Prediction and classification in nonlinear data analysis: Something old, something new, something borrowed, something blue

Psychometrika

Volumn 68, Issue 4, 2003, Pages 493-517

  Meulman, Jacqueline J ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Additive prediction components; Boosting; Data mining; Distance based clustering; Forward stagewise additive modeling; Monotonic regression; Multiple regression; Optimal scaling; Optimal scoring; Regression splines; Statistical learning

Indexed keywords

EID: 3042644467     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02295607     Document Type: Article

References (49)

1. Bock, R.D. (1960). Methods and applications of optimal scaling (Tech. Rep. 25). Chapel Hill, NC: University of North Carolina, L.L. Thurstone Psychometric Laboratory.
2. Boon, M.E., Zeppa, P., Ouwerkerk-Noordam, E., & Kok, L.P. (1990). Exploiting the tooth-pick effect of the cytobrush by plastic embedding of cervical samples. Acta Cytologica, 35, 57-63.
3. Breiman, L. (1996a). Bagging predictors. Machine Learning, 26, 123-140.
4. Breiman, L. (1996b). Stacked regressions. Machine Learning, 24, 51-64.
5. Breiman, L., & Friedman, J.H. (1985). Estimating optimal transformations for multiple regression and correlation. Journal of the American Statistical Association, 80, 580-598.
6. Breiman, L., & Friedman, J.H., Olshen, R.A., & Stone, C.J. (1984). Classification and regression trees. Belmont, CA: Wadsworth.
7. Buja, A. (1990). Remarks on functional canonical variates, alternating least squares methods and ACE. Annals of Statistics, 18, 1032-1069.
8. de Leeuw, J., & Heiser, W.J. (1980). Multidimensional scaling with restrictions on the configuration. In P.R. Krishnaiah (Ed.), Multivariate analysis, Vol. V (pp. 501-522). Amsterdam: North-Holland.
9. de Leeuw, J., Young, F.W., & Takane, Y. (1976). Additive structure in qualitative data. Psychometrika, 41, 471-503.
10. Duda, R., Hart, P. and Stork, D. (2000). Pattern classification (2nd ed.). New York, NY: John Wiley & Sons.
11. Freund, Y., & Schapire, R.E. (1996). Experiments with a new boosting algorithm. Machine Learning: Proceedings of the Thirteenth International Conference (pp. 148-156). San Francisco, CA: Morgan Kauffman.
12. Friedman, J.H. (2001). Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5), 1189-1232.
13. Friedman, J.H., Hastie, T., & Tibshirani, R. (2000). Additive logistic regression: A statistical view of boosting (with discussion). Annals of Statistics, 28, 337-307.
14. Friedman, J.H., & Meulman, J.J. (in press). Clustering objects on subsets of attributes, (with discussion). Journal of the Royal Statistical Society, Series B. Available at http://www-stat.stanford.edu/~jhf/ftp/cosa.pdf
15. Friedman, J.H., & Meulman, J.J. (2003a). Multiple additive regression trees with application in epidemiology. Statistics in Medicine. 22(9), 1365-1381.
16. Friedman, J.H., & Meulman, J.J. (2003b). COSA [Software]. Available at http://www-stat.stanford.edu/~jhf/COSA.html
17. Friedman, J., & Stuetzle, W. (1981). Projection pursuit regression. Journal of the American Statistical Association, 76, 817-823.
18. Gifi, A. (1990). Nonlinear multivariate analysis. Chichester, U.K.: John Wiley & Sons. (First edition, 1981, University of Leiden, Department of Data Theory)
19. Groenen, P.J.F., van Os, B.J., & Meulman, J.J. (2000). Optimal scaling by alternating length constrained nonnegative least squares: An application to distance based principal components analysis. Psychometrika, 65, 511-524.
20. Guttman, L. (1950). The principal components of scale analysis. In S.A. Stouffer, L. Guttman, E.A. Suchman, P.F. Lazarsfield, S.A. Star, & J.A. Clausen (Eds.), Measurement and prediction. Princeton, NJ: Princeton University Press.
21. Harrison, D., & Rubinfeld, D.L. (1978). Hedonic housing prices and the demand for clean air. Journal of Environmental Economics Management, 5, 81-102.
22. Hastie, T., & Tibshirani, R. (1990). Generalized additive models. New York, NY: Chapman and Hall.
23. Hastie, T., Tibshirani, R., & Buja, A. (1998). Flexible discriminant analysis by optimal scoring. Journal of the American Statistical Association, 89, 1255-1270.
24. Hastie, T., Tibshirani, R., & Friedman, J.H. (2001). The elements of statistical learning. New York, NY: Springer-Verlag.
