IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v184y2021ics0047259x21000324.html
   My bibliography  Save this article

Principal loading analysis

Author

Listed:
  • Bauer, Jan O.
  • Drabant, Bernhard

Abstract

This paper proposes a tool for dimension reduction where the dimension of the original space is reduced: the principal loading analysis. Principal loading analysis is a tool to reduce dimensions by discarding variables. The intuition is that variables are dropped which distort the covariance matrix only by a little. Our method is introduced and an algorithm for conducting principal loading analysis is provided. Further, we give bounds for the noise arising in the sample case.

Suggested Citation

  • Bauer, Jan O. & Drabant, Bernhard, 2021. "Principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000324
    DOI: 10.1016/j.jmva.2021.104754
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21000324
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104754?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. E. R. Mansfield & J. T. Webster & R. F. Gunst, 1977. "An Analytic Variable Selection Technique for Principal Component Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 34-40, March.
    2. Peres-Neto, Pedro R. & Jackson, Donald A. & Somers, Keith M., 2005. "How many principal components? stopping rules for determining the number of non-trivial axes revisited," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 974-997, June.
    3. 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.
    4. 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.
    5. 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.
    6. Kollo, T. & Neudecker, H., 1993. "Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 283-300, November.
    7. 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.
    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. J. O. Bauer & B. Drabant, 2021. "Regression based thresholds in principal loading analysis," Papers 2103.06691, arXiv.org, revised Mar 2022.
    2. Bauer, Jan O. & Drabant, Bernhard, 2023. "Regression based thresholds in principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

    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. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. 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.
    4. 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).
    5. Psaradakis, Zacharias & Vávra, Marián, 2014. "On testing for nonlinearity in multivariate time series," Economics Letters, Elsevier, vol. 125(1), pages 1-4.
    6. Bauer, Jan O. & Drabant, Bernhard, 2023. "Regression based thresholds in principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    7. 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.
    8. 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.
    9. Sergio Camiz & Valério D. Pillar, 2018. "Identifying the Informational/Signal Dimension in Principal Component Analysis," Mathematics, MDPI, vol. 6(11), pages 1-16, November.
    10. Joy R. Petway & Yu-Pin Lin & Rainer F. Wunderlich, 2019. "Analyzing Opinions on Sustainable Agriculture: Toward Increasing Farmer Knowledge of Organic Practices in Taiwan-Yuanli Township," Sustainability, MDPI, vol. 11(14), pages 1-27, July.
    11. Leise Kelli de Oliveira & Carla de Oliveira Leite Nascimento & Paulo Renato de Sousa & Paulo Tarso Vilela de Resende & Francisco Gildemir Ferreira da Silva, 2019. "Transport Service Provider Perception of Barriers and Urban Freight Policies in Brazil," Sustainability, MDPI, vol. 11(24), pages 1-17, December.
    12. Dray, Stephane, 2008. "On the number of principal components: A test of dimensionality based on measurements of similarity between matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2228-2237, January.
    13. Kokoszka, Piotr & Reimherr, Matthew, 2013. "Asymptotic normality of the principal components of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1546-1562.
    14. Xiao, Sinan & Lu, Zhenzhou & Xu, Liyang, 2017. "Multivariate sensitivity analysis based on the direction of eigen space through principal component analysis," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 1-10.
    15. Qingyong Wang & Hong-Ning Dai & Hao Wang, 2017. "A Smart MCDM Framework to Evaluate the Impact of Air Pollution on City Sustainability: A Case Study from China," Sustainability, MDPI, vol. 9(6), pages 1-17, May.
    16. Diego Bernardo Avanzini, 2009. "Designing Composite Entrepreneurship Indicators: An Application Using Consensus PCA," WIDER Working Paper Series RP2009-41, World Institute for Development Economic Research (UNU-WIDER).
    17. Aaron Fisher & Brian Caffo & Brian Schwartz & Vadim Zipunnikov, 2016. "Fast, Exact Bootstrap Principal Component Analysis for > 1 Million," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 846-860, April.
    18. Brint, Andrew & Genovese, Andrea & Piccolo, Carmela & Taboada-Perez, Gerardo J., 2021. "Reducing data requirements when selecting key performance indicators for supply chain management: The case of a multinational automotive component manufacturer," International Journal of Production Economics, Elsevier, vol. 233(C).
    19. Archimbaud, Aurore & Nordhausen, Klaus & Ruiz-Gazen, Anne, 2018. "ICS for multivariate outlier detection with application to quality control," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 184-199.
    20. Imran Ahmad & Jung-Yong Kim, 2018. "Assessment of Whole Body and Local Muscle Fatigue Using Electromyography and a Perceived Exertion Scale for Squat Lifting," IJERPH, MDPI, vol. 15(4), pages 1-12, April.

    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:184:y:2021:i:c:s0047259x21000324. 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.