Le biplot - outil d'exploration de données multidimensionnelles
Journal de la société française de statistique (2002)
- Volume: 143, Issue: 3-4, page 5-55
- ISSN: 1962-5197
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topGabriel, K. Ruben. "Le biplot - outil d'exploration de données multidimensionnelles." Journal de la société française de statistique 143.3-4 (2002): 5-55. <http://eudml.org/doc/199643>.
@article{Gabriel2002,
author = {Gabriel, K. Ruben},
journal = {Journal de la société française de statistique},
language = {fre},
number = {3-4},
pages = {5-55},
publisher = {Société française de statistique},
title = {Le biplot - outil d'exploration de données multidimensionnelles},
url = {http://eudml.org/doc/199643},
volume = {143},
year = {2002},
}
TY - JOUR
AU - Gabriel, K. Ruben
TI - Le biplot - outil d'exploration de données multidimensionnelles
JO - Journal de la société française de statistique
PY - 2002
PB - Société française de statistique
VL - 143
IS - 3-4
SP - 5
EP - 55
LA - fre
UR - http://eudml.org/doc/199643
ER -
References
top- ALLEN D. M. (1974). " The relationship between variable selection and data augmentation as a method of prediction." Technometrics, 16, 125-127. Zbl0286.62044MR343481
- BACCINI A., CAUSSINUS H. et FALGUEROLLES A. de (1993). " Analysing dependence in large contingency tables : Dimensionality and patterns in scatter-plots." Multivariate Analysis : Future Directions 2 (eds. C M . Cuadras et C.R. Rao). Amsterdam; Elsevier, pp. 245-263. Zbl0925.62212MR1268424
- BENZÉCRI J.-P. (1973). L'Analyse des Données, Tome 2 : L'Analyse des Correspondances. Paris : Dunod. Zbl0297.62039
- BENZÉCRI J.-P. (1978). « Sur l'analyse des tableaux binaires associés à une correspondance multiple.» Cahiers de l'Analyse des Données, 2, 55-71.
- BRADU D. et GABRIEL K. R. (1978). " The biplot as a diagnostic tool for models in two-way tables." Technometrics, 20, 47-68. Zbl0381.62004
- BRUTSCHY B. et LEBART L. (1991). " Contiguity analysis and projection pursuit." Applied Stochastic Models and Data Analysis (eds. R. Gutierrez et M.J.M.Valderrama). World Scientific, pp. 117-128. MR1201328
- CARLIER A. et KROONENBERG P.M. (1996). " Décompositions and biplots in three-way correspondence analysis." Psychometrika, 61, 355-373. Zbl0876.62048
- CAUSSINUS H. (1986). " Models and uses of principal component analysis.," en Multidimensional Data Analysis, (eds. J. de Leeuw, W. Heiser, J. Meulman et F. Critchley). Leiden, DSWO Press, pp. 149-170.
- CAUSSINUS H. (1992). « Projections révélatrices», en Modèles pour l'Analyse des Données Multidimensionnelles, (eds. J. J. Droesbeke, B. Fichet et P. Tassi). Paris, Economica, pp. 241-265.
- CAUSSINUS H. (1993). « Modèles probabilistes et analyse des données multidimensionnelles». Journal de la Société de Statistique de Paris, 134, 15-32.
- CAUSSINUS H. et FALGUEROLLES A. de (1987). « Tableaux carrés : modélisation et méthodes factorielles» Revue de Statistique Appliquée, XXXV, 35-52.
- CAUSSINUS H. et FERRÉ L. (1992). " Comparing the parameters of a model for several units by means of principal components analysis." Computational Statistics and Data Analysis, 13, 269-280. Zbl0800.62311
- CAUSSINUS H., HAKAM S., et RUIZ-GAZEN A. (2002). « Projections révélatrices contrôlées - recherche d'individus atypiques.» Revue de Statistique Appliquée, L(4), 81-94.
- CAUSSINUS H., HAKAM S., et RUIZ-GAZEN A. (2003). « Projections révélatrices contrôlées - groupements et structures complexes.» Revue de Statistique Appliquée, LI(1), 37-58.
- CAUSSINUS, H. et RUIZ A. (1990). " Interesting projections of multidimensional data by means of generalized principal component analysis." COMPSTAT 90. Heidelberg : Physica Verlag, pp. 121-36.
- CAUSSINUS H. et RUIZ-GAZEN A. (1993). " Projection pursuit and generalized principal component analysis," in New Directions in Statistical Data Analysis and Robustness. Basel : Birkhausen Verlag, pp.35-46. Zbl0819.62052MR1280272
- CAUSSINUS H. et RUIZ-GAZEN A. (1995). " Metrics for finding typical structures by means of principal component analysis," in Data Science and Its Applications. Harcourt Brace, pp. 177-92.
