Multivariate prediction with nonlinear principal components analysis: Theory

Quality and Quantity

Volumn 39, Issue 4, 2005, Pages 359-372

  Gower, John C ^a   Blasius, Jörg ^b  

^a OPEN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

Biplot; Large scale data analysis; Nonlinear principal components analysis; Prediction

Indexed keywords

EID: 23944472347     PISSN: 00335177     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11135-005-3005-1     Document Type: Review

References (20)

1. Blasius, J. & Gower, J. C. (to appear). Multivariate prediction with nonlinear principal components analysis: Application. Quality and Quantity 39.
2. Borg, I. & Groenen, P. (1997). Modern Multidimensional Scaling. New York: Springer.
3. Borg, I. & Shye, S. (1995). Facet Theory. Form and Content. Newbury Park, CA: Sage.
4. Chambers, J. M. (1998). Programming with Data: A Guide to the S Language. New York: Springer.
5. Eckart, C. & Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika 1: 211-218.
6. Gabriel, K. R. (1971). The biplot-graphic display of matrices with applications to principal components analysis. Biometrika 58: 453-467.
7. Gabriel, K. R. (1981). Biplot display of multivariate matrices for inspecting of data and diagnosis. In: V. Barnett (eds.), Interpreting Multivariate Data, Chichester: Wiley, pp. 147-174.
8. Genstat 5 Committee. (1993). Genstat 5 Release 3 Reference Manual. Oxford: Numerical Algorithms Group.
9. Gifi, A. (1990). Nonlinear Multivariate Analysis. Chichester: Wiley.
10. Gower, J. C. (1966): Some distance properties of latent-root and vector methods used in multivariate analysis. Biometrika 53: 325-338.
11. Gower, J. C. (1993). The construction of neighbour-regions in two dimensions for prediction with multi-level categorical variables. In: O. Opitz, B. Lausen & R. Klar (eds.), Information and Classification: Concepts-Methods-Applications Proceedings 16th Annual Conference of the Gesellschaft für Klassifikation, Dortmund, April 1992, Berlin: Springer, pp. 174-189.
12. Gower, J. C. (2002). Categories and quantities. In: S. Nishisato, Y. Baba, H. Bozdogan & K. Kamefuji (eds.), Measurement and Multivariate Analysis, Tokyo: Springer, pp. 1-12.
13. Gower, J. C. & Hand, D. J. (1996). Biplots. London: Chapman & Hall.
14. Gower, J. C. & Harding, S. (1998). Prediction regions for categorical variables. In: J. Blasius & M. Greenacre (eds.), Visualization of Categorical Data. San Diego: Academic Press, pp. 405-423.
15. Greenacre, M. J. (1993). Biplots in correspondence analysis. Journal of Applied Statistics 20: 251-269.
16. Guttman, L. (1965). A faceted definition of intelligence. Scripta Hierosolymitana 14: 166-181.
17. Heiser, W. J. & Meulman, J. J. (1994). Homogeneity analysis: exploring the distribution of variables and their nonlinear relationships. In: M. J. Greenacre & J. Blasius (eds.), Correspondence Analysis in the Social Sciences. Recent Developments and Applications, London: Academic Press, pp. 179-209.
18. Meulman, J. J. & Heiser, W. J. (1999). SPSS Categories 10.0. Chicago: SPSS Inc.
19. Payne, R. W., Lane, P. W., Baird, D. B., Gilmour, A. R., Harding, S. A., Morgan, G. W. Murray, D. A., Thompson, R., Todd, A. D., Tunicliffe-Wilson, G., Webster, R. & Welham, S. J. (1998). Genstat 5 Release 4.1 Reference Manual Supplement. Oxford: Numerical Algorithms Group.
20. SPSS. (1999). See Meulman and Heiser (1999).