IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v30y2015i4p1079-1096.html
   My bibliography  Save this article

Principal component analysis for compositional data vectors

Author

Listed:
  • Huiwen Wang
  • Liying Shangguan
  • Rong Guan
  • Lynne Billard

Abstract

Since Aitchison’s founding research work, compositional data analysis has attracted growing attention in recent decades. As a powerful technique for exploratory analysis, principal component analysis (PCA) has been extended to compositional data. Despite extensive efforts in PCA on compositional data parts as variables, this paper contributes to modeling PCA for compositional data vectors. Based on algebraic operators in Simplex space, the PCA process is deduced and transformed into calculating some inner products. Properties of principal components are also investigated. Two real-data examples illustrate the merits of the proposed PCA for compositional data vectors. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Huiwen Wang & Liying Shangguan & Rong Guan & Lynne Billard, 2015. "Principal component analysis for compositional data vectors," Computational Statistics, Springer, vol. 30(4), pages 1079-1096, December.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:4:p:1079-1096
    DOI: 10.1007/s00180-015-0570-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-015-0570-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-015-0570-1?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. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392, October.
    2. Federica Gioia & Carlo Lauro, 2006. "Principal component analysis on interval data," Computational Statistics, Springer, vol. 21(2), pages 343-363, June.
    3. Wang, Huiwen & Liu, Qiang & Mok, Henry M.K. & Fu, Linghui & Tse, Wai Man, 2007. "A hyperspherical transformation forecasting model for compositional data," European Journal of Operational Research, Elsevier, vol. 179(2), pages 459-468, June.
    4. Allan G. B. Fisher, 1939. "Production, Primary, Secondary And Tertiary," The Economic Record, The Economic Society of Australia, vol. 15(1), pages 24-38, June.
    5. Pallavi Sawant & Nedret Billor & Hyejin Shin, 2012. "Functional outlier detection with robust functional principal component analysis," Computational Statistics, Springer, vol. 27(1), pages 83-102, March.
    6. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    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. Xinping Xiao & Xue Li, 2023. "A novel compositional data model for predicting the energy consumption structures of Europe, Japan, and China," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(10), pages 11673-11698, October.
    2. Wenyang Huang & Huiwen Wang & Shanshan Wang, 2021. "Dimension reduction of open-high-low-close data in candlestick chart based on pseudo-PCA," Papers 2103.16908, arXiv.org.

    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. Javier Palarea-Albaladejo & Josep Martín-Fernández & Jesús Soto, 2012. "Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data," Journal of Classification, Springer;The Classification Society, vol. 29(2), pages 144-169, July.
    2. 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.
    3. Andreja Benkovic & Juan Felipe Mejía, 2008. "Tourism as a driver of economic development: The Colombian experience," Documentos de Trabajo de Valor Público 10630, Universidad EAFIT.
    4. B. Baris Alkan & Afsin Sahin, 2011. "Measuring inequalities in the distribution of health workers by bi-plot approach: The case of Turkey," Journal of Economics and Behavioral Studies, AMH International, vol. 2(2), pages 57-66.
    5. Seppo Kuula & Harri Haapasalo & Arto Tolonen, 2018. "Cost-efficient co-creation of knowledge intensive business services," Service Business, Springer;Pan-Pacific Business Association, vol. 12(4), pages 779-808, December.
    6. Rao, Congjun & Zhang, Yue & Wen, Jianghui & Xiao, Xinping & Goh, Mark, 2023. "Energy demand forecasting in China: A support vector regression-compositional data second exponential smoothing model," Energy, Elsevier, vol. 263(PC).
    7. Maryam Sabreen & Deepak Kumar Behera, 2020. "Changing Structure of Rural Employment in Bihar: Issues and Challenges," The Indian Journal of Labour Economics, Springer;The Indian Society of Labour Economics (ISLE), vol. 63(3), pages 833-845, September.
    8. Borgersen, Trond-Arne & King, Roswitha M., 2014. "Structural origins of debt-sustainability in mature and transition economies: Domar, Balassa–Samuelson and Maastricht," Structural Change and Economic Dynamics, Elsevier, vol. 30(C), pages 101-119.
    9. Michael Greenacre, 2016. "Selection and statistical analysis of compositional ratios," Economics Working Papers 1551, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Fourcroy, Charlotte & Gallouj, Faiz & Decellas, Fabrice, 2012. "Energy consumption in service industries: Challenging the myth of non-materiality," Ecological Economics, Elsevier, vol. 81(C), pages 155-164.
    11. Drago, Carlo & Gatto, Andrea, 2022. "Policy, regulation effectiveness, and sustainability in the energy sector: A worldwide interval-based composite indicator," Energy Policy, Elsevier, vol. 167(C).
    12. Giovanni C. Porzio & Giancarlo Ragozini & Domenico Vistocco, 2008. "On the use of archetypes as benchmarks," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 419-437, September.
    13. Amitava Krishna Dutt, 1989. "Sectoral Balance: A Survey," WIDER Working Paper Series wp-1989-056, World Institute for Development Economic Research (UNU-WIDER).
    14. Michael Greenacre & Paul Lewi, 2005. "Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data," Economics Working Papers 908, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2007.
    15. Matteo Lucchese, 2011. "Innovation, demand and structural change in Europe," Working Papers 1109, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2011.
    16. Anna Maria Fiori & Francesco Porro, 2023. "A compositional analysis of systemic risk in European financial institutions," Annals of Finance, Springer, vol. 19(3), pages 325-354, September.
    17. J. Le-Rademacher & L. Billard, 2013. "Principal component histograms from interval-valued observations," Computational Statistics, Springer, vol. 28(5), pages 2117-2138, October.
    18. Valeriy V. Mironov & Liudmila D. Konovalova, 2019. "Structural changes and economic growth in the world economy and Russia," Russian Journal of Economics, ARPHA Platform, vol. 5(1), pages 1-26, April.
    19. Andrzej Młodak, 2014. "On the construction of an aggregated measure of the development of interval data," Computational Statistics, Springer, vol. 29(5), pages 895-929, October.
    20. Nayak, Purusottam & Mishra, SK, 2009. "Structural Change in Meghalaya: Theory and Evidence," MPRA Paper 15728, University Library of Munich, Germany.

    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:compst:v:30:y:2015:i:4:p:1079-1096. 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.