A 50-year personal journey through time with principal component analysis

N. Al-Kandari, Variable selection and interpretation in principal component analysis (Ph.D. thesis), University of Aberdeen, 1998, Unpublished. Al-Kandari, 2001, Variable selection and interpretation of covariance principal components, Comm. Statist. Simulation Comput., 30, 339, 10.1081/SAC-100002371 Al-Kandari, 2005, Variable selection and interpretation in correlation principal components, Environmetrics, 16, 659, 10.1002/env.728 Anderson, 1963, Asymptotic theory for principal component analysis, Ann. Math. Stat., 34, 122, 10.1214/aoms/1177704248 Beale, 1967, The discarding of variables in multivariate analysis, Biometrika, 54, 357, 10.1093/biomet/54.3-4.357 J. Benasseni, Sensitivity of principal component analysis to data perturbation, in: Fifth International Symposium: Data Analysis and Informatics Tome, Vol. 1, 1987, pp. 249–256. Benasseni, 1990, Sensitivity coefficients for the subspaces spanned by the principal components, Commun. Stat. – Theory Methods, 19, 2021, 10.1080/03610929008830306 Bilodeau, 2002, Principal component analysis from the multivariate familial correlation matrix, J. Multivariate Anal., 82, 457, 10.1006/jmva.2001.2027 Boente, 1987, Asymptotic theory for robust principal components, J. Multivariate Anal., 21, 67, 10.1016/0047-259X(87)90099-6 Bongiorno, 2019, Describing the concentration of income populations by functional principal component analysis on Lorenz curves, J. Multivariate Anal., 170, 10, 10.1016/j.jmva.2018.09.005 Boudou, 1994, Principal component analysis for a stationary random function defined on a locally compact Abelian group, J. Multivariate Anal., 51, 1, 10.1006/jmva.1994.1046 Bru, 1989, Diffusions of perturbed principal components, J. Multivariate Anal., 29, 127, 10.1016/0047-259X(89)90080-8 J.F.C.L Cadima, Topics in descriptive principal component analysis (Ph.D. thesis), University of Kent at Canterbury, 1992, Unpublished. Cadima, 1995, Loadings and correlations in the interpretation of principal components, J. Appl. Stat., 22, 203, 10.1080/757584614 Cadima, 1996, Size and shape-related principal component analysis, Biometrics, 52, 710, 10.2307/2532909 Cadima, 2001, Variable selection and the interpretation of principal subspaces, J. Agric. Biol. Environ. Stat., 6, 62, 10.1198/108571101300325256 Cadima, 2009, On relationships between uncentred and column centred principal component analysis, Pak. J. Statist., 25, 473 P. Calder, Influence functions in multivariate analysis (Ph.D. thesis), University of Kent at Canterbury, 1986, Unpublished. Craddock, 1965, A meteorological application of principal component analysis, Statistician, 15, 143, 10.2307/2987388 Critchley, 1985, Influence in principal components analysis, Biometrika, 72, 627, 10.1093/biomet/72.3.627 Dauxois, 1982, Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference, J. Multivariate Anal., 12, 136, 10.1016/0047-259X(82)90088-4 Dumbgen, 1995, Likelihood ratio teats for principal components, J. Multivariate Anal., 52, 245, 10.1006/jmva.1995.1012 El Faouzi, 1999, Rates of convergence for spline estimates of additive principal components, J. Multivariate Anal., 68, 120, 10.1006/jmva.1998.1781 Fang, 2018, Integrative sparse principal component analysis, J. Multivariate Anal., 166, 1, 10.1016/j.jmva.2018.02.002 Girshick, 1936, Principal components, J. Amer. Statist. Assoc., 31, 519, 10.1080/01621459.1936.10503354 Girshick, 1939, On the sampling theory of roots of determinantal equations, Ann. Math. Stat., 10, 203, 10.1214/aoms/1177732180 Gower, 1966, Some distance properties of latent root and vector methods used in multivariate analysis, Biometrika, 53, 325, 10.1093/biomet/53.3-4.325 Gu, 2001, Influence diagnostics in common principal component analysis, J. Multivariate Anal., 79, 275, 10.1006/jmva.2000.1964 Hannachi, 2006, In search of simple structures in climate: Simplifying EOFs, Int. J. Climatol., 26, 7, 10.1002/joc.1243 Hotelling, 1933, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol., 24, 10.1037/h0070888 Hotelling, 1936, Simplified computation of principal components, Psychometrika, 1, 27, 10.1007/BF02287921 Jackson, 1991 Jeffers, 1967, Two case studies in the application of principal component analysis, Appl. Statist., 16, 225, 10.2307/2985919 Jolliffe, 1972, Discarding variables in a principal component analysis I: Artificial data, Appl. Statist., 21, 160, 10.2307/2346488 Jolliffe, 1973, Discarding variables in a principal component analysis II: Real data, Appl. Statist., 22, 21, 10.2307/2346300 Jolliffe, 1982, A note on the use of principal components in regression, Appl. Statist., 31, 300, 10.2307/2348005 Jolliffe, 1986 Jolliffe, 1987, Rotation of principal components: Some comments, J. Climatol., 7, 507, 10.1002/joc.3370070506 Jolliffe, 1989, Rotation of ill-defined principal components, Appl. Statist., 38, 139, 10.2307/2347688 