifies orm1 as a novel gene controlling thrombin generation potential, Blood, vol.123, issue.5, pp.777-785, 2014.

A. Rocañín-arjó, J. Dennis, P. Suchon, D. Aïssi, V. Truong et al., Thrombin generation potential and whole-blood dna methylation, Thrombosis research, vol.135, issue.3, pp.561-564, 2015.

K. Drobin, P. Nilsson, and J. M. Schwenk, Highly multiplexed antibody suspension bead arrays for plasma protein profiling, The Low Molecular Weight Proteome, pp.137-145, 2013.

T. Oudot-mellakh, W. Cohen, M. Germain, N. Saut, C. Kallel et al., Genome wide association study for plasma levels of natural anticoagulant inhibitors and protein c anticoagulant pathway: the martha project, British journal of haematology, vol.157, issue.2, pp.230-239, 2012.

K. Cao, D. Rossouw, C. Robert-granié, and P. Besse, A sparse pls for variable selection when integrating omics data, Statistical applications in genetics and molecular biology, vol.7, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00300204

T. Hastie, R. Mazumder, J. D. Lee, and R. Zadeh, Matrix completion and low-rank svd via fast alternating least squares, The Journal of Machine Learning Research, vol.16, issue.1, pp.3367-3402, 2015.

J. Josse and F. Husson, missmda: a package for handling missing values in multivariate data analysis, Journal of Statistical Software, vol.70, issue.1, pp.1-31, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01314945

V. Vapnik, The nature of statistical learning theory, Springer science & business media, 2013.

L. Breiman, Random forests, Machine learning, vol.45, issue.1, pp.5-32, 2001.

H. Lorenzo, J. Saracco, and R. Thiébaut, Supervised learning for multiblock incomplete data, 2019.

A. Buil, D. Trégouët, J. C. Souto, N. Saut, M. Germain et al., C4bpb/c4bpa is a new susceptibility locus for venous thrombosis with unknown protein s independent mechanism: results from genome-wide association and gene expression analyses followed by case-control studies, Blood, p.2010, 2010.

G. Destefanis, A. Brugiapaglia, M. T. Barge, and E. Dal-molin, Relationship between beef consumer tenderness perception and Warner-Bratzler shear force, Meat Sci, vol.78, pp.153-156, 2008.

W. J. Platter, J. D. Tatum, K. E. Belk, P. L. Chapman, J. A. Scanga et al., Relationships of consumer sensory ratings, marbling score, and shear force value to consumer acceptance of beef strip loin steaks, J. Anim. Sci, vol.81, pp.2741-2750, 2003.

I. Cassar-malek and B. Picard, Expression marker-based strategy to improve beef quality, Sci. World J, 2016.

B. Picard, B. Lebret, I. Cassar-malek, L. Liaubet, C. Berri et al., Recent advances in omic technologies for meat quality management, Meat sci, vol.109, pp.18-26, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01594439

B. Picard and M. Gagaoua, Proteomic Investigations of Beef Tenderness, Proteomics in Food Science, pp.177-197, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01580641

H. Lorenzo, J. Saracco, and R. Thiébaut, Supervised Learning for Multi-Block Incomplete Data, p.14, 2019.

H. Lorenzo, M. Razzaq, P. Morange, J. Saracco, D. Trégouët et al., High-dimensional multi-block analysis of factors associated with thrombin generation potential, Proceedings of the 32th International Symposium on Computer-Based Medical Systems, pp.5-7, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02429302

J. B. Belew, J. C. Brooks, D. R. Mckenna, and J. W. Savell, Warner-Bratzler shear evaluations of 40 bovine muscles, Meat Sci, vol.64, pp.507-512, 2003.

R. I. Crosley, P. H. Heinz, and J. F. De-bruyn, The relationship between beef tenderness and age classification of beef carcasses in South Africa, Proceedings of the 8th Meat Symposium: Meat, Le Needs of the South Africaner Consumer, pp.57-66, 1995.

R. D. Warner, P. L. Greenwood, D. W. Pethick, and D. M. Ferguson, Genetic and environmental effects on meat quality, Meat Sci, vol.86, pp.171-183, 2010.

E. Veiseth-kent, M. E. Pedersen, S. B. Rønning, and R. Rødbotten, Can postmortem proteolysis explain tenderness differences in various bovine muscles?, Meat Sci, vol.137, pp.114-122, 2018.

M. S. Rhee, T. L. Wheeler, S. D. Shackelford, and M. Koohmaraie, Variation in palatability and biochemical traits within and among eleven beef muscles, J. Anim. Sci, vol.82, pp.534-550, 2004.

J. Bouley, C. Chambon, and B. Picard, Mapping of bovine skeletal muscle proteins using two-dimensional gel electrophoresis and mass spectrometry, Proteomics, vol.4, pp.1811-1824, 2004.

