Abstract
In recent years, advanced data analysis techniques to get valuable knowledge from data using computing power of today are required. Clustering is one of the unsupervised classification technique of the data analysis. Information on a real space is transformed to data in a pattern space and analyzed in clustering. However, the data should be often represented not by a point but by a set because of uncertainty of the data, e.g., measurement error margin, data that cannot be regarded as one point, and missing values in data.
These uncertainties of data have been represented as interval range and many clustering algorithms for these interval ranges of data have been constructed. However, the guideline to select an available distance in each case has not been shown so that this selection problem is difficult. Therefore, methods to calculate the dissimilarity between such uncertain data without introducing a particular distance, e.g., nearest neighbor one and so on, have been strongly desired. From this viewpoint, we proposed a concept of tolerance. The concept represents a uncertain data not as an interval but as a point with a tolerance vector. However, the distribution of uncertainty which represents the tolerance is uniform distribution and it it difficult to handle other distributions of uncertainty in the framework of tolerance, e.g., the Gaussian distribution, with HCM or FCM.
In this paper, we try to construct an clustering algorithm based on the EM algorithm which handles uncertain data which are represented by the Gaussian distributions through solving the optimization problem.Moreover, effectiveness of the proposed algorithm will be verified.
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
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39(1), 1–38 (1977)
Takata, O., Miyamoto, S.: Fuzzy clustering of Data with Interval Uncertainties. Journal of Japan Society for Fuzzy Theory and Systems 12(5), 686–695 (2000) (in Japanese)
Endo, Y., Horiuchi, K.: On Clustering Algorithm for Fuzzy Data. In: Proc. 1997 International Symposium on Nonlinear Theory and Its Applications, pp. 381–384 (November 1997)
Endo, Y.: Clustering Algorithm Using Covariance for Fuzzy Data. In: Proc. 1998 International Symposium on Nonlinear Theory and Its Applications, pp. 511–514 (September 1998)
Endo, Y., Murata, R., Haruyama, H., Miyamoto, S.: Fuzzy c-Means for Data with Tolerance. In: Proc. 2005 International Symposium on Nonlinear Theory and Its Applications, pp. 345–348 (2005)
Murata, R., Endo, Y., Haruyama, H., Miyamoto, S.: On Fuzzy c-Means for Data with Tolerance. Journal of Advanced Computational Intelligence and Intelligent Informatics 10(5), 673–681 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Kinoshita, N., Endo, Y. (2014). EM-Based Clustering Algorithm for Uncertain Data. In: Huynh, V., Denoeux, T., Tran, D., Le, A., Pham, S. (eds) Knowledge and Systems Engineering. Advances in Intelligent Systems and Computing, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-02821-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-02821-7_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02820-0
Online ISBN: 978-3-319-02821-7
eBook Packages: EngineeringEngineering (R0)