IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v188y2022ics0047259x21000981.html
   My bibliography  Save this article

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

Author

Listed:
  • Jolliffe, Ian

Abstract

Principal component analysis (PCA) is one of the most widely used multivariate techniques. A little more than 50 years ago I first encountered PCA and it has played an important role in my career and beyond, for many years since. I have been persuaded that an account of my 50-year journey through time with PCA would be a suitable topic for inclusion in the Jubilee Issue of JMVA and this is the result.

Suggested Citation

  • Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21000981
    DOI: 10.1016/j.jmva.2021.104820
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21000981
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104820?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Merola, Giovanni Maria & Chen, Gemai, 2019. "Projection sparse principal component analysis: An efficient least squares method," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 366-382.
    2. Nakayama, Yugo & Yata, Kazuyoshi & Aoshima, Makoto, 2021. "Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    3. W. J. Krzanowski, 1987. "Selection of Variables to Preserve Multivariate Data Structure, Using Principal Components," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(1), pages 22-33, March.
    4. Fang, Kuangnan & Fan, Xinyan & Zhang, Qingzhao & Ma, Shuangge, 2018. "Integrative sparse principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 1-16.
    5. Neuenschwander, Beat E. & Flury, Bernard D., 2000. "Common Principal Components for Dependent Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 163-183, November.
    6. Boudou, A. & Dauxois, J., 1994. "Principal Component Analysis for a Stationary Random Function Defined on a Locally Compact Abelian Group," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 1-16, October.
    7. El Faouzi, Nour Eddin & Sarda, Pascal, 1999. "Rates of Convergence for Spline Estimates of Additive Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 120-137, January.
    8. Gu, Hong & Fung, Wing K., 2001. "Influence Diagnostics in Common Principal Components Analysis," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 275-294, November.
    9. Lazar, Drew & Lin, Lizhen, 2017. "Scale and curvature effects in principal geodesic analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 64-82.
    10. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.
    11. Bongiorno, Enea G. & Goia, Aldo, 2019. "Describing the concentration of income populations by functional principal component analysis on Lorenz curves," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 10-24.
    12. Song, Jun & Li, Bing, 2021. "Nonlinear and additive principal component analysis for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    13. Lakraj, Gamage Pemantha & Ruymgaart, Frits, 2017. "Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 122-132.
    14. Ocaña, F. A. & Aguilera, A. M. & Valderrama, M. J., 1999. "Functional Principal Components Analysis by Choice of Norm," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 262-276, November.
    15. Qian, G. Q. & Gabor, G. & Gupta, R. P., 1994. "Principal Components Selection by the Criterion of the Minimum Mean Difference of Complexity," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 55-75, April.
    16. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    17. I. T. Jolliffe, 1973. "Discarding Variables in a Principal Component Analysis. Ii: Real Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(1), pages 21-31, March.
    18. S. K. Vines, 2000. "Simple principal components," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 441-451.
    19. Michael E. Mann & Raymond S. Bradley & Malcolm K. Hughes, 1998. "Global-scale temperature patterns and climate forcing over the past six centuries," Nature, Nature, vol. 392(6678), pages 779-787, April.
    20. Kalogridis, Ioannis & Van Aelst, Stefan, 2019. "Robust functional regression based on principal components," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 393-415.
    21. Schneeweiss, H. & Mathes, H., 1995. "Factor Analysis and Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 105-124, October.
    22. Bilodeau, Martin & Duchesne, Pierre, 2002. "Principal Component Analysis from the Multivariate Familial Correlation Matrix," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 457-470, August.
    23. Ian T. Jolliffe, 1982. "A Note on the Use of Principal Components in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 300-303, November.
    24. Ruymgaart, F. H., 1981. "A robust principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 485-497, December.
    25. Waternaux, Christine M., 1984. "Principal components in the nonnormal case: The test of equality of Q roots," Journal of Multivariate Analysis, Elsevier, vol. 14(3), pages 323-335, June.
    26. Boente, Graciela, 1987. "Asymptotic theory for robust principal components," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 67-78, February.