Jolliffe, 1995, Rotation of principal components: choice of normalization constraints, J. Appl. Stat., 22, 29, 10.1080/757584395 Jolliffe, 2002 Jolliffe, 2016, Principal component analysis: a review and recent developments, Phil. Trans. Roy. Soc. A – Math. Phys. Eng. Sci., 374 Jolliffe, 2003, A modified principal component technique based on the LASSO, J. Comput. Graph. Statist., 12, 531, 10.1198/1061860032148 Jolliffe, 2000, The simplified component technique - an alternative to rotated principal components, J. Comput. Graph. Statist., 9, 689 Jolliffe, 2002, Simplified EOFs – three alternatives to rotation, Clim. Res., 20, 271, 10.3354/cr020271 Kalogridis, 2019, Robust functional regression based on principal components, J. Multivariate Anal., 173, 393, 10.1016/j.jmva.2019.04.003 Kamiya, 2001, A class of robust principal component vectors, J. Multivariate Anal., 77, 239, 10.1006/jmva.2000.1936 Kim, 2016, Sparse PCA-based on high-dimensional Itô processes with measurement errors, J. Multivariate Anal., 152, 172, 10.1016/j.jmva.2016.08.006 Krzanowski, 1987, Selection of variables to preserve multivariate structure, using principal components, Appl. Statist., 36, 22, 10.2307/2347842 Lakraj, 2017, Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space, J. Multivariate Anal., 155, 122, 10.1016/j.jmva.2016.12.004 Lazar, 2017, Scale and curvature effects in principal geodesic analysis, J. Multivariate Anal., 153, 64, 10.1016/j.jmva.2016.09.009 Li, 2018, Spatial functional principal component analysis with applications to brain image data, J. Multivariate Anal., 170, 263, 10.1016/j.jmva.2018.11.004 Mann, 2012 Mann, 1998, Global-scale temperature patterns and climate forcing over the past six centuries, Nature, 392, 779, 10.1038/33859 McIntyre, 2005, Hockey sticks, principal components and spurious significance, Geophys. Res. Lett., 32, L03710 Merola, 2019, Projection sparse principal component analysis: An efficient least squares method, J. Multivariate Anal., 173, 366, 10.1016/j.jmva.2019.04.001 Nakayama, 2021, Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings, J. Multivariate Anal., 185, 10.1016/j.jmva.2021.104779 Neuenschwander, 2000, Common principal components for dependent random vectors, J. Multivariate Anal., 75, 163, 10.1006/jmva.2000.1908 Ocãna, 1999, Functional principal components analysis by choice of norm, J. Multivariate Anal., 71, 262, 10.1006/jmva.1999.1844 Pack, 1988, Influential observations in principal component analysis: A case study, J. Appl. Stat., 15, 39, 10.1080/02664768800000004 Pearson, 1901, On lines and planes of closest fit to systems of points in space, Phil. Mag., 2, 559, 10.1080/14786440109462720 Preisendorfer, 1988 Qian, 1994, Principal component selection by the criterion of the minimum mean difference of complexity, J. Multivariate Anal., 49, 55, 10.1006/jmva.1994.1013 Rao, 1964, The use and interpretation of principal component analysis in applied research, Sankhyā A, 26, 329 Richman, 1986, Rotation of principal components, J. Climatol., 6, 293, 10.1002/joc.3370060305 Richman, 1987, Rotation of principal components: A reply, J. Climatol., 7, 511, 10.1002/joc.3370070507 Risbey, 2021, The identification of long-lived Southern Hemisphere flow events using archetypes and principal components, Mon. Weather Rev., 149, 1987 Ruymgaart, 1981, A robust principal component analysis, J. Multivariate Anal., 11, 485, 10.1016/0047-259X(81)90091-9 Schneeweiss, 1995, Factor Analysis and principal components, J. Multivariate Anal., 55, 105, 10.1006/jmva.1995.1069 Song, 2021, Nonlinear and additive principal component analysis for functional data, J. Multivariate Anal., 181, 10.1016/j.jmva.2020.104675 Tanaka, 1988, Sensitivity analysis in principal component analysis: Influence on the subspace spanned by principal components, Commun. Stat. – Theory Methods, 17, 3157, 10.1080/03610928808829796 Y. Tanaka, T. Tarumi, A numerical investigation of sensitivity analysis in multivariate methods, in: Fifth International Symposium: Data Analysis and Informatics Tome, Vol. 1, 1987, pp. 237–247. ter Braak, 1983, Principal component biplots and alpha and beta diversity, Ecology, 64, 454, 10.2307/1939964 Tibshirani, 1996, Regression shrinkage and selection via the Lasso, J. Roy. Statist. Soc. B, 58, 267 Trendafilov, 2006, Projected gradient approach to the numerical solution of the SCoTLASS, Comput. Statist. Data Anal., 50, 242, 10.1016/j.csda.2004.07.017 M. Uddin, Interpretation of results from simplified principal components (Ph.D. thesis), University of Aberdeen, 1999, Unpublished. Vines, 2000, Simple principal components, Appl. Statist., 49, 441 Waternaux, 1984, Principal components in the nonnormal case: The test of equality of Q roots, J. Multivariate Anal., 14, 323, 10.1016/0047-259X(84)90037-X Zou, 2006, Sparse principal component analysis, J. Comput. Graph. Statist., 15, 265, 10.1198/106186006X113430