Abstract
Gaussian mixture modelling is used to provide a semi-parametric density description for a given data set. The fundamental problem with this approach is that the number of mixtures required to adequately describe the data is not known in advance. In our previous work [12] we introduced a new concept, termed Predictive Validation as a basis for an automatic method to select the number of components. In this paper we investigate the inuence of the various parameters in our model selection method in order to develop it into an operational tool. We also demonstrate the utility of our model validation method to two applications in which the selected models are used for supervised classification and outlier detection tasks.
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References
H. Akaike. A new look at the statistical model identification. IEEE trans. on Automatic Control, AC-19(6):716–723, 1974.
A. Barron and T. Cover. Minimum complexity density-estimation. IEEE trans. on Information Theory, 37(4):1034–1054, 1991.
A Dempster, N Laird, and D Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, 39(1):1–38, 1977.
K Fukunaga. Introduction to Statistical Pattern Recognition. Academic Press, 1990.
A. Genz. Comparison of methods for computation of multi-variate normal probabilities. Computing Science and Statistics, 25:400–405, 1993.
N Kehtarnavaz and E Nakamura. Generalization of the em algorithm for mixture density estimation. Pattern recognition letters, 19:133–140, February 1998.
K Messer, D. de Ridder, and J Kittler. Adaptive texture representation methods for automatic target recognition. In Proc British Machine Vision Conference BMVC99, September 1999.
K Messer, J Kittler, and M Sadeghi. Predicitive validation. Technical report, University of Surrey, 2000.
P Pudil, J Novovicova, and J Kittler. Floating search methods in feature selection. Pattern Recognition Letters, 15:1119–1125, 1994.
J. Rissanen. Stochastic complexity. Journal of The Royal Statistical Society, Series B, 49(3):223–239 and 252-265, 1987.
L. Sardo and J. Kittler. Complexity analysis of rbf networks for pattern recognition. In Proceedings of CVPR96 (Computer Vision and Pattern Recognition Conference), San Francisco, pages 574–579, 18-20 June 1996.
L Sardo and J Kittler. Model complexity validation for pdf estimation using gaussian mixtures. In S Venkatesh A K Jain and B C Lovell, editors, International Conference on Pattern Recognition, pages 195–197, 1998.
G. Schwarz. Estimating the dimension of a model. The Annals of Statistics, 6(2):461–464, 1978.
N. Vlassis, G. Papakonstantinou, and P. Tsanakas. Mixture density estimation on maximum likelihood and sequential test statistics. Neural Processing Letters, 1999.
G. Watson and S. Watson. Detection and clutter rejection in image sequences based on multivariate conditional probability. In SPIE: Signal and Data Procssing of Small Targets, volume 3809, pages 107–118, 1999.
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Kittler, J., Messer, K., Sadeghi, M. (2001). Model Validation for Model Selection. In: Singh, S., Murshed, N., Kropatsch, W. (eds) Advances in Pattern Recognition — ICAPR 2001. ICAPR 2001. Lecture Notes in Computer Science, vol 2013. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44732-6_25
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DOI: https://doi.org/10.1007/3-540-44732-6_25
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