Abstract
We propose a novel approach to perform unsupervised and non parametric clustering of multidimensional data upon a Bayesian framework. The developed iterative approach is derived from the Classification Expectation- Maximization (CEM) algorithm [5], in which the parametric modelling of the mixture density is replaced by a non parametric modelling using local kernels, and posterior probabilities account for the coherence of current clusters through the measure of class-conditional entropies. Applications of this method to synthetic and real data including multispectral imagery are presented. Our algorithm is compared with other recent unsupervised approaches, and we show experimentally that it provides a more reliable estimation of the number of clusters while giving slightly better average rates of correct classification.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aeberhard, S., Coomans, D., De Vel, O.: The classification performance of RDA. Technical report, 92-01, Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University, North Queensland, Australia (1992)
Bezdek, J.: Pattern Recognition With Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Cariou, C., Chehdi, K., Nagle, A.: Gravitational transform for data clustering - application to multicomponent image classification. In: Proc. IEEE ICASSP 2005, Philadelphia, USA, vol. 2, pp. 105–108 (2005)
Celeux, G., Diebolt, J.: A probabilistic teacher algorithm for iterative maximum likelihood estimation. In: Classification and Related Methods of Data Analysis, pp. 617–623. Elsevier, North-Holland, Amsterdam (1987)
Celeux, G., Govaert, G.: A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis 3, 315–332 (1992)
Cohen, J.: A Coefficient of Agreement for Nominal Scales. Educational and Psychological Measurement 20, 37–46 (1960)
Dempster, A., Laird, N., Rubin, D.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39(1), 1–38 (1977)
Dunn, J.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Journal of Cybernetics 3(3), 32–57 (1973)
Fisher, R.: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7(2), 179–188 (1936)
Gustafson, D., Kessel, W.: Fuzzy clustering with a covariance matrix. In: Proc. IEEE Conference on Decision and Control, pp. 761–766 (1979)
Huang, J., Ng, M.: Automated variable weighting in k-means type clustering. IEEE Trans. Pattern Analysis and Machine Intelligence 27(5), 657–668 (2005)
Laszlo, M., Mukherjee, S.: A genetic algorithm using hyper-quadtrees for low-dimensional k-means clustering. IEEE Trans. Pattern Analysis and Machine Intelligence 28(4), 533–543 (2006)
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)
Masson, P., Pieczynski, W.: SEM algorithm and unsupervised statistical segmentation of satellite images. IEEE Trans. Geoscience and Remote Sensing 31(3), 618–633 (1993)
Michalski, R.S.: Learning by being told and learning from examples: an experimental comparison of the two methods of knowledge acquisition in the context of developing an expert system for soybean desease diagnosis. Intern. J. of Policy Analysis and Information Systems 4(2), 125–161 (1980)
Same, A., Govaert, G., Ambroise, C.: A mixture model-based on-line cem algorithm. In: Proc. 6th International Symposium on Data Analysis, IDA 2005, Madrid, Spain, October 8-10 (2005)
Tran, T., Wehrens, R., Buydens, L.: Clustering multispectral images: a tutorial. Chemometrics and Intelligent Laboratory Systems 77, 3–17 (2005)
Tran, T., Wehrens, R., Buydens, L.: KNN-kernel density-based clustering for high-dimensional multivariate data. Computational Statistics and Data Analysis 51, 513–525 (2006)
Zribi, M., Ghorbel, F.: An unsupervised and non-parametric Bayesian classifier. Pattern Recognition Letters 24(1), 97–112 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bougenière, G., Cariou, C., Chehdi, K., Gay, A. (2008). Non Parametric Stochastic Expectation Maximization for Data Clustering. In: Filipe, J., Obaidat, M.S. (eds) E-business and Telecommunications. ICETE 2007. Communications in Computer and Information Science, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88653-2_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-88653-2_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88652-5
Online ISBN: 978-3-540-88653-2
eBook Packages: Computer ScienceComputer Science (R0)