Abstract
The aim of this paper is to obtain discrete-valued weights of the variables by constraining them to Hausman weights (−1, 0, 1) in principal component analysis. And this is done in two steps: First, we start with the centroid method, which produces the most restricted optimal weights −1 and 1; then extend the weights to −1,0 or 1.
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References
BURT, C. (1917): The Distribution And Relations Of Educational Abilities. P.S. King & Son: London.
CADIMA, J., and JOLLIFFE, I.T. (1995): Loadings and correlations in the interpretation of principal components. Journal of Applied Statistics, 22, 203–214.
CHIPMAN, H.A., and GU, H. (2003): Interpretable dimension reduction. To appear in Journal of Applied Statistics.
CHOULAKIAN, V. (2001): Robust Q-mode principal component analysis in L1. Computational Statistics and Data Analysis, 37, 135–150.
CHOULAKIAN, V. (2003): The optimality of the centroid method. Psychometriks, 68, 473–475.
CHOULAKIAN, V. (2005a): Transposition invariant principal component analysis in L1. Statistics and Probability Letters, 71,1, 23–31.
CHOULAKIAN, V. (2005b): L1-norm projection pursuit principal component analysis. Computational Statistics and Data Analysis, in press.
Hausman, R.E. (1982): Constrained multivariate analysis. Studies in Management Sciences, 19, 137–151.
JACKSON, J.E. (1991): A User’s Guide To Principal Components. Wiley: New York.
JOLLIFFE, I.T. (2002): Principal Component Analysis. Springer Verlag: New York, 2nd edition.
ROUSSON and GASSER (2004): Simple component analysis. Applied Statistics, 53, 539–556.
THURSTONE, L.L. (1931): Multiple factor analysis. Psychological Review, 38, 406–427.
VINES, S.K. (2000): Simple principal components. Applied Statistics, 49, 441–451.
WOLD, H. (1966): Estimation of principal components and related models by iterative least squares. In Krishnaiah, P.R., ed.: Multivariate Analysis, Academic Press, N.Y., pp. 391–420.
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Choulakian, V., Dambra, L., Simonetti, B. (2006). Hausman Principal Component Analysis. In: Spiliopoulou, M., Kruse, R., Borgelt, C., Nürnberger, A., Gaul, W. (eds) From Data and Information Analysis to Knowledge Engineering. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31314-1_35
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DOI: https://doi.org/10.1007/3-540-31314-1_35
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