M. M. Bradford, A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding, Anal. Biochem, vol.72, pp.248-254, 1976.

N. Guillemin, B. Meunier, C. Jurie, I. Cassar-malek, J. F. Hocquette et al., Validation of a dot-blot quantitative technique for large scale analysis of beef tenderness biomarkers, J. Physiol. Pharmacol, vol.60, pp.91-97, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01211921

N. Guillemin, M. Bonnet, C. Jurie, and B. Picard, Functional analysis of beef tenderness, J. Proteom, vol.75, pp.352-365, 2011.

B. Picard, C. Barboiron, D. Chadeyron, and C. Jurie, Protocol for high-resolution electrophoresis separation of myosin heavy chain isoforms in bovine skeletal muscle, Electrophoresis, vol.32, pp.1804-1806, 2011.

R. J. Talmadge and R. R. Roy, Electrophoretic separation of rat skeletal muscle myosin heavy-chain isoforms, J. Appl. Physiol, vol.75, pp.2337-2340, 1993.

B. Picard, C. Barboiron, M. P. Duris, H. Gagniere, C. Jurie et al., Electrophoretic separation of bovine muscle myosin heavy chain isoforms, Meat Sci, vol.53, pp.1-7, 1999.

. Nf-iso-13300, Sensory Analysis-General Guidance for the Staff of a Sensory Evaluation Laboratory; International Organization for Standardization, 2006.

S. D. Shackelford, T. L. Wheeler, and M. Koohmaraie, Technical Note: Use of belt grill cookery and slice shear force for assessment of pork longissimus tenderness1, J. Anim. Sci, vol.82, pp.238-241, 2004.

, The R Project for Statistical Computing, 2019.

T. Lian, L. Wang, and Y. Liu, A new insight into the role of calpains in post-mortem meat tenderization in domestic animals: A review. Asian Aus, J. Anim. Sci, vol.26, 2013.

J. D. Glass, D. G. Culver, A. I. Levey, and N. R. Nash, Very early activation of m-calpain in peripheral nerve during Wallerian degeneration, J. Neurol. Sci, vol.196, pp.9-20, 2002.

M. Koohmaraie, Biochemical factors regulating the toughening and tenderization processes of meat, Meat Sci, vol.43, pp.193-201, 1996.

C. M. Kemp, P. L. Sensky, R. G. Bardsley, P. J. Buttery, and T. Parr, Tenderness-An enzymatic view, Meat Sci, vol.84, pp.248-256, 2010.

M. P. Kent, M. J. Spencer, and M. Koohmaraie, Postmortem proteolysis is reduced in transgenic mice overexpressing calpastatin, J. Anim. Sci, vol.82, pp.794-801, 2004.

N. Guillemin, C. Jurie, G. Renand, J. Hocquette, D. Micol et al., Different phenotypic and proteomic markers explain variability of beef tenderness across muscles, Int. J. Biol, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01000621

B. Picard, M. Gagaoua, D. Micol, I. Cassar-malek, J. Hocquette et al., Inverse relationships between biomarkers and beef tenderness according to contractile and metabolic properties of the muscle, J. Agric. Food Chem, vol.62, pp.9808-9818, 2014.

A. L. Goldberg, Protein degradation and protection against misfolded or damaged proteins, Nature, vol.426, 2003.

C. Bernard, I. Cassar-malek, M. Le-cunff, H. Dubroeucq, G. Renand et al., New indicators of beef sensory quality revealed by expression of specific genes, J. Agric. Food Chem, vol.55, pp.5229-5237, 2007.

N. Guillemin, C. Jurie, I. Cassar-malek, J. Hocquette, G. Renand et al., Variations in the abundance of 24 protein biomarkers of beef tenderness according to muscle and animal type, Animal, vol.5, pp.885-894, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01000706

T. T. Paull, E. P. Rogakou, V. Yamazaki, C. U. Kirchgessner, M. Gellert et al., A critical role for histone H2AX in recruitment of repair factors to nuclear foci after DNA damage, Curr. Biol, vol.10, pp.886-895, 2000.

G. S. Stewart, B. Wang, C. R. Bignell, A. M. Taylor, and S. J. Elledge, MDC1 is a mediator of the mammalian DNA damage checkpoint, Nature, vol.421, p.961, 2003.

J. Kao, M. T. Milano, A. Javaheri, M. C. Garofalo, S. J. Chmura et al., ?-H2AX as a therapeutic target for improving the efficacy of radiation therapy, Curr. Cancer Drug Targets, vol.6, pp.197-205, 2006.

