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On the number of principal components: A test of dimensionality based on measurements of similarity between matrices

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  • Dray, Stephane

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  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:4:p:2228-2237
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    References listed on IDEAS

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    1. Besse, Philippe, 1992. "PCA stability and choice of dimensionality," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 405-410, April.
    2. Atanu Sinha & Bruce Buchanan, 1995. "Assessing the stability of principal components using regression," Psychometrika, Springer;The Psychometric Society, vol. 60(3), pages 355-369, September.
    3. 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.
    4. Peres-Neto, Pedro R. & Jackson, Donald A. & Somers, Keith M., 2005. "How many principal components? stopping rules for determining the number of non-trivial axes revisited," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 974-997, June.
    5. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    6. 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.
    7. Michel Tenenhaus & Forrest Young, 1985. "An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 91-119, March.
    8. James Lingoes & Peter Schönemann, 1974. "Alternative measures of fit for the Schönemann-carroll matrix fitting algorithm," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 423-427, December.
    9. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
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    2. Kelly P. Murillo & Eugenio M. Rocha, 2018. "The Portuguese Manufacturing Sector during 2013-2016 after the Troika Austerity Measures," World Journal of Applied Economics, WERI-World Economic Research Institute, vol. 4(1), pages 21-38, June.
    3. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    4. Santos, David Ferreira Lopes & Basso, Leonardo Fernando Cruz & Kimura, Herbert, 2018. "The trajectory of the ability to innovate and the financial performance of the Brazilian industry," Technological Forecasting and Social Change, Elsevier, vol. 127(C), pages 258-270.
    5. Beaton, Derek & Chin Fatt, Cherise R. & Abdi, Hervé, 2014. "An ExPosition of multivariate analysis with the singular value decomposition in R," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 176-189.
    6. Julie Josse & Jérôme Pagès & François Husson, 2011. "Multiple imputation in principal component analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(3), pages 231-246, October.
    7. Josse, Julie & Husson, François, 2012. "Selecting the number of components in principal component analysis using cross-validation approximations," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1869-1879.
    8. Ulisse Gomarasca & Mirco Migliavacca & Jens Kattge & Jacob A. Nelson & Ülo Niinemets & Christian Wirth & Alessandro Cescatti & Michael Bahn & Richard Nair & Alicia T. R. Acosta & M. Altaf Arain & Mire, 2023. "Leaf-level coordination principles propagate to the ecosystem scale," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    9. Archimbaud, Aurore & Nordhausen, Klaus & Ruiz-Gazen, Anne, 2018. "ICS for multivariate outlier detection with application to quality control," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 184-199.
    10. Sergio Camiz & Valério D. Pillar, 2018. "Identifying the Informational/Signal Dimension in Principal Component Analysis," Mathematics, MDPI, vol. 6(11), pages 1-16, November.
    11. Brusco, Michael J., 2014. "A comparison of simulated annealing algorithms for variable selection in principal component analysis and discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 38-53.
    12. Nordhausen, Klaus & Oja, Hannu & Tyler, David E., 2022. "Asymptotic and bootstrap tests for subspace dimension," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. Bada, Oualid & Kneip, Alois, 2014. "Parameter cascading for panel models with unknown number of unobserved factors: An application to the credit spread puzzle," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 95-115.
    14. Georgeta Vintila & Stefan Gherghina, 2014. "On the Use of Multidimensional Data Analysis Techniques for Corporate Valuation," Modern Applied Science, Canadian Center of Science and Education, vol. 8(3), pages 202-202, June.

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