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Volumn 2, Issue 4, 2010, Pages 433-459

Principal component analysis

Author keywords

[No Author keywords available]

Indexed keywords

CORRESPONDENCE ANALYSIS; CROSS-VALIDATION TECHNIQUE; DATA TABLES; DEPENDENT VARIABLES; EIGEN DECOMPOSITION; MULTIPLE FACTOR ANALYSIS; PCA MODEL; POSITIVE SEMIDEFINITE MATRICES; PRINCIPAL COMPONENTS; RECTANGULAR MATRIX;

EID: 77957553895     PISSN: 19395108     EISSN: 19390068     Source Type: Journal    
DOI: 10.1002/wics.101     Document Type: Review
Times cited : (8004)

References (67)
  • 1
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • Pearson K. On lines and planes of closest fit to systems of points in space. Philos Mag A 1901, 6:559-572.
    • (1901) Philos Mag A , vol.6 , pp. 559-572
    • Pearson, K.1
  • 4
    • 0009290262 scopus 로고
    • Mémoire sur les formes bilinéaires
    • Jordan C. Mémoire sur les formes bilinéaires. J Math Pure Appl 1874, 19:35-54.
    • (1874) J Math Pure Appl , vol.19 , pp. 35-54
    • Jordan, C.1
  • 5
    • 0027879547 scopus 로고
    • On the early history of the singular value decomposition
    • Stewart GW. On the early history of the singular value decomposition. SIAM Rev 1993, 35:551-566.
    • (1993) SIAM Rev , vol.35 , pp. 551-566
    • Stewart, G.W.1
  • 7
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • Hotelling H. Analysis of a complex of statistical variables into principal components. J Educ Psychol 1933, 25:417-441.
    • (1933) J Educ Psychol , vol.25 , pp. 417-441
    • Hotelling, H.1
  • 10
    • 84889874129 scopus 로고    scopus 로고
    • Principal component analysis: Application to statistical process control
    • Govaert G, ed. London: John Wiley & Sons
    • Saporta G, Niang N. Principal component analysis: application to statistical process control. In: Govaert G, ed. Data Analysis. London: John Wiley & Sons; 2009, 1-23.
    • (2009) Data Analysis , pp. 1-23
    • Saporta, G.1    Niang, N.2
  • 11
    • 34948874711 scopus 로고    scopus 로고
    • Singular value decomposition (SVD) and generalized singular value decomposition(GSVD)
    • Salkind NJ ed. Thousand Oaks: Sage Publications
    • Abdi H. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition(GSVD). In: Salkind NJ, ed. Encyclopedia of Measurement and Statistics. Thousand Oaks: Sage Publications; 2007, 907-912.
    • (2007) Encyclopedia of Measurement and Statistics , pp. 907-912
    • Abdi, H.1
  • 12
    • 53849097916 scopus 로고    scopus 로고
    • Eigen-decomposition: Eigenvalues and eigenvectors
    • Salkind NJ, ed Thousand Oaks: Sage Publications
    • Abdi H. Eigen-decomposition: eigenvalues and eigenvectors. In: Salkind NJ, ed. Encyclopedia of Measurement and Statistics. Thousand Oaks: Sage Publications; 2007, 304-308.
    • (2007) Encyclopedia of Measurement and Statistics , pp. 304-308
    • Abdi, H.1
  • 13
    • 3142728708 scopus 로고    scopus 로고
    • Relationships among various kinds of eigenvalue and singular value decompositions
    • Yanai H, Okada A, Shigemasu K, Kano Y, Meulman J, eds Tokyo: Springer Verlag
    • Takane Y. Relationships among various kinds of eigenvalue and singular value decompositions. In: Yanai H, Okada A, Shigemasu K, Kano Y, Meulman J, eds. New Developments in Psychometrics. Tokyo: Springer Verlag; 2002, 45-56.
    • (2002) New Developments in Psychometrics , pp. 45-56
    • Takane, Y.1
  • 15
    • 0012427741 scopus 로고
    • Factor analysis and principal component analysis: Bilinear methods
    • Kruskal WH, Tannur JM, eds. New York: The Free Press
    • Kruskal JB. Factor analysis and principal component analysis: Bilinear methods. In: Kruskal WH, Tannur JM, eds. International Encyclopedia of Statistics. New York: The Free Press; 1978, 307-330.
    • (1978) International Encyclopedia of Statistics , pp. 307-330
    • Kruskal, J.B.1
  • 16
    • 0002968611 scopus 로고
    • Statistical methods of comparing different multivariate analyses of the same data
    • Hodson F, Kendall D, Tautu P, eds. Edinburgh: Edingburh University Press