J. S. Dickey, C. E. Redon, A. J. Nakamura, B. J. Baird, O. A. Sedelnikova et al., Functional roles and potential applications, vol.118, pp.683-692, 2009.

, kernelPCA ACP à noyaux -ou kernelPCA, vol.8, p.168, 2001.

, Correspond à la réduction de la norme de l'estimateur. Réalisé dans le spectre par les estimateurs Ridge et PCR et en norme L 1 pour le Lasso, par exemple, vol.29, p.168

, ACP Analyse en Composantes Principales -ou PCA pour Principal Component Analysis, vol.50, p.181, 1933.

, AFM Analyse Factorielle Multiple (Escofier et collab, vol.49, p.168, 1984.

, AIC Critère d'Information d'Akaike -ou Akaike Information Criterion, vol.39, p.168, 1973.

, aLasso Lasso adaptatif, vol.35, p.168, 2006.

. Als-si, Imputation Simple par Alternance -ou Alternate Simple-Imputation, vol.57, p.168, 2006.

. Bic-critère-d, Information Bayésienne -ou Bayesian Information Criterion (Schwarz et collab, vol.39, p.168, 1978.

. Blue-meilleur-estimateur, Linéaire sans Biais -ou Best Linear Unbiased Estimator (Pearson, 1901), vol.18, p.168

, CBMS Computer-Based Medical Systems, p.168

, CCA Analyse Canonique des Corrélations -ou Canonical Correlation Analysis (Hotelling, 1936), vol.48, p.168

, CMTF Factorisation Tensorielle pour une Collection de Matrices -ou Collective Matrix Tensor Factorization (Acar et collab, vol.51, p.168, 2011.

. Cmtf-als, Factorisation ALternée Tensorielle pour une Collection de Matrices -ou Alternate Collective Matrix Tensor Factorization (Acar et collab, p.168, 2013.

. Cmtf-opt, Factorisation Tensorielle Optimale pour une Collection de Matrices -ou Optimal Collective Matrix Tensor Factorization (Acar et collab, p.168, 2013.

. Cmtf-wopt, Factorisation Tensorielle Optimale Pondérée pour une Collection de Matrices -ou Weighted Optimal Collective Matrix Tensor Factorization (Acar et collab, vol.57, p.168, 2013.

C. Parafac, Optimale Pondérée -ou Weighted Optimal PARAFAC (Acar et collab, vol.57, p.168, 2011.

, CRAN Comprehensive R Archival Network Miscellaneous (R Core Team, vol.33, issue.3, p.168, 2019.

C. T. Acronymes, C. Seuillage-de-covariance--ou, and . Thresholding, , vol.36, p.168

, DCCA Analyse Canonique Profonde des Corrélations -ou Deep Canonical Correlation Analysis, p.168

, ddsPLS data-driven sparse PLS (Lorenzo et collab., 2019b). vii, vol.3, pp.165-168

, dGN Gauss-Newton amorti -ou damped Gauss, vol.168

, Elastic-net Réseau Élastique -ou Elastic Network, méthode de régularisation, vol.26, p.168, 2005.

. Gcv-validation-croisée-généralisée, Golub et collab, vol.43, p.168, 1979.

, gPLS PLS groupée -ou group PLS (Liquet et collab, vol.33, p.168, 2015.

, INDAFAC paraFAC pour Données INcomplètes -ou INcomplete DAta paraFAC (Tomasi et, vol.57, p.168, 2005.

. Pca-(josse and . Husson, , vol.56, p.168, 2012.

, LARS Régression à Corrélations Minimales Hiérarchique -ou Least Angle Regression Stagewise (Jolliffe et collab, vol.22, p.168, 2003.

, Lasso Least Absolute Shrinkage and Selection Operator, vol.60, p.186, 1996.

K. Wangen, MBPLS Moindres Carrés Partiels Multi Blocs -ou Multiblocks pls, vol.47, p.168, 1989.

, MCO Critère des Moindres Carrés Ordinaires -ou OLS pour Ordinary Least Squares criterion, vol.1, p.186

, MMMF Factorisation de Matrice à Marge Maximale -ou Maximum-Margin Matrix Factorization (Hastie et collab, vol.55, p.168, 2015.

, MSE Erreur Quadratique Moyenne -ou Mean Squared Error, vol.168

, multibloc Données formées par plusieurs groupes de variables ne partagean pas forcemment la même structure ni la même nature. 2, 3, 8, vol.33, p.173

, multivoie Données formées par plusieurs modalités d'un même ensemble de variables, vol.167, p.168

, NIPALS PLS Itérative Non linéaire -ou Nonlinear Iterative Partial Least Squares, vol.32, p.180, 1989.

. Npls-pls-À-n-voies, , vol.50, p.168, 1996.

