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Principal component analysis for compositional data vectors

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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.
    3. 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.

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