GTM: The Generative Topographic Mapping

Neural Computation

Volumn 10, Issue 1, 1998, Pages 215-234

  Bishop, Christopher M ^a   Svensén, Markus ^a   Williams, Christopher K I ^a  

^a ASTON UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347963789     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976698300017953     Document Type: Article

References (27)

1. Bishop, C. M. (1995). Neural networks for pattern recognition. New York: Oxford University Press.
2. Bishop, C. M., & James, G. D. (1993). Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nuclear Instruments and Methods in Physics Research, A327, 580-593.
3. Bishop, C. M., Svensén, M., & Williams, C. K. I. (1996). A fast EM algorithm for latent variable density models. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems, 8 (pp. 465-471). Cambridge, MA: MIT Press.
4. Bishop, C. M., Svensén, M., & Williams, C. K. I. (in press). Magnification factors for the GTM algorithm. In Proceedings of the Fifth IEE International Conference on Artificial Neural Networks. Cambridge, U.K., IEE, (pp. 64-69).
5. Buhmann, J., & Kühnel, K. (1993). Vector quantization with complexity costs. IEEE Transactions on Information Theory, 39(4), 1133-1145.
6. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, B 39(1), 1-38.
7. Durbin, R., & Willshaw, D. (1987). An analogue approach to the travelling salesman problem. Nature, 326, 689-691.
8. Erwin, E., Obermayer, K., & Schulten, K. (1992). Self-organizing maps: Ordering, convergence properties and energy functions. Biological Cybernetics, 67, 47-55.
9. Hastie, T., & Stuetzle, W. (1989). Principal curves. Journal of the American Statistical Association, 84(406), 502-516.
10. Hinton, G. E., Williams, C. K. I., & Revow, M. D. (1992). Adaptive elastic models for hand-printed character recognition. In J. E. Moody, S. J. Hanson, & R. P. Lippmann (Eds.), Advances in neural information processing systems, 4 (pp. 512-519). San Mateo, CA: Morgan Kauffman.
11. Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59-69.
12. Kohonen, T. (1995). Self-organizing maps. Berlin: Springer-Verlag.
13. LeBlanc, M., & Tibshirani, R. (1994). Adaptive principal surfaces. Journal of the American Statistical Association, 89(425), 53-64.
14. Little, R. J. A., & Rubin, D. B. (1987). Statistical analysis with missing data. New York: John Wiley.
15. Luttrell, S. P. (1990). Derivation of a class of training algorithms. IEEE Transactions on Neural Networks, 1(2), 229-232.
16. Luttrell, S. P. (1994). A Bayesian analysis of self-organizing maps. Neural Computation, 6(5), 767-794.
17. Luttrell, S. P. (1995). Using self-organizing maps to classify radar range profiles. Proc. 5th IEE Conf. on Artificial Neural Networks, 335-340.
18. MacKay, D. J. C. (1995). Bayesian neural networks and density networks. Nuclear Instruments and Methods in Physics Research, A 354(1), 73-80.
19. Mardia, K., Kent, J., & Bibby, M. (1979). Multivariate analysis. New York: Academic Press.
20. Mulier, F., & Cherkassky, V. (1995). Self-organization as an iterative kernel smoothing process. Neural Computation, 7(6), 1165-1177.
21. Nadaraya, É. A. (1964). On estimating regression. Theory of Probability and Its Applications, 9(1), 141-142.
22. Ritter, H. (1993). Parameterized self-organizing maps. In Proceedings ICANN'93 International Conference on Artificial Neural Networks, Amsterdam (pp. 568-575). Berlin: Springer-Verlag.
23. Robbins, H., & Monro, S. (1951). A stochastic approximation method. Annals of Mathematical Statistics, 22, 400-407.
24. Tibshirani, R. (1992). Principal curves revisited. Statistics and Computing, 2, 183-190.
25. Tipping, M. E., & Bishop, C. M. (1997). Probabilistic Principal Component Analysis. Tech. Rep. NCRG/97/010, Neural Computing Research Group, Dept. of Computer Science & Applied Mathematics, Aston Univ., Birmingham B4 7ET, U.K.
26. Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. New York: Wiley.
27. Watson, G. S. (1964). Smooth regression analysis. Sankhyā: The Indian Journal of Statistics, series A, 26, 359-372.