. Parafac/cp, Analyse Factorielle PARAallèle -ou PARAllel FACtor analysis, aussi appelée CandecomP (CP) (Harshman, 1970), vol.57, p.168

, PCR Régression sur Composantes Principales (Hotelling, 1957), vol.33, p.169

, PLASM Probing Least Absolute Squares Modelling, vol.26, p.168, 1999.

, PLS Moindres Carrés Partiels -ou Partial Least Squares, vol.2, p.168, 1983.

P. Pls-da-analyse-discriminante-par, , vol.63, p.168, 2003.

P. Modeling, , vol.60, p.168, 2013.

, PPCA Probabilist ACP (PPCA) (Caussinus, p.168, 1986.

, PRESS Somme des Carrés Résiduels de l'Erreur en Prédiction -ou Predictive Residual Error Sum of Squares, vol.58, p.168

, RDA Analyse des Redondances -ou Redundancy Analysis (van den Wollenberg, vol.48, p.168, 1977.

, RGCCA Analyse Canonique des Corrélations Régularisée Généralisée -ou Regularized Generalized Canonical Correlation Analysis (Tenenhaus et Tenenhaus, vol.48, p.168, 2011.

, Ridge Principe de régularisation limitant à un espace atteignable par les paramètres du problème à une hyperboule de norme 2 et de rayon le paramètre ? (voir Hoerl et Kennard, vol.173, p.185, 1970.

, RMSE Erreur Quadratique Moyenne sous Racine-ou Root Mean Squared Error, p.168

, SCAD Smoothly Clipped Absolute Deviation Penalty, vol.35, p.168, 2009.

, SCE Somme des Carrés Expliqués, vol.37, p.168

, SCoTLASS Simplification de Méthode à Composantes par Lasso -ou Simplified Component Technique-Lasso, vol.33, p.168, 2003.

, SCR Somme des Carrés des Résidus, vol.37, p.168

, SDP Programmation Positive -ou Semi-Definite Programming (d'Aspremont et collab, vol.36, p.168, 2005.

, SE Erreur Quadratique -ou Squared Error, p.168

, SGCCA Analyse Canonique des Corrélations Généralisée Parcimonieuse -ou Sparse Generalized Canonical Correlation Analysis (Tenenhaus et collab, vol.48, p.168, 2014.

, sgPLS PLS parcimonieuse groupée -ou sparse group PLS (Liquet et collab, vol.33, p.168, 2015.

L. Johnstone, sparseACP Analyse en Composantes Principales Parcimonieuse -ou sparse PCA, vol.34, p.168, 2004.

, Acronymes SPCA Sensible Principal Component Analysis (SPCA), p.168

, sPLS PLS parcimonieuse -ou sparse PLS (Lê Cao et collab, vol.30, p.168, 2008.

, SRM Minimisation du Risque Structurel -ou Structural Risk Minimization (Vapnik et Chervonenkis, vol.10, p.168, 2015.

, STATIS Structuration de Tableaux À Trois Indices de la Statistique (L'Hermier des Plantes, vol.49, p.168, 1976.

, SVD Décomposition en Valeurs Singulières -ou Singular Value Decomposition, vol.17, p.178, 1901.

, SVM Machine à Vecteur de Support -ou Support Vector Machine, 1995.

, Tucker3 Three-mode principal component model (Tucker3) (Kroonenberg, 1983), vol.50, p.168

, VC Dimension de Vapnik-Chervonenkis, vol.168

. .. , The monoblock to multiblock differences of explained variances" where a positive value, respectively negative value, means monoblock, respectively multiblock, performs better. Parameters are p 1 " p 2 " 50, through 100 simulations per set of parameters for q 1 P rr1, 10ss, and q 2 " 20´q 1 and n " 100, The norm of differences of regression matrices" in bottom left corner and filled in red : the higher it is the more different are the estimated regression matrices from both of the approaches, vol.20

, Soient f et g 1 ,..,g p des fonctions de classe C 1 sur un ouvert U de R n , à valeurs dans R et X l'ensemble défini par X " x P U|g 1 pxq

, Si la restriction de f à X admet un extremum local en a et si les différentielles dg 1 paq, . . . , dg p paq sont des formes linéaires indépendantes, alors il existe des réels uniques ? 1, p.que

A. Remarque, Les coefficients ? i sont appelés les multiplicateurs de Lagrange et on appelle "lagrangien" la fonction Lpx

A. Remarque, Théorème précédent on dit que les contraintes sont actives lorsque le point critique considéré est bien dans X

, Pseudo-inverses On remarque que pour toute matrice inversible A, la matrice A´1 est aussi pseudo-inverse de A. Il est possible de montrer que l'ensemble des pseudo-inverses de A est infini

A. Définition, Soit une matrice réelle A P R n?p quelconque, on appelle matrice pseudo-inverse de A toute matrice B P R n?n qui vérifie ABA " A

, Cette définition permet aussi d'introduire la pseudo-inverse de Moore-Penrose, qui est un cas particulier de pseudo-inverse 178

A. Annexe, Notions mathématiques

, Alors la pseudo inverse de Moore-Penrose de A, notée A, 1956.

