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. 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.
    2. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    3. 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.
    4. Federica Gioia & Carlo Lauro, 2006. "Principal component analysis on interval data," Computational Statistics, Springer, vol. 21(2), pages 343-363, June.
    5. 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.
    6. 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.
    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. Caiyue Xu & Xinping Xiao & Hui Chen, 2024. "A novel method for forecasting renewable energy consumption structure based on compositional data: evidence from China, the USA, and Canada," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(2), pages 5299-5333, February.
    3. 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. Kox, Henk L.M. & Rubalcaba, Luis, 2007. "Business services and the changing structure of European economic growth," MPRA Paper 3750, University Library of Munich, Germany.
    6. Montobbio, Fabio, 2002. "An evolutionary model of industrial growth and structural change," Structural Change and Economic Dynamics, Elsevier, vol. 13(4), pages 387-414, December.
    7. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
    8. 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.
    9. Martin Gornig & Jan Goebel, 2014. "Deindustrialization and Tertiarization and the Polarization of Household Incomes: The Example of German Agglomerations," ERSA conference papers ersa14p1172, European Regional Science Association.
    10. Pandit, Kavita, 2000. "Expanding the "Region" in Regional Science: How Third World Experience Can Enrich Our Research," The Review of Regional Studies, Southern Regional Science Association, vol. 30(1), pages 75-78, Summer.
    11. Sadik-Zada, Elkhan Richard & Gatto, Andrea, 2021. "The puzzle of greenhouse gas footprints of oil abundance," Socio-Economic Planning Sciences, Elsevier, vol. 75(C).
    12. 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).
    13. 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.
    14. 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.
    15. Michael Greenacre, 2016. "Selection and statistical analysis of compositional ratios," Economics Working Papers 1551, Department of Economics and Business, Universitat Pompeu Fabra.
    16. 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.
    17. 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).
    18. 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.
    19. Terence C. Mills, 2009. "Forecasting obesity trends in England," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 107-117, January.
    20. Amitava Krishna Dutt, 1989. "Sectoral Balance: A Survey," WIDER Working Paper Series wp-1989-056, World Institute for Development Economic Research (UNU-WIDER).

    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.