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Transposition invariant principal component analysis in L1 for long tailed data

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  • Choulakian, Vartan

Abstract

Similar to the ordinary principal component analysis (PCA), we develop PCA in L1 satisfying an invariance property: The objective function, which is a matrix norm, is transposition invariant. The new method is robust and specifically useful for long-tailed data. An example is provided.

Suggested Citation

  • Choulakian, Vartan, 2005. "Transposition invariant principal component analysis in L1 for long tailed data," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 23-31, January.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:23-31
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    References listed on IDEAS

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    1. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    2. Choulakian, V., 2001. "Robust Q-mode principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 37(2), pages 135-150, August.
    3. Heiser, Willem J., 1987. "Correspondence analysis with least absolute residuals," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 337-356, September.
    4. Vartan Choulakian, 2003. "The optimality of the centroid method," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 473-475, September.
    5. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    6. Galpin, Jacqueline S. & Hawkins, Douglas M., 1987. "Methods of L1 estimation of a covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 305-319, September.
    7. 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.
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    Cited by:

    1. Choulakian, V., 2006. "L1-norm projection pursuit principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1441-1451, March.
    2. Choulakian, V. & Allard, J. & Almhana, J., 2006. "Robust centroid method," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 737-746, November.
    3. Vartan Choulakian & Jules Tibeiro, 2013. "Graph Partitioning by Correspondence Analysis and Taxicab Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 397-427, October.
    4. T. F. Cox & D. S. Arnold, 2018. "Simple components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 83-99, January.
    5. Vartan Choulakian & Biagio Simonetti & Thu Pham Gia, 2014. "Some new aspects of taxicab correspondence analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 401-416, August.

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