, Il est possible de démontrer que pour toute matrice réelle, sa pseudo-inverse de Moore-Penrose existe et est unique (voir par exemple Rao et collab, 1972.

, Décomposition SVD Afin de déterminer la forme de la pseudo-inverse de Moore-Penrose, il convient d

E. Acar, D. M. Dunlavy, and T. G. Kolda, «A scalable optimization approach for fitting canonical tensor decompositions, Journal of Chemometrics, vol.25, issue.2, pp.67-86, 2011.

E. Acar, T. G. Kolda, and D. M. Dunlavy, «All-at-once optimization for coupled matrix and tensor factorizations, 2011.

E. Acar, M. A. Rasmussen, F. Savorani, T. Naes, and R. Bro, «Understanding data fusion within the framework of coupled matrix and tensor factorizations, vol.129, pp.53-63, 2013.

H. Akaike, «Information theory and an extension of the maximum likelihood principle, dans 2nd International Symposium on Information Theory, pp.267-281, 1973.

D. M. Allen, «The relationship between variable selection and data agumentation and a method for prediction, Technometrics, vol.16, issue.1, pp.125-127, 1974.

S. Arlot, , 2018.

S. Bakin, Adaptive regression and model selection in data mining problems, 1999.

M. Barker and W. Rayens, «Partial least squares for discrimination, Journal of Chemometrics : A Journal of the Chemometrics Society, vol.17, issue.3, pp.166-173, 2003.

E. Becht, L. Mcinnes, J. Healy, C. Dutertre, I. W. Kwok et al., Newell. 2019, «Dimensionality reduction for visualizing single-cell data using umap», Nature biotechnology, vol.37, issue.1, p.38

P. J. Bickel and E. Levina, «Regularized estimation of large covariance matrices, The Annals of Statistics, vol.36, issue.1, pp.199-227, 2008.

S. Bougeard, E. M. Qannari, C. Lupo, and M. Hanafi, From multiblock partial least squares to multiblock redundancy analysis, Informatica, vol.22, issue.1, pp.11-26, 2011.

L. Breiman, «Bagging predictors, Machine learning, vol.24, issue.2, pp.123-140, 1996.

L. Breiman, Machine learning, vol.45, issue.1, pp.5-32, 2001.

L. Breiman and P. Spector, «Submodel selection and evaluation in regression. the x-random case, International statistical review/revue internationale de Statistique, pp.291-319, 1992.

R. Bro, «Multiway calibration. multilinear pls», Journal of chemometrics, vol.10, issue.1, pp.47-61, 1996.

J. D. Carroll and J. Chang, «Analysis of individual differences in multidimensional scaling via an n-way generalization of "eckart-young" decomposition, Psychometrika, vol.35, issue.3, pp.283-319, 1970.

H. Caussinus, «Models and uses of principal component analysis, Multidimensional data analysis, vol.86, pp.149-170, 1986.

G. Celeux, «The sem algorithm : a probabilistic teacher algorithm derived from the em algorithm for the mixture problem, Computational statistics quarterly, vol.2, pp.73-82, 1985.

H. Chun and S. Kele?, «Sparse partial least squares regression for simultaneous dimension reduction and variable selection», Journal of the Royal Statistical Society : Series B (Statistical Methodology), vol.72, issue.1, pp.3-25, 2010.

L. Clemmensen, T. Hastie, D. Witten, and B. Ersbøll, Sparse discriminant analysis, vol.53, pp.406-413, 2011.

A. Cornuéjols and L. Miclet, Apprentissage artificiel : Concepts et algorithmes, 2010.

C. Cortes and V. Vapnik, Machine learning, vol.20, issue.3, pp.273-297, 1995.

A. Aspremont, L. E. Ghaoui, M. I. Jordan, and G. R. Lanckriet, «A direct formulation for sparse pca using semidefinite programming», dans Advances in neural information processing systems, pp.41-48, 2005.

D. Jong and S. , «Pls shrinks, Journal of chemometrics, vol.9, issue.4, pp.323-326, 1995.

A. P. Dempster, N. M. Laird, and D. B. Rubin, «Maximum likelihood from incomplete data via the em algorithm, Journal of the Royal Statistical Society : Series B (Methodological), vol.39, issue.1, pp.1-22, 1977.