    • Gower J. Statistical methods of comparing different multivariate analyses of the same data. In: Hodson F, Kendall D, Tautu P, eds. Mathemematics in the Archæological and Historical Sciences. Edinburgh: Edingburh University Press; 1971, 138-149.
    • (1971) Mathemematics in the Archæological and Historical Sciences , pp. 138-149
    • Gower, J.1
  • 17
    • 0000566665 scopus 로고
    • Alternative measures of fit for the Schönemann-Carrol matrix fitting algorithm
    • Lingoes J, Schönemann P. Alternative measures of fit for the Schönemann-Carrol matrix fitting algorithm. Psychometrika 1974, 39:423-427.
    • (1974) Psychometrika , vol.39 , pp. 423-427
    • Lingoes, J.1    Schönemann, P.2
  • 18
    • 33846525831 scopus 로고    scopus 로고
    • RV cofficient and congruence coefficient
    • Salkind NJ, ed. Thousand Oaks: Sage Publications
    • Abdi H. RV cofficient and congruence coefficient. In: Salkind NJ, ed. Encyclopedia of Measurement and Statistics. Thousand Oaks: Sage Publications; 2007, 849-853.
    • (2007) Encyclopedia of Measurement and Statistics , pp. 849-853
    • Abdi, H.1
  • 19
    • 35948933029 scopus 로고    scopus 로고
    • On the number of principal components: A test of dimensionality based on measurements of similarity between matrices
    • Dray S. On the number of principal components: a test of dimensionality based on measurements of similarity between matrices. Comput Stat Data Anal 2008, 52:2228-2237.
    • (2008) Comput Stat Data Anal , vol.52 , pp. 2228-2237
    • Dray, S.1
  • 20
    • 0001610304 scopus 로고
    • Notes on bias and estimation
    • Quenouille M. Notes on bias and estimation. Biometrika 1956, 43:353-360.
    • (1956) Biometrika , vol.43 , pp. 353-360
    • Quenouille, M.1
  • 23
    • 19044395321 scopus 로고    scopus 로고
    • How many principal components? stopping rules for determining the number of non-trivial axes revisited
    • Peres-Neto PR, Jackson DA, Somers KM. How many principal components? stopping rules for determining the number of non-trivial axes revisited. Comput Stat Data Anal 2005, 49:974-997.
    • (2005) Comput Stat Data Anal , vol.49 , pp. 974-997
    • Peres-Neto, P.R.1    Jackson, D.A.2    Somers, K.M.3
  • 24
    • 84937549955 scopus 로고
    • The scree test for the number of factors
    • Cattell RB. The scree test for the number of factors. Multivariate Behav Res 1966, 1:245-276.
    • (1966) Multivariate Behav Res , vol.1 , pp. 245-276
    • Cattell, R.B.1
  • 25
    • 84977693791 scopus 로고
    • A note on Guttman's lower bound for the number of common factors
    • Kaiser HF. A note on Guttman's lower bound for the number of common factors. Br J Math Stat Psychol 1961, 14:1-2.
    • (1961) Br J Math Stat Psychol , vol.14 , pp. 1-2
    • Kaiser, H.F.1
  • 26
    • 0027561417 scopus 로고
    • A low dimensional representation of faces in the higher dimensions of the space
    • O'Toole AJ, Abdi H, Deffenbacher KA, Valentin D. A low dimensional representation of faces in the higher dimensions of the space. J Opt Soc Am [Ser A] 1993, 10:405-411.
    • (1993) J Opt Soc Am [Ser A] , vol.10 , pp. 405-411
    • O'toole, A.J.1    Abdi, H.2    Deffenbacher, K.A.3    Valentin, D.4
  • 27
    • 0015973904 scopus 로고
    • A predictive approach to the random effect model
    • Geisser S. A predictive approach to the random effect model. Biometrika 1974, 61:101-107.
    • (1974) Biometrika , vol.61 , pp. 101-107
    • Geisser, S.1
  • 29
    • 0000629975 scopus 로고
    • Cross-validatory choice and assessment of statistical prediction
    • Stone M. Cross-validatory choice and assessment of statistical prediction. J R Stat Soc [Ser A] 1974, 36:111-133.
    • (1974) J R Stat Soc [Ser A] , vol.36 , pp. 111-133
    • Stone, M.1
  • 30
    • 0000295654 scopus 로고
    • PLS for multivariate linear modeling
    • van de Waterbeemd H, ed. Weinheim: Wiley-VCH Verlag
    • Wold S. PLS for multivariate linear modeling. In: van de Waterbeemd H, ed. Chemometric Methods in Molecular Design. Weinheim: Wiley-VCH Verlag; 1995, 195-217.