25. Hayashi, C. (1952). On the prediction of phenomena from qualitative data and the quantification of qualitative data from the mathematico-statistical point of view. Annals of the Institute of Statitical Mathematics, 2, 93-96.
26. Heiser, W.J. (1995). Convergent computation by iterative majorization: Theory and applications in multidimensional data analysis. In W.J. Krzanowski (Ed.), Recent advances in descriptive multivariate analysis (pp. 157-189). Oxford, U.K.: Oxford University Press.
27. Kruskal, J.B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1-28.
28. Kruskal, J.B. (1964b). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
29. Kruskal, J.B. (1965). Analysis of factorial experiments by estimating monotone transformations of the data. Journal of the Royal Statistical Society, Series B, 27, 251-263.
30. Max, J. (1960). Quantizing for minimum distortion. Proceedings IEEE (Information Theory), 6, 7-12.
31. McLachlan, G.J. (1992). Discriminant analysis and statistical pattern recognition. New York, NY: John Wiley & Sons.
32. Meulman, J.J. (2000). Discriminant analysis with optimal scaling. In R. Decker & W. Gaul (Eds.), Classification and information processing at the turn of the millenium (pp. 32-39). Heidelberg-Berlin, Germany: Springer-Verlag.
33. Meulman, J.J., Zeppa, P., Boon, M.E., & Rietveld, W.J. (1992). Prediction of various grades of cervical preneoplasia and neoplasia on plastic embedded cytobrush samples: Discriminant analysis with qualitative and quantitative predictors. Analytical and Quantitative Cytology and Histology, 14, 60-72.
34. Meulman J.J., & van der Kooij, A.J. (2000, May). Transformations towards independence through optimal scaling. Paper presented at the International Conference on Measurement and Multivariate Analysis (ICMMA), Banff, Canada.
35. Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications. Toronto, Canada: University of Toronto Press.
36. Nishisato, S. (1994). Elements of dual scaling: An introduction to practical data analysis. Hillsdale, NJ: Lawrence Erlbaum.
37. Ramsay, J.O. (1988). Monotone regression splines in action. Statistical Science, 4, 425-461.
38. Ripley, B.D. (1996). Pattern recognition and neural networks. Cambridge, U.K.: Cambridge University Press.
39. Takane, Y. (1998). Nonlinear multivariate analysis by neural network models. In C. Hayashi, N. Ohsumi, K. Yajima, Y. Tanaka, H.H. Bock, & Y. Baba (Eds.), Data science, classification, and related methods (pp. 527-538). Tokyo: Springer.
40. Takane, Y., & Oshima-Takane, Y. (2002). Nonlinear generalized canonical correlation analysis by neural network models. In S. Nishisato, Y. Baba, H. Bozdogan, & K. Kanefuji (Eds.), Measurement and multivariate analysis (pp. 183-190). Tokyo: Springer-Verlag.
41. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 58, 267-288.
42. van der Greef J., Davidov E., Verheij E., Vogels J., van der Heijden R., Adourian A.S., Oresic M., Marple E.W., & Naylor S. (2003). The role of metabolomics in drug discovery: A new vision for drug discovery and development. In G.G. Harrigan & R. Goodacre (Eds.), Metabolic profiling: Its role in biomarker discovery and gene function analysis (pp. 170-198). Boston, MA: Dordrecht; London: Kluwer Academic Publishers.
43. van der Kooij, A.J., & Meulman, J.J. (1999). Regression with optimal scaling. In J.J. Meulman, W.J. Heiser, & SPSS Inc. (Eds.), SPPS Categories 10.0. (pp. 1-8, 77-101). Chicago, IL: SPSS.
44. van der Kooij, A.J., Meulman, J.J., & Heiser W.J. (2003). Local minima in categorical multiple regression. Manuscript mubmitted for publication.
45. Vapnik, V. (1996). The nature of statistical learning theory. New York, NY: Springer-Verlag.
46. Whittaker, J.L. (1990). Graphical models in applied multivariate statistics. New York, NY: John Wiley & Sons.
47. Winsberg, S., & Ramsay, J.O. (1980). Monotonic transformations to additivity using splines. Biometrika, 67, 669-674.
48. Yanai, H., Okada, A., Shigemasu, K,. Kano, T., & Meulman, J.J. (Eds.) (2003). New developments in psychometrics. Tokyo: Springer-Verlag
49. Young, F.W., de Leeuw, J., & Takane, Y. (1976). Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features. Psychometrika, 41, 505-528.