Y. Deshpande and A. Montanari, Sparse pca via covariance thresholding, vol.17, pp.1-41, 2016.

P. Domingos, «A unified bias-variance decomposition, dans Proceedings of 17th International Conference on Machine Learning, pp.231-238, 2000.

D. Eddelbuettel and R. François, Rcpp : Seamless R and C++ integration, vol.40, pp.1-18, 2011.

B. Efron, Estimating the error rate of a prediction rule : improvement on crossvalidation», Journal of the American statistical association, vol.78, pp.316-331, 1983.

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, Least angle regression, vol.32, pp.407-499, 2004.

B. Escofier, «L'analyse factorielle multiple, Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche, vol.42, pp.3-68, 1984.

J. Fan, Comments on «wavelets in statistics : A review, vol.6, p.131, 1997.

S. Geisser, «The predictive sample reuse method with applications, Journal of the American statistical Association, vol.70, pp.320-328, 1975.

S. Geman, E. Bienenstock, and R. Doursat, Neural networks and the bias/variance dilemma», vol.4, pp.1-58, 1992.

R. Genuer, J. Poggi, and C. Tuleau-malot, «Variable selection using random forests, Pattern Recognition Letters, vol.31, pp.2225-2236, 2010.

R. Genuer, J. Poggi, and C. Tuleau-malot, «Vsurf : an r package for variable selection using random forests, The R Journal, 2015.

J. R. Van-ginkel and P. M. Kroonenberg, «Evaluation of multiple-imputation procedures for three-mode component models, Journal of Statistical Computation and Simulation, vol.87, pp.3059-3081, 2017.

G. H. Golub, M. Heath, and G. Wahba, «Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, vol.21, issue.2, pp.215-223, 1979.

M. Hanafi, S. S. Ouertani, J. Boccard, G. Mazerolles, and S. Rudaz, «Multi-way pls regression : Monotony convergence of tri-linear pls2 and optimality of parameters, Computational Statistics & Data Analysis, vol.83, pp.129-139, 2015.

R. Harshman, «Foundations of the parafac procedure : Models and conditions for an "explanatory" multi-modal factor analysis, UCLA Working Papers in Phonetics, vol.16, 1970.

T. Hastie, R. Mazumder, J. D. Lee, and R. Zadeh, «Matrix completion and low-rank svd via fast alternating least squares, Journal of Machine Learning Research, vol.16, issue.1, pp.3367-3402, 2015.

A. E. Hoerl and R. W. Kennard, «Ridge regression : Biased estimation for nonorthogonal problems, Technometrics, vol.12, issue.1, pp.55-67, 1970.

H. Hotelling, Analysis of a complex of statistical variables into principal components.», Journal of educational psychology, vol.24, issue.6, p.417, 1933.

H. Hotelling, «Relations between two sets of variates, Biometrika, vol.28, pp.321-377, 1936.

H. Hotelling, «The relations of the newer multivariate statistical methods to factor analysis, British Journal of Statistical Psychology, vol.10, issue.2, pp.69-79, 1957.

M. Hubert and J. , Van Kerckhoven et T. Verdonck. 2012, «Robust parafac for incomplete data, Journal of Chemometrics, vol.26, issue.6, pp.290-298

F. Husson and J. Josse, «Handling missing values in multiple factor analysis, Food quality and preference, vol.30, issue.2, pp.77-85, 2013.

J. L. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, vol.30, pp.175-193, 1906.

I. M. Johnstone and A. Y. Lu, Sparse principal components analysis», Unpublished manuscript, vol.7, 2004.

I. M. Johnstone and A. Y. Lu, «On consistency and sparsity for principal components analysis in high dimensions, Journal of the American Statistical Association, vol.104, pp.682-693, 2009.

I. T. Jolliffe, N. T. Trendafilov, and M. Uddin, «A modified principal component technique based on the lasso, Journal of computational and Graphical Statistics, vol.12, issue.3, pp.531-547, 2003.

J. Josse and F. Husson, «Handling missing values in exploratory multivariate data analysis methods», Journal de la Société Française de Statistique, vol.153, issue.2, pp.79-99, 2012.

J. Josse and F. Husson, «missmda : a package for handling missing values in multivariate data analysis, Journal of Statistical Software, vol.70, issue.1, pp.1-31, 2016.

J. Josse, F. Husson, and J. Pagès, «Gestion des données manquantes en analyse en composantes principales», Journal de la Société Française de Statistique, vol.150, issue.2, pp.28-51, 2009.

H. A. Kiers, «Weighted least squares fitting using ordinary least squares algorithms, Psychometrika, vol.62, issue.2, pp.251-266, 1997.

V. Koltchinskii, Sparsity in penalized empirical risk minimization», dans Annales de l'IHP Probabilités et statistiques, vol.45, pp.7-57, 2009.