- CHUANG J.L.C., GABRIEL K. R., et THERNEAU T. M. (1986). Use of 3-D biplots for diagnosing models to fit high-dimensional data. University of Rochester, Department of Statistics Technical report 86/06.
- CLEVELAND W. S. (1993). Visualizing Data. Murray Hill, NJ, AT&T Bell.
- CORSTEN L.C.A. et GABRIEL K. R. (1976). " Graphical exploration in comparing variance matrices." Biometrics, 32, 851-863. Zbl0343.62049
- DAIGLE G. et RIVEST L. P. (1992). " A robust biplot." Canadian Journal of Statistics, 20, 241-255. Zbl0756.62001MR1190569
- EASTMENT H.T. et KRZANOWSKI W.J. (1982). " Cross-validatory choice of the number of components from a principal component analysis". Technometrics, 24, 73-77. MR653115
- ESCOUFIER Y. (1973). « Le traitement des variables vectorielles». Biométries, 29, 751-760. MR334416
- FALGUEROLLES A. de (2000). « Trop de camemberts tuent le camembert». Journal de la Société Française de Statistique, 141, 45-49.
- FALGUEROLLES A. de (1998). " Log-bilinear biplots in action," in Visualization Of Categorical Data (eds. J. Blasius and M. Greenacre). San Diego : Academic Press, 527-539.
- FALGUEROLLES A. de et FRANCIS B. (1992). " Algorithmic approaches for fitting bilinear models," in COMPSTAT 92 : Computational Statistics, Vol. 1, (eds. Y. Dodge and J. Whittaker). Heidelberg, Physica-Verlag, pp. 77-82. MR1214804
- FARAJ A. (1993). « Analyse de contiguïté : une analyse discriminante généralisée à plusieurs variables qualitatives». Revue de Statistique Appliquée, 4 1 , 73-84.
- FARAJ A. (1994). " Interpretation tools for generalized discriminant analysis," in New Approaches in Classification and Data Analysis (eds. E, Diday, Y. Lechevallier, M. Schader, P. Bertrand et B. Burtschy). Berlin, Springer-Verlag, 285-291. MR1415847
- FARAJ A., et CAILLY F. (2001). " Spatial contiguity analysis : a method for describing spatial structures of seismic data." Journal of Petroleum Science and Engineering, 31 , 93-111.
- FERRÉ L. (1995). " Improvement of some multidimensional estimates by reduction of dimensionality." Journal of Multivariate Analysis, 54, 147-162. Zbl0845.62042MR1345532
- FINE J. (1992). « Modèles fonctionels et structurels», en Modèles pour l'Analyse des Données Multidimensionelles, (eds. J. J. Droesbeke, B. Fichet et P. Tassi). Paris, Economica, pp. 21-60.
- FINLAY K.W. et WILKINSON G.N. (1963). " The analysis of adaptation in a plant breeding programme," Austrahan Journal of Agricultural Research, 14, 742-754.
- FISHER R. A. (1935). The Design of Experiments. Edinburgh, Oliver and Boyd. JFM61.0566.03
- FRIENDLY M., et DENIS D. (2000). " The roots and branches of modern statistical graphies." Journal de la Société Française de Statistique, 141, 51-60.
- GABRIEL K. R. (1971). " The biplot - graphical display of matrices with application to principal component analysis." Biometrika, 58, 453-467. Zbl0228.62034MR312645
- GABRIEL K. R. (1972). " Analysis of meteorological data by means of canonical decomposition and biplots." Journal of Applied Meteorology, 11, 1071-77.
- GABRIEL K. R. ( 1978a). " Least squares approximation of matrices by additive and multiplicative models." Journal of the Royal Statistical Society, B, 40, 186-196. Zbl0393.62019MR517440
- GABRIEL K. R. ( 1978b). " The complex correlational biplot," en Theory Construction and Data Analysis in the Behavioral Sciences (ed. S. Shye). San Francisco, Jossey-Bass, pp. 350-370.
- GABRIEL K. R. (1981). " Biplot display of multivariate matrices for inspection of data and diagnosis," en Interpreting Multivariate Data (ed. V. Barnett). Chichester, Wiley, pp. 147-173. MR656974
- GABRIEL K. R. (1982). " Biplot," en Encyclopedia of Statistical Sciences, Vol. I (eds. S. Kotz and N.L. Johnson). New York : Wiley, pp. 262-265. MR1044999
- GABRIEL K. R. (1987). " Some thoughts on comparing multivariate data with the map locations at which they were observed," en Proceedings of the 19th Symposium on the Interface : Computer Science and Statistics (eds. R. M. Heiberger et M. T. Martin). Alexandria, Virginia : American Statistical Association, pp. 139-146.
