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A robust automatic clustering algorithm for probability density functions with application to categorizing color images.(English)Zbl 07550091

Summary: This study develops a robust automatic algorithm for clustering probability density functions based on the previous research. Unlike other existing methods that often pre-determine the number of clusters, this method can self-organize data groups based on the original data structure. The proposed clustering method is also robust in regards to noise. Three examples of synthetic data and a real-world COREL dataset are utilized to illustrate the accurateness and effectiveness of the proposed approach.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)

Cite

References:

[1]Banerjee, A.; Dhillon, I. S.; Ghosh, J.; Sra, S., Clustering on the unit hypersphere using von Mises-Fisher distribution, Journal of Machine Learning Research, 6, 1-39
[2]Caliński, T.; Harabasz, J., A dendrite method for cluster analysis, Communications in Statistics: Theory and Methods, 3, 1-27 ·Zbl 0273.62010
[3]Chen, T. L.; Shiu, S. Y., JSM Proceedings, Statistical Computing Section, Salt Lake City, Utah, A new clustering algorithm based on self-updating process, 2034-2038
[4]Chen, T. L.; Hsieh, D. N.; Hung, H.; Tu, I. P.; Wu, P. S.; Wu, Y. M.; Chang, W. H.; Huang, S. Y., γ-SUP: A clustering algorithm for cryo-electron microscopy images of asymmetric particles, The Annals of Applied Statistics, 8, 259-285 ·Zbl 1454.62527
[5]Chen, J. H.; Hung, W. L., An automatic clustering algorithm for probability density functions, Journal of Statistical Computation and Simulation, 85, 3047-3063 ·Zbl 1457.62197
[6]Cheng, Y., Mean shift, mode seeking, and clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 790-799
[7]Goh, A.; Vidal, R., Unsupervised Riemannian clustering of probability density functions, ECML PKDD, Part I, LNAI, 5211, 377-392
[8]Havens, T. C.; Bezdek, J. C.; Leckie, C.; Hall, L. O.; Palaniswami, M., Fuzzy c-means algorithms for very large data, IEEE Transactions on Fuzzy Systems, 20, 1130-1146
[9]Hung, W. L.; Chang-Chien, S. J.; Yang, M. S., Self-updating clustering algorithm for estimating the parameters in mixtures of von Mises distributions, Journal of Applied Statistics, 39, 2259-2274 ·Zbl 1514.62109
[10]Kohonen, T., The self-organizing map, Neurocomputing, 21, 1-6 ·Zbl 0917.68176
[11]Kohonen, T., Self-Organizing Map, Berlin: Springer, Berlin
[12]Kwedlo, W., A clustering method combining differential evolution with the K-means algorithm, Pattern Recognition Letters, 32, 1613-1621
[13]Masoud, H.; Saeed, J.; Hasheminejad, S. M. H., Dynamic clustering using combinatorial particle swarm optimization, Applied intelligence, 38, 289-314
[14]McQueen, J. B., Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and probability, 1, Some methods for classification and analysis of multivariate observations, 281-297, Berkeley, CA: University of California Press, Berkeley, CA
[15]Montanari, A.; Caló, D. G., Model-based clustering of probability density functions, Advances in Data Analysis and Classification, 7, 301-319 ·Zbl 1273.62140
[16]Olkin, I.; Liu, R., A bivariate beta distribution, Statistics and Probability Letters, 62, 407-412 ·Zbl 1116.60309
[17]Pham-Gia, T.; Turkkan, N.; Bekker, A., Bayesian analysis in the L^1-norm of the mixing proportion using discriminant analysis, Metrika, 64, 1-22 ·Zbl 1099.62026
[18]Pham-Gia, T.; Turkkan, N.; Van, T. V., Statistical discriminant analysis using the maximum function, Communications in Statistics: Simulation and Computation, 37, 320-336 ·Zbl 1132.62049
[19]Silverman, B. W., Density Estimation for Statistics and Data Analysis, New York: Chapman and Hall, New York ·Zbl 0617.62042
[20]Van, T. V.; Pham-Gia, T., Clustering probability distributions, Journal of Applied Statistics, 37, 1891-1910 ·Zbl 1511.62142
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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