    27. I. T. Jolliffe, 1972. "Discarding Variables in a Principal Component Analysis. I: Artificial Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 160-173, June.
    28. Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 127-136, April.
    29. Kamiya, Hidehiko & Eguchi, Shinto, 2001. "A Class of Robust Principal Component Vectors," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 239-269, May.
    30. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    31. J. N. R. Jeffers, 1967. "Two Case Studies in the Application of Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 16(3), pages 225-236, November.
    32. Trendafilov, Nickolay T. & Jolliffe, Ian T., 2006. "Projected gradient approach to the numerical solution of the SCoTLASS," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 242-253, January.
    33. Kim, Donggyu & Wang, Yazhen, 2016. "Sparse PCA-based on high-dimensional Itô processes with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 172-189.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bai, Xiwen & Cheng, Liangqi & Yang, Dong & Cai, Ouchen, 2022. "Does the traffic volume of a port determine connectivity? Revisiting port connectivity measures with high-frequency satellite data," Journal of Transport Geography, Elsevier, vol. 102(C).
    2. Federica Maschietto & Uriel N. Morzan & Florentina Tofoleanu & Aria Gheeraert & Apala Chaudhuri & Gregory W. Kyro & Peter Nekrasov & Bernard Brooks & J. Patrick Loria & Ivan Rivalta & Victor S. Batist, 2023. "Turning up the heat mimics allosteric signaling in imidazole-glycerol phosphate synthase," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    3. Di Wu & Zhenning Xu & Seung Bach, 2023. "Using Google Trends to predict and forecast avocado sales," Journal of Marketing Analytics, Palgrave Macmillan, vol. 11(4), pages 629-641, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cumming, J.A. & Wooff, D.A., 2007. "Dimension reduction via principal variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 550-565, September.
    2. Pacheco, Joaquín & Casado, Silvia & Porras, Santiago, 2013. "Exact methods for variable selection in principal component analysis: Guide functions and pre-selection," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 95-111.
    3. Bauer, Jan O. & Drabant, Bernhard, 2021. "Principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Brusco, Michael J., 2014. "A comparison of simulated annealing algorithms for variable selection in principal component analysis and discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 38-53.
    5. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Martínez-Ventura, Constanza & Mariño-Martínez, Ricardo & Miguélez-Márquez, Javier, 2023. "Redundancy of Centrality Measures in Financial Market Infrastructures," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 4(4).
    7. Luca Scrucca, 2006. "Subset selection in dimension reduction methods," Quaderni del Dipartimento di Economia, Finanza e Statistica 23/2006, Università di Perugia, Dipartimento Economia.
    8. Trendafilov, Nickolay T. & Vines, Karen, 2009. "Simple and interpretable discrimination," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 979-989, February.
    9. Sabatier, Robert & Reynès, Christelle, 2008. "Extensions of simple component analysis and simple linear discriminant analysis using genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4779-4789, June.
    10. Christian Acal & Manuel Escabias & Ana M. Aguilera & Mariano J. Valderrama, 2021. "COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression," Mathematics, MDPI, vol. 9(11), pages 1-23, May.
    11. Fraiman, Ricardo & Pateiro-López, Beatriz, 2012. "Quantiles for finite and infinite dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 1-14.
    12. António Pedro Duarte Silva, 2002. "Discarding Variables in a Principal Component Analysis: Algorithms for All-Subsets Comparisons," Computational Statistics, Springer, vol. 17(2), pages 251-271, July.
    13. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    14. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    15. Christian Acal & Ana M. Aguilera & Manuel Escabias, 2020. "New Modeling Approaches Based on Varimax Rotation of Functional Principal Components," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    16. Doyo Enki & Nickolay Trendafilov, 2012. "Sparse principal components by semi-partition clustering," Computational Statistics, Springer, vol. 27(4), pages 605-626, December.
    17. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    18. Sergio Camiz & Valério D. Pillar, 2018. "Identifying the Informational/Signal Dimension in Principal Component Analysis," Mathematics, MDPI, vol. 6(11), pages 1-16, November.
    19. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    20. Fernandez-Haddad, Zaira & Quiroga, Sonia, 2011. "Adaptation Of Mediterranean Crops To Water Pressure In The Ebro Basin: A Water Efficiency Index," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114358, European Association of Agricultural Economists.

    More about this item

    Keywords

    Principal component analysis;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21000981. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.