- GABRIEL K. R. (1988). " Relating multivariate data to geographical location," en Data Analysis, Expert Knowledge and Decisions (eds. W. Gaul et M. Schader). Berlin : Springer, pp. 341-354.
- GABRIEL K. R. ( 1995a). " Biplot display of multivariate categorical data, with comments on multiple correspondence analysis," en Recent Advances in Descriptive Multivariate Analysis (ed. W.J. Krzanowski). Oxford : Clarendon. Chapter 9. MR1380311
- GABRIEL K.R. ( 1995b). " MANOVA biplots for two-way contingency tables," in Recent Advances m Descriptive Multivariate Analysis (ed. W.J. Krzanowski). Oxford : Clarendon. Chapter 10.
- GABRIEL K.R. (1997). " The effect of metrics on biplot display," en Statistical and Mathematical Modelling in the Fields of Food Science, Biotechnology and Environment, (ed. Ute Rmisch). Berlin : Frauenhofer Institut.
- GABRIEL K.R. (1998). " Generalized bilinear regression." Biometrika, 85, 689-700. Zbl0918.62060MR1665834
- GABRIEL K.R. (2002). " Goodness of fit of biplots and correspondence analysis." Biometrika, 89, 423-436. Zbl1019.62059MR1913969
- GABRIEL K.R. ( 2003a). " Lower rank fits and biplots from incomplete data." (In préparation).
- GABRIEL K.R. ( 2003b). " Cross-validation and choice of dimension for lower rank fits and biplots." (In préparation).
- GABRIEL K.R., GALINDO M.P. et VICENTE-VILLARDÓN, J.L. (1998). " Use of Biplots to diagnose independence models in contingency tables," in Visualization Of Categorical Data (eds. J. Blasius and M. Greenacre). San Diego : Academic Press, 391-404.
- GABRIEL K.R. et ODOROFF C. L. (1984). " Résistant lower rank approximation of matrices," in Data Analysis and Informatics III, (eds. E. Diday, M. Jambu, L. Lebart, J. Pages, and R. Tomassone). Amsterdam : North-Holland, 23-30. MR787632
- GABRIEL K.R. et ODOROFF C. L. (1990). " Biplots in biomedical research." Statistics in Medicine, 9, 469-485.
- GABRIEL K.R. et ZAMIR S. (1979). " Lower rank approximation of matrices by least squares with any choice of weights." Technometrics, 2 1 , 489-498. Zbl0471.62004
- GALINDO VILLARDÓN P. (1986). " Una alternativa de representacion simultanea : HJ-biplot." Questio, 10, 13-23.
- GAUCH H. G. (1992). Statistical Analysis of Regional Yield Trials : AMMI Analysis of Factorial Designs. Amsterdam : Elsevier.
- GAUCH H. G. et ZOBEL R. W. (1997). " Identifying mega-environment and targeting genotypes." Crop Science, 37, 311-326.
- GEARY R. C. (1954). " The contiguity ratio and statistical mapping." The Incorporated Statistician, 5, 115-154.
- GHEVA D. (1986). " The biplot graphic technique for the representation of multivariate time series." European Journal of Operational Research, 27, 95-103. Zbl0594.62104
- GOODALL C. (1991). " Procrustes methods in the analysis of shape." Journal of the Royal Statistical Society, Series B, 53, 285-339. Zbl0800.62346MR1108330
- GOODMAN L. A. (1991). " Measures, models, and graphical displays in the analysis of cross-classified data." Journal of the American Statistical Association, 86, 1085-1138. Zbl0850.62093MR1146354
- GOWER J.C. (1971). " Statistical methods of comparing different multivariate analyses of the same data," in Mathematics in the Archeological and Historical Sciences (eds. F.R. Hodson, D.G. Kendall, et P. Tautu ). Edinburgh : University Press, 138-149. Zbl0302.62027
- GOWER J. C. et HAND D. J. (1996). Biplots. London : Chapman and Hall. Zbl0867.62053MR1382860
- GREENACRE M. J. (1984). Theory and Application of Correspondence Analysis. London : Academic Press. Zbl0555.62005MR767260
- GREENACRE M. J. (1988). " Correspondence analysis of multivariate categorical data by weighted least squares." Biometrika, 75, 457-467. Zbl0651.62054MR967584
- GREENACRE M. J. (1993). " Biplots in Correspondence Analysis." Journal of Applied Statistics, 20, 251-269.
- HABER M. (1975). The Singular Value Decomposition of Random Matrices. Thèse de Ph.D., Jerusalem, Hebrew University.
