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Transposition invariant principal component analysis in L1 for long tailed data

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  • Choulakian, Vartan
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    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.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 1 (January)
    Pages: 23-31

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:23-31
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    1. Vartan Choulakian, 2003. "The optimality of the centroid method," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 473-475, September.
    2. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    3. 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.
    4. 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.
    5. 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.
    6. Choulakian, V., 2001. "Robust Q-mode principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 37(2), pages 135-150, August.
    7. Heiser, Willem J., 1987. "Correspondence analysis with least absolute residuals," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 337-356, September.
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