R. Krauthgamer, B. Nadler, and D. Vilenchik, «Do semidefinite relaxations solve sparse pca up to the information limit ?, The Annals of Statistics, vol.43, issue.3, pp.1300-1322, 2015.

P. M. Kroonenberg, Three-mode principal component analysis : Theory and applications, vol.2, 1983.

J. B. Kruskal, Three-way arrays : rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear algebra and its applications, vol.18, issue.2, pp.95-138, 1977.

,. Lê-cao, I. González, and S. Déjean, «integromics : an r package to unravel relationships between two omics data sets, Bioinformatics, vol.25, pp.2855-2856, 2009.

,. Lê-cao, D. Rossouw, C. Robert-granié, and P. Besse, «A sparse pls for variable selection when integrating omics data, Statistical applications in genetics and molecular biology, vol.7, p.1, 2008.

Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, «Gradient-based learning applied to document recognition, Proceedings of the IEEE, vol.86, pp.2278-2324, 1998.

H. Lorenzo and B. ,

B. Liquet, P. L. De-micheaux, B. P. Hejblum, and R. Thiébaut, Group and sparse group partial least square approaches applied in genomics context, Bioinformatics, vol.32, issue.1, pp.35-42, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01288891

J. Lohmöller, Latent variable path modeling with partial least squares, 2013.

H. Lorenzo, M. Ellies-oury, C. Denoyelle, J. Saracco, and B. Picard, «An original methodology for the selection of biomarkers of tenderness in five different muscles, vol.8, p.206, 2019.

H. Lorenzo, J. Saracco, and R. Thiébaut, «Supervised learning for multi-block incomplete data, 2019.

D. Louwerse, A. K. Smilde, and H. A. Kiers, «Cross-validation of multiway component models, Journal of Chemometrics : A Journal of the Chemometrics Society, vol.13, issue.5, pp.491-510, 1999.

L. Van-der-maaten and G. Hinton, «Visualizing data using t-sne», Journal of machine learning research, vol.9, pp.2579-2605, 2008.

C. L. Mallows, Technometrics, vol.15, issue.4, pp.661-675, 1973.

D. W. Marquardt, «An algorithm for least-squares estimation of nonlinear parameters, Journal of the society for Industrial and Applied Mathematics, vol.11, issue.2, pp.431-441, 1963.

R. Mazumder, T. Hastie, and R. Tibshirani, «Spectral regularization algorithms for learning large incomplete matrices, Journal of machine learning research, vol.11, pp.2287-2322, 2010.

Y. Nesterov, Gradient methods for minimizing composite functions», Mathematical Programming, vol.140, pp.125-161, 2013.

D. W. Osten, «Selection of optimal regression models via cross-validation», Journal of Chemometrics, vol.2, issue.1, pp.39-48, 1988.

K. Pearson, On lines and planes of closest fit to systems of point in space, Philosophical Magazine, vol.2, pp.559-572, 1901.

R. Penrose, «On best approximate solutions of linear matrix equations, dans Mathematical Proceedings of the Cambridge Philosophical Society, vol.52, pp.17-19, 1956.

H. L'hermier-des-plantes, Structuration des tableaux à trois indices de la statistique, 1976.

S. J. Qin, S. Valle, and M. J. Piovoso, «On unifying multiblock analysis with application to decentralized process monitoring, Journal of chemometrics, vol.15, issue.9, pp.715-742, 2001.

. R-core-team, R : A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, 2019.

C. R. Rao and S. K. Mitra, «Generalized inverse of a matrix and its applications, dans Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Theory of Statistics, vol.1, pp.601-620, 1972.

J. D. Rennie and N. Srebro, «Fast maximum margin matrix factorization for collaborative prediction, dans Proceedings of the 22nd international conference on Machine learning, pp.713-719, 2005.

S. Rosset, J. Zhu, and T. Hastie, «Boosting as a regularized path to a maximum margin classifier, Journal of Machine Learning Research, vol.5, pp.941-973, 2004.

A. J. Rothman, E. Levina, and J. Zhu, «Generalized thresholding of large covariance matrices», Journal of the American Statistical Association, vol.104, pp.177-186, 2009.

S. T. Roweis, «Em algorithms for pca and spca», dans Advances in neural information processing systems, pp.626-632, 1998.

D. B. Rubin, «Inference and missing data, Biometrika, vol.63, issue.3, pp.581-592, 1976.

J. L. Schafer and J. W. Graham, «Missing data : our view of the state of the art, Psychological methods, vol.7, issue.2, p.147, 2002.

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

G. Schwarz, «Estimating the dimension of a model, The annals of statistics, vol.6, pp.461-464, 1978.

N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, «A sparse-group lasso, Journal of Computational and Graphical Statistics, vol.22, issue.2, pp.231-245, 2013.