- HENRION R. and HENRION G. (1995). Multivariate Datenanalyse. Berlin, Springer. Zbl0838.62048
- HEO M. (1996). On the fit of sample graphical displays to pattems in populations. University of Rochester, Ph.D thesis. MR2694159
- HEO M. et GABRIEL K. R. (2001). " The fit of graphical displays to patterns of expectations." Computational Statistics and Data Analysis, 36, 47-67. Zbl1080.62501MR1847234
- HOUSEHOLDER A.S. et YOUNG G. (1938). " Matrix approximation and latent roots." American Mathematical Monthly, 45, 165-171. Zbl0019.14701MR1524223JFM64.0046.03
- IMMER F. R., HAYES H. K. et LE ROY POWERS (1934). " Statistical determination of barley varietal adaptation." Journal of the American Society of Agronomy, 26, 403-419.
- JAMBU M. (1977). « Sur l'utilisation conjointe d'une classification hiérarchique et de l'analyse factorielle en composantes principales». Revue de Statistique Appliquée, 25, 4, 5-35.
- JOLLIFFE I. T. (2002). Principal Component Analysis, 2e ed. Springer, New York. Zbl1011.62064MR2036084
- KEMPTON R. A. (1984). " The use of biplots in interpreting variety by environment interactions." Journal of Agricultural Science, 103, 123-135.
- LEBART L. (1969). Analyse Statistique de la Contiguïté, Publ. de l'ISUP, XVIII, 81-112. Zbl0223.62129
- LEBART L. (2001). « Classification, analyse de contiguïté et plus proches voisins», Journées de Statistique XXVII, Nantes, Paris : ASU, 503-506.
- LINGOES J. C. et SCHÖNEMANN P. H. (1974). " Alternative measures for fit for the Schnemann-Carroll matrix fitting algorithm." Psychometrika, 39, 423-427. Zbl0295.92022MR403195
- LUBISCHEW A. A. (1962). " On the use of discriminant functions in taxonomy." Biometrics, 18, 455-477. Zbl0112.11602
- MANDEL J. (1961). " Non-additivity in two-way analysis of variance." Journal of the American Statistical Association, 56, 878-888. Zbl0109.12405MR131934
- RAMSAY J. O., ten BERGE, J., et STYAN G. P. H. (1984). " Matrix correlation." Psychometrika, 49, 403-423. Zbl0581.62048MR760205
- RUIZ-GAZEN A. (1996). " A very simple robust estimator for a dispersion matrix." Computational Statistics and Data Analysis, 2 1 , 463-473. Zbl0900.62274
- SAPORTA G. (1990). Probabilités, Analyse des Données et Statistique. Paris, Dunod. Zbl0703.62003
- SPARKS R., ADOLPHSON A. et PHATAK A. (1997). " Multivariate process monitoring using the dynamic biplot." International Statistical Review, 65, 325-349. Zbl0910.62102
- ter BRAAK C.J.F. (1990). " Interpreting canonical correlation analysis through biplots of structure and weights." Psychometrika, 55, 519-532.
- ter BRAAK C.J.F. (1994). " Biplots in reduced rank regression." Biometrical Journal, 8, 983-1003. Zbl0850.62495
- TORGERSON W. S. (1958). Theory and Methods of Scaling. New York : Wiley.
- TSIANCO M.C., et GABRIEL K.R. (1984), " Modeling temperature data : An illustration of the use of biplots and bimodels in non-linear modeling." Journal of Applied Meteorology, 23, 787-799.
- TUKEY J.W. (1949). " One degree of freedom for non-additivity." Biometrics, 5, 232-242.
- UNDERHILL L. G. (1990). " The coefficient of variation biplot." Journal of Classification, 7, 41-56.
- VALOIS J.-P. (2000). « Approche graphique en analyse de données». Journal de la Société Française de Statistique, 141, 5-40.
- van EEUWIJK F. A. (1995). " Multiplicative interaction in generalised linear models." Biometrics 5 1 , 1017-32. Zbl0875.62330
- VENABLES W. N. et RIPLEY B.D. (1999). Modern Applied Statistics, 3e édition. New York : Springer. Zbl0927.62002
- VERBOON P. (1994). A Robust Approach to Nonlinear Multivariate Analysis. Leiden, DSWO Press. Zbl0868.62052MR1281389
- WOLD H. (1966). " Nonlinear estimation by iterative least squares procedures." Research Papers in Statistics (F. N. David, ed.). New York, Wiley, pp. 411-444. Zbl0161.15901MR210250
- WOLD S. (1976). " Cross-validatory estimation of the number of components in factor and principal component analysis." Technometrics, 20, 397-405. Zbl0403.62032
- YAN W., HUNT L. A., SHENG Q. et SZLAVNICS Z. (2000). " Cultivar evaluation and mega-environment investigation based on the GGE biplot." Crop Science, 40, 597-605.
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