L’Analyse Factorielle Discriminante de Tableaux Multiples
Journal de la société française de statistique, Tome 156 (2015) no. 4, pp. 1-20.

L’objet de cet article est de proposer une nouvelle technique, l’analyse factorielle discriminante de Tableaux Multiples, qui généralise l’analyse factorielle discriminante et l’analyse canonique généralisée, et s’applique à des tableaux dont les variables sont partitionnées en blocs et les individus sont partitionnés en groupes ; l’AFD-TM détermine une ou plusieurs variables synthétiques pour chacun des tableaux, de telle manière que les variables synthétiques des différents tableaux soient le plus liées entre elles tout en ayant un pouvoir discriminant le plus élevé possible pour la partition des individus donnée.

The aim of this paper is to propose a new method, multiblock linear discriminant analysis which generalizes linear discriminant analysis and generalized canonical correlation analysis,and is a method for analyzing multiblock and multigroup data tables ; MLDA computes one or several new variables for each data table, such as these new variables take into account both relationships between sets of variables and canonical correlation between each data table and the partition of individuals.

Mot clés : tableaux multiples, analyse factorielle discriminante, analyse canonique généralisée, tableau multi-blocs, tableau multi-groupes
Keywords: multivariate data table, linear discriminant analysis, generalized canonical analysis, multi-block data analysis, multi-group data analysis 
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     volume = {156},
     number = {4},
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Casin, Philippe. L’Analyse Factorielle Discriminante de Tableaux Multiples. Journal de la société française de statistique, Tome 156 (2015) no. 4, pp. 1-20. http://archive.numdam.org/item/JSFS_2015__156_4_1_0/

[1] Carroll, J-D. Generalization of canonical correlation analysis to three or more sets of variables., Proceedings of the 76th annual convention of the Americain Psychological Association, Volume 3 (1968), pp. 227-228

[2] Casin, Ph. A generalization of principal components analysis to k sets of variables, Computational Statistics and Data Analysis, Volume 35 (2001), pp. 417-428 | MR | Zbl

[3] Casin, Ph. L’analyse en composantes principales généralisée, Revue de statistique appliquée, Volume XLIV (3) (1996), pp. 63-81

[4] Cazes, P. Quelques méthodes d’analyse factorielle d’une série de tableaux de données, Modulad, Volume 31.2004 (2004), pp. 1-31

[5] Escofier, B.; Pagès, J. Multiple factor analysis (AFMULT package), Computational Statistics and Data Analysis, Volume 18.1994 (1994), pp. 121-140 | Zbl

[6] Eslami, A.; Qannari, E.M.; Kohler, A.; Bougeard, S. Analyse factorielle de données structurées en groupes d’individus, Journal de la Société Française de Statistique, Volume 154(3) (2013), pp. 44-57 | Numdam | MR | Zbl

[7] Eslami, A.; Qannari, E.M.; Kohler, A.; Bougeard, S. Multivariate analysis of multiblock and multigroup data, Chemometrics and Intelligent Laboratory Systems, Volume 133 (2014), pp. 63-69

[8] Fisher, R-A. The use of multiple measurements in taxonomics problems, Annals of eugenics, Volume 7-(2) (1936), pp. 179-188

[9] Gardner, S.; Gower, J.; Le Roux, N-C. A synthesis of canonical variate analysis, generalised canonical correlation and Procustes analysis, Computational Statistics and Data Analysis, Volume 50 (2006), pp. 107-134 | MR | Zbl

[10] Husson, F.; Josse, J.; Le, S.; Mazet, J. FactorMineR : Mutivariate Exploratory Data Analysis and Data Mining with R, R package version 1.14, 2010

[11] Hotelling, H. Relations between two sets of variants, Biometrika, Volume 28 (1936), pp. 321-337 | JFM | Zbl

[12] Jollife, I-T. Principal Component Analysis, Springer, 2002 | MR

[13] Kettenring, J-R. Canonical analysis of several sets of variables, Biometrika, Volume 58 (3) (1971), pp. 333-351 | MR | Zbl

[14] Kang, M.; Kim, D-C.; Liu, C.; Gao, J. Multiblock Discriminant Analysis for Integrative Genomic Study, Biomed Research International (2015), pp. 1-10

[15] Krzysko, M.; Smialowki, T.; Wolinsky, W. Analysis of multivariate repeated measures data using a MANOVA model and principal components, Biometrical Letters, Volume 51 (2014), pp. 103-124

[16] Lavit, C. Analyse conjointe de tableaux quantitatifs, Masson, Paris, 1988

[17] Lavit, C.; Escoufier, Y.; Sabatier, R.; Traissac, P ; The ACT (STATIS method), Computational Statistics and Data Analysis, Volume 18 (1994), pp. 97-119 | MR | Zbl

[18] Louwerse, D.; Tates, A.; Smilde, A.; Koot, G.; Berndt, H. PLS discriminant analysis with contribution plots to determine differences between parallel batch reactorsin the process industry, Chemometrics and Intelligent Laboratory Systems, Volume 46 (1999), pp. 197-206

[19] Morand, E.; Pagès, J. Procustes multiple factor analysis to analyse the overall perception of food products, Food quality and preference, Volume 17 (2006), pp. 36-42

[20] Saporta, G. Liaison entre plusieurs ensembles de variables et codage de variables qualitatives, Thèse, Université de Paris VI. (1976)

[21] Shen, C.; Sun, M.; Tang, M.; Priebe, C.E. Generalized canonical correlation analysis for classification, Journal of Multivariate Analysis, Volume 130 (2014), pp. 310-322 | MR | Zbl

[22] Sabatier, R.; Vivien, M.; Reynès, C. Une nouvelle proposition, l’analyse discriminante Multitableaux : STATIS-LDA, Journal de la Société Française de Statistique, Volume 154 (2013), pp. 31-43 | Numdam | MR | Zbl

[23] Tenenhaus, A.; Tenenhaus, M. Regularized generalized canonical correlation analysis for multiblock or multigroup data analysis, European Journal of operational research, Volume 238 (2014), pp. 391-403 | MR | Zbl

[24] Vallejo-Arnadela, A.; Vincente-Villardon, J.; Gamindo-Villaedon, M. Canonical-STATIS : Biplot analysis of multi-group structured data based on STATIS-act methodology, Computational Statistics and Data Analysis, Volume 46 (2007), pp. 4193-4205 | MR | Zbl

[25] Zarraga, A.; Goitisolo, B. Simultaneous analysis and multiple factor analysis for contingency tables : Two methods for the joint study of contingency tables, Computational Statistics and Data Analysis, Volume 53 (2009), pp. 3171 -3182 | MR | Zbl