Abstract
K-means is one of the most popular data mining and unsupervised learning algorithms that solve the well known clustering problem. The procedure follows a simple and easy way to classify a given data set through a pre-specified number of clusters K, therefore the problem of determining “the right number of clusters” has attracted considerable interest. However, to the authors’ knowledge, no experimental results of their comparison have been reported so far. This paper presents results of such a comparison involving eight selection options presenting four approaches. We generate data according to a Gaussian-mixture distribution with clusters’ spread and spatial sizes variant. Most consistent results are shown by the least squares and least modules version of an intelligent version of the method, iK-Means by Mirkin [14]. However, the right K is reproduced best by the Hartigan’s [5] method. This leads us to propose an adjusted iK-Means method, which performs well in the current experiment setting.
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References
Banfield, J.D., Raftery, A.E.: Model-based Gaussian and non-Gaussian clustering. Biometrics 49, 803–821 (1993)
Calinski, T., Harabasz, J.: A Dendrite method for cluster analysis. Communications in Statistics 3(1), 1–27 (1974)
Chiang Mark, M.T., Mirkin, B.: Determining the number of clusters in the Straight K-means: Experimental comparison of eight options. In: Proceeding of the 2006 UK workshop on Computational Intelligence, pp. 119–126 (2006)
Generation of Gaussian mixture distributed data, NETLAB neural network software (2006), http://www.ncrg.aston.ac.uk/netlab
Hartigan, J.A.: Clustering Algorithms. J. Wiley & Sons, New York (1975)
Hubert, L.J., Arabie, P.: Comparing partitions. Journal of Classification 2, 193–218 (1985)
Jain, A.K, Dubes, R.C.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1988)
Kaufman, L., Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. J. Wiley & Son, New York (1990)
Krzanowski, W., Lai, Y.: A criterion for determining the number of groups in a dataset using sum of squares clustering. Biometrics 44, 23–34 (1985)
McLachlan, G., Basford, K.: Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York (1988)
McQueen, J.: Some methods for classification and analysis of multivariate observations. In: Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. II, pp. 281–297 (1967)
Milligan, G.W., Cooper, M.C.: An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159–179 (1985)
Mirkin, B.: Eleven ways to look at the Pearson chi squares coefficient at contingency tables. The American Statistician 55(2), 111–120 (2001)
Mirkin, B.: Clustering for Data Mining: A Data Recovery Approach. Chapman and Hall/CRC, Boca Raton Fl (2005)
Monti, S., Tamayo, P., Mesirov, J., Golub, T.: Consensus clustering: A resampling-based method for class discovery and visualization of gene expression microarray data. Machine Learning 52, 91–118 (2003)
Roweis, S.: EM algorithms for PCA and SPCA. In: Jordan, M., Kearns, M., Solla, S. (eds.) Advances in Neural Information Processing Systems, vol. 10, pp. 626–632. MIT Press, Cambridge (1998)
Sugar, C.A., James, G.M.: Finding the number of clusters in a data set: An information-theoretic approach. Journal of American Statistical Association 98(463), 750–778 (2003)
Tibshirani, R., Walther, G., Hastie, T.: Estimating the number of clusters in a dataset via the Gap statistics. Journal of the Royal Statistical Society B 63, 411–423 (2001)
Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. J. Roy. Statist. Soc. Ser. B 61, 611–622 (1999)
Wasito, I., Mirkin, B.: Nearest neighbours in least-squares data imputation algorithms with different missing patterns. Computational Statistics & Data Analysis 50, 926–949 (2006)
Yeung, K.Y., Ruzzo, W.L.: Details of the Adjusted Rand index and clustering algorithms. Bioinformatics 17, 763–774 (2001)
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Chiang, M.MT., Mirkin, B. (2007). Experiments for the Number of Clusters in K-Means. In: Neves, J., Santos, M.F., Machado, J.M. (eds) Progress in Artificial Intelligence. EPIA 2007. Lecture Notes in Computer Science(), vol 4874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77002-2_33
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DOI: https://doi.org/10.1007/978-3-540-77002-2_33
Publisher Name: Springer, Berlin, Heidelberg
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