IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v31y2022i2d10.1007_s10260-021-00575-5.html
   My bibliography  Save this article

Chunk-wise regularised PCA-based imputation of missing data

Author

Listed:
  • A. Iodice D’Enza

    (Univeristà degli studi di Napoli Federico II)

  • A. Markos

    (Democritus University of Thrace)

  • F. Palumbo

    (Univeristà degli studi di Napoli Federico II)

Abstract

Standard multivariate techniques like Principal Component Analysis (PCA) are based on the eigendecomposition of a matrix and therefore require complete data sets. Recent comparative reviews of PCA algorithms for missing data showed the regularised iterative PCA algorithm (RPCA) to be effective. This paper presents two chunk-wise implementations of RPCA suitable for the imputation of “tall” data sets, that is, data sets with many observations. A “chunk” is a subset of the whole set of available observations. In particular, one implementation is suitable for distributed computation as it imputes each chunk independently. The other implementation, instead, is suitable for incremental computation, where the imputation of each new chunk is based on all the chunks analysed that far. The proposed procedures were compared to batch RPCA considering different data sets and missing data mechanisms. Experimental results showed that the distributed approach had similar performance to batch RPCA for data with entries missing completely at random. The incremental approach showed appreciable performance when the data is missing not completely at random, and the first analysed chunks contain sufficient information on the data structure.

Suggested Citation

  • A. Iodice D’Enza & A. Markos & F. Palumbo, 2022. "Chunk-wise regularised PCA-based imputation of missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 365-386, June.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:2:d:10.1007_s10260-021-00575-5
    DOI: 10.1007/s10260-021-00575-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-021-00575-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-021-00575-5?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. Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 251-266, June.
    2. Marco Geraci & Alessio Farcomeni, 2016. "Probabilistic principal component analysis to identify profiles of physical activity behaviours in the presence of non-ignorable missing data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 51-75, January.
    3. Sébastien Loisel & Yoshio Takane, 2019. "Comparisons among several methods for handling missing data in principal component analysis (PCA)," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 495-518, June.
    4. P. Robert & Y. Escoufier, 1976. "A Unifying Tool for Linear Multivariate Statistical Methods: The RV‐Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 257-265, November.
    5. Hervé Cardot & David Degras, 2018. "Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?," International Statistical Review, International Statistical Institute, vol. 86(1), pages 29-50, April.
    Full references (including those not matched with items on IDEAS)

    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. Qing Li & Long Hai Vo, 2021. "Intangible Capital and Innovation: An Empirical Analysis of Vietnamese Enterprises," Economics Discussion / Working Papers 21-02, The University of Western Australia, Department of Economics.
    2. Joost Ginkel & Pieter Kroonenberg, 2014. "Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 242-269, July.
    3. Husson, François & Josse, Julie & Saporta, Gilbert, 2016. "Jan de Leeuw and the French School of Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i06).
    4. de Leeuw, Jan, 2006. "Principal component analysis of binary data by iterated singular value decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 21-39, January.
    5. Cling, Jean-Pierre & Delecourt, Clément, 2022. "Interlinkages between the Sustainable Development Goals," World Development Perspectives, Elsevier, vol. 25(C).
    6. Delimiro Visbal-Cadavid & Mónica Martínez-Gómez & Rolando Escorcia-Caballero, 2020. "Exploring University Performance through Multiple Factor Analysis: A Case Study," Sustainability, MDPI, vol. 12(3), pages 1-24, January.
    7. Florence Jacquet & A Aboul-Naga & Bernard Hubert, 2020. "The contribution of ARIMNet to address livestock systems resilience in the Mediterranean region," Post-Print hal-03625860, HAL.
    8. Rauf Ahmad, M., 2019. "A significance test of the RV coefficient in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 116-130.
    9. Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2013. "Measuring Association and Dependence Between Random Vectors," LIDAM Discussion Papers ISBA 2013026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Roberta De Vito & Ruggero Bellio & Lorenzo Trippa & Giovanni Parmigiani, 2019. "Multi‐study factor analysis," Biometrics, The International Biometric Society, vol. 75(1), pages 337-346, March.
    11. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Camila Kolling & José Luis Duarte Ribeiro & Donato Morea & Gianpaolo Iazzolino, 2023. "Corporate social responsibility and circular economy from the perspective of consumers: A cross‐cultural analysis in the cosmetic industry," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 30(3), pages 1226-1243, May.
    13. Ziwei Zhu & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional principal component analysis with heterogeneous missingness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 2000-2031, November.
    14. Carmen C. Rodríguez-Martínez & Mitzi Cubilla-Montilla & Purificación Vicente-Galindo & Purificación Galindo-Villardón, 2023. "X-STATIS: A Multivariate Approach to Characterize the Evolution of E-Participation, from a Global Perspective," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    15. Dorota Toczydlowska & Gareth W. Peters, 2018. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics," Econometrics, MDPI, vol. 6(3), pages 1-45, July.
    16. Reza Salimi & Kamran Pakizeh, 2024. "The extension of Pearson correlation coefficient, measuring noise, and selecting features," Papers 2402.00543, arXiv.org.
    17. Jarek Duda, 2023. "Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series," Papers 2304.03069, arXiv.org, revised Apr 2023.
    18. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    19. Namgil Lee & Jong-Min Kim, 2018. "Block tensor train decomposition for missing data estimation," Statistical Papers, Springer, vol. 59(4), pages 1283-1305, December.
    20. Zhu, Ziwei & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional principal component analysis with heterogeneous missingness," LSE Research Online Documents on Economics 117647, London School of Economics and Political Science, LSE Library.

    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:spr:stmapp:v:31:y:2022:i:2:d:10.1007_s10260-021-00575-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.