A. K. Smilde, J. A. Westerhuis, and R. Boque, «Multiway multiblock component and covariates regression models, Journal of Chemometrics : A Journal of the Chemometrics Society, vol.14, issue.3, pp.301-331, 2000.

D. J. Stekhoven and P. Bühlmann, Missforest-non-parametric missing value imputation for mixed-type data, Bioinformatics, vol.28, issue.1, pp.112-118, 2011.

M. Stone, «Cross-validatory choice and assessment of statistical predictions, Journal of the Royal Statistical Society : Series B (Methodological), vol.36, issue.2, pp.111-133, 1974.

A. Tenenhaus, C. Philippe, V. Guillemot, K. Cao, and J. , Grill et V. Frouin. 2014, «Variable selection for generalized canonical correlation analysis, Biostatistics, vol.15, issue.3, pp.569-583

A. Tenenhaus and M. Tenenhaus, Regularized generalized canonical correlation analysis, Psychometrika, vol.76, issue.2, p.257, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00554101

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

H. Lorenzo and B. , , p.203

A. N. Tikhonov, On the stability of inverse problems, vol.39, pp.195-198, 1943.

M. E. Tipping and C. M. Bishop, «Probabilistic principal component analysis, Journal of the Royal Statistical Society : Series B (Statistical Methodology), vol.61, issue.3, pp.611-622, 1999.

G. Tomasi and R. Bro, Chemometrics and Intelligent Laboratory Systems, vol.75, pp.163-180, 2005.

G. Tomasi and R. Bro, «A comparison of algorithms for fitting the parafac model, Computational Statistics & Data Analysis, vol.50, issue.7, pp.1700-1734, 2006.

V. Vapnik, «Principles of risk minimization for learning theory», Advances in neural information processing systems, pp.831-838, 1992.

V. Vapnik, «Statistical learning theory, 1998.

V. Vapnik, The Nature of Statistical Learning Theory, 1999.

V. N. Vapnik, «An overview of statistical learning theory, IEEE transactions on neural networks, vol.10, issue.5, pp.988-999, 1999.

V. N. Vapnik and A. Y. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, pp.11-30, 2015.

W. N. Venables and B. D. Ripley, Modern Applied Statistics with S, 4 e éd, 2002.

P. Verhulst, 1838, «Notice sur la loi que la population suit dans son accroissement, Corresp. Math. Phys, vol.10, pp.113-126

L. Wangen and B. Kowalski, «A multiblock partial least squares algorithm for investigating complex chemical systems, Journal of chemometrics, vol.3, issue.1, pp.3-20, 1989.

J. A. Westerhuis, P. M. Coenegracht, and C. F. Lerk, «Multivariate modelling of the tablet manufacturing process with wet granulation for tablet optimization and in-process control, International journal of Pharmaceutics, vol.156, issue.1, pp.109-117, 1997.

J. A. Westerhuis and A. K. Smilde, «Deflation in multiblock pls, Journal of chemometrics, vol.15, issue.5, pp.485-493, 2001.

S. Wold, Three pls algorithms according to sw», dans Proc. : Symposium MULDAST (multivariate analysis in science and technology), pp.26-30, 1984.

S. Wold and N. , Kettaneh-Wold et B. Skagerberg. 1989, «Nonlinear pls modeling, Chemometrics and intelligent laboratory systems, vol.7, pp.53-65

S. Wold, H. Martens, and H. Wold, «The multivariate calibration problem in chemistry solved by the pls method», dans Matrix pencils, pp.286-293, 1983.

S. Wold, M. Sjöström, and L. Eriksson, «Pls-regression : a basic tool of chemometrics, Chemometrics and intelligent laboratory systems, vol.58, pp.109-130, 2001.

, Analyse supervisée multibloc en grande dimension 204 BIBLIOGRAPHIE van den Wollenberg, A. L. 1977, «Redundancy analysis an alternative for canonical correlation analysis, Psychometrika, vol.42, issue.2, pp.207-219

M. Yuan and Y. Lin, «Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society : Series B (Statistical Methodology), vol.68, issue.1, pp.49-67, 2006.

P. Zhao and B. Yu, «On model selection consistency of lasso, Journal of Machine learning research, vol.7, pp.2541-2563, 2006.

H. Zou, «The adaptive lasso and its oracle properties, Journal of the American statistical association, vol.101, pp.1418-1429, 2006.

H. Zou and T. Hastie, «Regularization and variable selection via the elastic net, Journal of the royal statistical society : series B (statistical methodology), vol.67, pp.301-320, 2005.

H. Zou, T. Hastie, and R. Tibshirani, «Sparse principal component analysis, Journal of computational and graphical statistics, vol.15, issue.2, pp.265-286, 2006.