    • (1995) Chemometric Methods in Molecular Design , pp. 195-217
    • Wold, S.1
  • 32
    • 0020089191 scopus 로고
    • Cross-validatory choice of the number of components from a principal component analysis
    • Eastment HT, KrzanowskiWJ. Cross-validatory choice of the number of components from a principal component analysis. Technometrics 1982, 24:73-77.
    • (1982) Technometrics , vol.24 , pp. 73-77
    • Eastment, H.T.1    Krzanowski, W.J.2
  • 33
    • 84951601886 scopus 로고
    • Cross-validatory estimation of the number of components in factor and principal component analysis
    • Wold S. Cross-validatory estimation of the number of components in factor and principal component analysis. Technometrics 1978, 20:397-405.
    • (1978) Technometrics , vol.20 , pp. 397-405
    • Wold, S.1
  • 34
    • 0020748239 scopus 로고
    • Computer intensive methods in statistics
    • Diaconis P, Efron B. Computer intensive methods in statistics. Sci Am 1983, 248:116-130.
    • (1983) Sci Am , vol.248 , pp. 116-130
    • Diaconis, P.1    Efron, B.2
  • 35
    • 1542760583 scopus 로고
    • Using the bootstrap and the Rv coefficient in the multivariate context
    • Diday E, ed. New York: Nova Science
    • Holmes S. Using the bootstrap and the Rv coefficient in the multivariate context. In: Diday E, ed. Data Analysis, Learning, Symbolic and Numeric Knowledge. New York: Nova Science; 1989, 119-132.
    • (1989) Data Analysis, Learning, Symbolic and Numeric Knowledge , pp. 119-132
    • Holmes, S.1
  • 37
    • 0027332773 scopus 로고
    • Stopping rules in principal aomponents analysis: A comparison of heuristical and statistical approaches
    • Jackson DA. Stopping rules in principal aomponents analysis: a comparison of heuristical and statistical approaches. Ecology 1993, 74:2204-2214.
    • (1993) Ecology , vol.74 , pp. 2204-2214
    • Jackson, D.A.1
  • 38
    • 0029103850 scopus 로고
    • Bootstrapped principal components analysis: A reply to Mehlman et al
    • Jackson DA. Bootstrapped principal components analysis: a reply to Mehlman et al. Ecology 1995, 76:644-645.
    • (1995) Ecology , vol.76 , pp. 644-645
    • Jackson, D.A.1
  • 39
    • 0029111249 scopus 로고
    • Bootstrapping principal components analysis: A comment
    • Mehlman DW, Sheperd UL, Kelt DA. Bootstrapping principal components analysis: a comment. Ecology 1995, 76:640-643.
    • (1995) Ecology , vol.76 , pp. 640-643
    • Mehlman, D.W.1    Sheperd, U.L.2    Kelt, D.A.3
  • 40
    • 34250165671 scopus 로고    scopus 로고
    • Multivariate analysis
    • Lewis-Beck M, Bryman A, Futing T, eds. Thousand Oaks, CA: Sage Publications
    • Abdi H. Multivariate analysis. In: Lewis-Beck M, Bryman A, Futing T, eds. Encyclopedia for Research Methods for the Social Sciences. Thousand Oaks, CA: Sage Publications 2003, 669-702.
    • (2003) Encyclopedia for Research Methods for the Social Sciences , pp. 669-702
    • Abdi, H.1
  • 41
    • 34250922831 scopus 로고
    • The varimax criterion for analytic rotation in factor analysis
    • Kaiser HF. The varimax criterion for analytic rotation in factor analysis. Psychometrika 1958, 23:187-200.
    • (1958) Psychometrika , vol.23 , pp. 187-200
    • Kaiser, H.F.1
  • 44
    • 76349111180 scopus 로고    scopus 로고
    • Partial least square regression, Projection on latent structures Regression, PLS-Regression
    • Abdi H. Partial least square regression, Projection on latent structures Regression, PLS-Regression. Wiley Interdisciplinary Reviews: Computational Statistics, 2 2010, 97-106.
    • (2010) Wiley Interdisciplinary Reviews: Computational Statistics , vol.2 , pp. 97-106
    • Abdi, H.1
  • 49
    • 46249120116 scopus 로고    scopus 로고
    • Multiple correspondence analysis
    • Salkind NJ, ed. Thousand Oaks, CA: Sage Publications
    • Abdi H, Valentin D. Multiple correspondence analysis. In: Salkind NJ, ed. Encyclopedia of Measurement and Statistics. Thousand Oaks, CA: Sage Publications; 2007, 651-657.
