K-means inverse regression

Technometrics

Volumn 46, Issue 4, 2004, Pages 421-429

  Setodji, C Messen ^a   Cook, R Dennis ^b  

^a RAND CORPORATION   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Central subspaces; Dimension reduction; Functional data analysis; K means clustering; Multivariate regression; Regression graphics; Sliced inverse regression

Indexed keywords

CENTRAL SUBSPACES; DATA SETS; DIMENSION REDUCTION; FUNCTIONAL DATA ANALYSIS; K-MEANS CLUSTERING; MULTIVARIATE REGRESSION; REGRESSION GRAPHICS; SLICED INVERSE REGRESSION (SIR);

ALGORITHMS; COMPUTER SIMULATION; CORRELATION METHODS; DATA REDUCTION; GRAPHIC METHODS; MATHEMATICAL TRANSFORMATIONS; RANDOM PROCESSES; VECTORS;

REGRESSION ANALYSIS;

EID: 8344246982     PISSN: 00401706     EISSN: None     Source Type: Trade Journal    
DOI: 10.1198/004017004000000437     Document Type: Article

References (34)

1. Abraham, C., Cornillon, P. A., Matzner-Løber, E., and Molinan, N. (2003), "Unsupervised Curve Clustering Using B-Spline," Scandinavian Journal of Statistics, 30, 581-595.
2. Aragon, Y. (1997), "A Gauss Implementation of Multivariate Sliced Inverse Regression," Computational Statistics, 12, 355-372.
3. Box, G. E. P., and Draper, N. (1987), Empirical Model-Building and Response Surfaces, New York: Wiley.
4. Bradley, P. S., and Fayyad, U. M. (1998), "Refining Initial Points for K-Means Clustering," in Proceedings of the 15th International Conference on Machine Learning, San Francisco: Morgan Kaufmann, pp. 91-99.
5. Bura, E., and Cook, R. D. (2001a), "Estimating the Structural Dimension of Regressions via Parametric Inverse Regression," Journal of the Royal Statistical Society, Ser. B, 63, 393-410.
6. Bura, E., and Cook, R. D. (2001b), "Extending Sliced Inverse Regression: The Weighted Chi-Squared Test," Journal of the American Statistical Association, 96, 996-1003.
7. Chen, C.-H., and Li, K. C. (1998), "Can SIR Be as Popular as Multiple Linear Regression?" Statistics Sinica, 8, 289-316.
8. Cook, R. D. (1994), "Using Dimension-Reduction Subspaces to Identify Important Inputs in Models of Physical Systems," in Proceedings of the Section on Physical and Engineering Sciences, American Statistical Association, pp. 18-25.
9. _ (1996), "Graphics for Regression With a Binary Response," Journal of the American Statistical Association, 91, 983-992.
10. _ (1998), Regression Graphics, New York: Wiley.
11. Cook, R. D., and Setodji, C. M. (2003),. "A Model-Free Test for Reduced Rank in Multivariate Regression," Journal of the American Statistical Association, 98, 340-351.
12. Cook, R. D., and Weisberg, S. (1991), Discussion of "Sliced Inverse Regression," by K. C. Li, Journal of the American Statistical Association, 86, 328-332.
13. Dauxois, J., Ferré, L., and Yao, A. (2001), "Un Modèle Semi-Paramétrique Pour Variables Aléatoires Hilbertiennes," Comptes Rendus de L'Academie des Sciences, Série I, 333, 947-952.
14. Faraway, J. J. (1997), "Regression Analysis for a Functional Response," Technometrics, 39, 254-261.
15. Flury, B. (1990), "Principal Points," Biometrika, 77, 33-41.
16. Forgy, E. (1965), "Cluster Analysis of Multivariate Data: Efficiency vs. Interpretability of Classifications," Biometrics, 21, 768.
17. Gaido, J. J., and Terhune, H. D. (1961), "Evaluation of Variables in the Pressure-Kier Bleaching of Cotton," American Dyestuffs Reporter, 50, 23-26, 32.
18. Hall, P., and Li, K. C. (1993), "On Almost Linearity of Low Dimensional Projections From High-Dimensional Data," The Annals of Statistics, 21, 867-889.
19. Hartigan, J. A. (1975), Clustering Algorithms, New York: Wiley.
20. Hotelling, H. (1935), "The Most Predictable Criterion," Journal of Educational Psychology, 26, 139-142.
21. Hsing, T. (1999), "Nearest-Neighbor Inverse Regression," The Annals of Statistics, 27, 697-731.
22. Hsing, T., and Carroll, R. J. (1992), "An Asymptotic Theory of Sliced Inverse Regression," The Annals of Statistics, 20, 1040-1061.
23. James, G. M., and Sugar, C. A. (2003), "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, 98, 397-408.
24. Kanazawa, Y. (1992), "An Optimal Variable Cell Histogram Based on the Sample Spacings," The Annals of Statistics, 20, 291-304.
25. Li, K. C. (1991), "Sliced Inverse Regression for Dimension Reduction" (with discussion), Journal of the American Statistical Association, 86, 316-342.
26. Li, K. C., Aragon, Y., Shedden, K., and Agnan, C. T. (2003), "Dimension Reduction for Multivariate Response Data," Journal of the American Statistical Association, 98, 99-109.
27. MacQueen, J. (1967), "Some Methods for Classification and Analysis of Multivariate Observations," in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 281-296.
28. Naik, P. A., Hagerty, M. R., and Tsai, C. L. (2000), "A New Dimension-Reduction Approach for Data-Rich Marketing Environments: Sliced Inverse Regression," Journal of Marketing Research, 37, 88-101.
29. Pollard, D. (1981), "Strong Consistency of k-Means Clustering," The Annals of Statistics, 9, 135-140.
30. _ (1982), "A Central Limit Theorem for k-Means Clustering," The Annals of Probability, 10, 919-926.
31. Tarpey, T., and Flury, B. (1996), "Self-Consistency: A Fundamental Concept in Statistics," Statistical Science. 11, 229-243.
32. Yeo, L. K., and Johnson, R. (2000), "A New Family of Power Transformations to Improve Normality or Symmetry," Biometrika, 87, 954-959.
33. Zhu, L. X., and Fang, K. T. (1996), "Asymptotics for Kernel Estimates of Sliced Inverse Regression," The Annals of Statistics, 24, 1053-1068.
34. Zhu, L. X., and Ng, K. W. (1995), "Asymptotics of Sliced Inverse Regression," Statistica Sinica, 5, 727-736.