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PCA stability and choice of dimensionality

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  • Besse, Philippe

Abstract

A Criterion of stability for PCA scatterplots is defined based on a classical distance between projectors. It is constructed as a risk function and can be estimated by bootstrap or jackknife methods. Furthermore, perturbation theory is used to write down a Taylor expansion of the jackknife estimate for reasons of computational cost and in order to obtain an analytic expression for the approximation. The comparative study of these three estimates on real data shows that the last one is easy to compute, sufficiently accurate and helpful in choosing dimensionality in PCA.

Suggested Citation

  • Besse, Philippe, 1992. "PCA stability and choice of dimensionality," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 405-410, April.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:5:p:405-410
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    Citations

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    Cited by:

    1. Besse, Philippe C. & Cardot, Herve & Ferraty, Frederic, 1997. "Simultaneous non-parametric regressions of unbalanced longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 255-270, May.
    2. Li, Luyi & Lu, Zhenzhou, 2018. "A new method for model validation with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 579-592.
    3. Dray, Stephane, 2008. "On the number of principal components: A test of dimensionality based on measurements of similarity between matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2228-2237, January.
    4. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    5. Ferre, Louis, 1995. "Selection of components in principal component analysis: A comparison of methods," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 669-682, June.
    6. Peijun Sang & Liangliang Wang & Jiguo Cao, 2017. "Parametric functional principal component analysis," Biometrics, The International Biometric Society, vol. 73(3), pages 802-810, September.
    7. Jiyeon Song & Seung Jun Shin, 2018. "Stability approach to selecting the number of principal components," Computational Statistics, Springer, vol. 33(4), pages 1923-1938, December.
    8. Lamboni, Matieyendou & Monod, Hervé & Makowski, David, 2011. "Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 450-459.

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