    • (2007) Encyclopedia of Measurement and Statistics , pp. 651-657
    • Abdi, H.1    Valentin, D.2
  • 50
    • 78651522947 scopus 로고    scopus 로고
    • Correspondence analysis, multiple correspondence analysis and recent developments
    • Millsap R, Maydeu-Olivares A, eds. London: Sage Publications
    • Hwang H, Tomiuk MA, Takane Y. Correspondence analysis, multiple correspondence analysis and recent developments. In: Millsap R, Maydeu-Olivares A, eds. Handbook of Quantitative Methods in Psychology. London: Sage Publications 2009, 243-263.
    • (2009) Handbook of Quantitative Methods in Psychology , pp. 243-263
    • Hwang, H.1    Tomiuk, M.A.2    Takane, Y.3
  • 51
    • 77957563448 scopus 로고    scopus 로고
    • Correspondence analysis
    • Salkind NJ, ed. Thousand Oaks: Sage Publications, (In press)
    • Abdi H, Williams LJ. Correspondence analysis. In: Salkind NJ, ed. Encyclopedia of Research Design. Thousand Oaks: Sage Publications; 2010, (In press).
    • (2010) Encyclopedia of Research Design
    • Abdi, H.1    Williams, L.J.2
  • 52
    • 78651581002 scopus 로고
    • Faut-il pondérer les données linguistiques
    • Brunet E. Faut-il pondérer les données linguistiques. CUMFID 1989, 16:39-50.
    • (1989) CUMFID , vol.16 , pp. 39-50
    • Brunet, E.1
  • 55
    • 33846500525 scopus 로고    scopus 로고
    • Multiple factor analysis (mfa)
    • Salkind NJ, ed. Thousand Oaks, CA: Sage Publications
    • Abdi H, Valentin D. Multiple factor analysis (mfa). In: Salkind NJ, ed. Encyclopedia of Measurement and Statistics. Thousand Oaks, CA: Sage Publications; 2007, 657-663.
    • (2007) Encyclopedia of Measurement and Statistics , pp. 657-663
    • Abdi, H.1    Valentin, D.2
  • 59
    • 78651585662 scopus 로고    scopus 로고
    • Correspondence analysis and classification
    • Greenacre M, Blasius J, eds. Boca Raton, FL: Chapman & Hall
    • Saporta G, Niang N. Correspondence analysis and classification. In: Greenacre M, Blasius J, eds. Multiple Correspondence Analysis and Related Methods. Boca Raton, FL: Chapman & Hall; 2006, 371-392.
    • (2006) Multiple Correspondence Analysis and Related Methods , pp. 371-392
    • Saporta, G.1    Niang, N.2
  • 60
    • 63049097886 scopus 로고    scopus 로고
    • Discriminant correspondence analysis
    • Salkind NJ, ed. Thousand Oaks, CA: Sage Publications
    • Abdi H. Discriminant correspondence analysis. In: Salkind NJ, ed. Encyclopedia of Measurement and Statistics. Thousand Oaks, CA: Sage Publications; 2007, 270-275.
    • (2007) Encyclopedia of Measurement and Statistics , pp. 270-275
    • Abdi, H.1
  • 61
    • 77957566813 scopus 로고    scopus 로고
    • Barycentric discriminant analyis (BADIA)
    • Salkind NJ, ed. Thousand Oaks, CA: Sage, (In press)
    • Abdi H, Williams LJ. Barycentric discriminant analyis (BADIA). In: Salkind NJ, ed. Encyclopedia of Research Design. Thousand Oaks, CA: Sage; 2010, (In press).
    • (2010) Encyclopedia of Research Design
    • Abdi, H.1    Williams, L.J.2
  • 65
    • 0014595721 scopus 로고
    • Some applications of the singular value decomposition of a matrix
    • Good I. Some applications of the singular value decomposition of a matrix. Technometrics 1969, 11:823-831.
    • (1969) Technometrics , vol.11 , pp. 823-831
    • Good, I.1
  • 66
    • 0000802374 scopus 로고
    • The approximation of a matrix by another of a lower rank
    • Eckart C, Young G. The approximation of a matrix by another of a lower rank. Psychometrika 1936, 1:211-218.
    • (1936) Psychometrika , vol.1 , pp. 211-218
    • Eckart, C.1    Young, G.2
  • 67
    • 6344222582 scopus 로고    scopus 로고
    • Factor rotations
    • Lewis-Beck M, Bryman A., Futimg T., eds. Thousand Oaks, CA: Sage Publications
    • Abdi H. Factor Rotations. In Lewis-Beck M, Bryman A., Futimg T., eds. Encyclopedia for Research Methods for the Social Sciences. Thousand Oaks, CA: Sage Publications; 2003, 978-982.
    • (2003) Encyclopedia for Research Methods for the Social Sciences , pp. 978-982
    • Abdi, H.1


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