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Comparing SOM neural network with fuzzy \(c\)-means, \(K\)-means and traditional hierarchical clustering algorithms. (English) Zbl 1103.62057
Summary: We present a comparison among some nonhierarchical and hierarchical clustering algorithms including SOM (Self-Organization Map) neural network and fuzzy c-means methods. Data were simulated considering correlated and uncorrelated variables, nonoverlapping and overlapping clusters with and without outliers. A total of 2530 data sets were simulated. The results showed that fuzzy c-means had a very good performance in all cases being very stable even in the presence of outliers and overlapping. All other clustering algorithms were very affected by the amount of overlapping and outliers. SOM neural networks did not perform well in almost all cases being very affected by the number of variables and clusters. The traditional hierarchical clustering and \(K\)-means methods presented similar performance.

MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
68T05 Learning and adaptive systems in artificial intelligence
Software:
SAS; SAS/STAT
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[1] Anderberg, M.R., Cluster analysis for applications, (1972), Academic Press New York
[2] Balakrishnan, P.V.; Cooper, M.C.; Jacob, V.S.; Lewis, P.A., A study of the classification of neural networks using unsupervised learning: A comparison with K-means clustering, Psychometrika, 59, 4, 509-525, (1994) · Zbl 0850.92057
[3] Balakrishnan, P.V.; Cooper, M.C.; Jacob, V.S.; Lewis, P.A., Comparative performance of the FSCL neural net and K-means algorithm for market segmentation, European journal of operational research, 93, 1, 346-357, (1996) · Zbl 0912.90190
[4] Bezdek, J.C., Pattern recognition with fuzzy objective function algorithms, (1981), Plenum Press New York · Zbl 0503.68069
[5] Bezdek, J.C.; Keller, J.; Krishnapuram, R.; Pal, N., Algorithms for pattern recognition and image processing, (1999), Kluwer Boston
[6] Carpenter, G.A.; Grossberg, S.; Rosen, D.B., Fuzzy art: stable learning and categorization of analog patterns by adaptive resonance system, Neural networks, 4, 1, 759-771, (1991)
[7] Everitt, B.S., Cluster analysis, (2001), John Wiley & Sons New York · Zbl 0406.62042
[8] Gallant, S.I., Neural network learning and expert systems, (1993), MIT Press Cambridge · Zbl 0850.68281
[9] Gordon, A.D., A review of hierarchical classification, Journal of royal statistical society, 150, 2, 119-137, (1987) · Zbl 0616.62086
[10] Gower, J.C., A comparison of some methods of cluster analysis, Biometrics, 23, 4, 623-638, (1967)
[11] Hathaway, R.J.; Bezdek, J.C., Clustering incomplete relational data using the non-Euclidean relational fuzzy c-means algorithm, Pattern recognition letters, 23, 1-3, 151-160, (2002) · Zbl 0993.68108
[12] Hebb, D.O., The organization of behavior, (1949), John Wiley New York
[13] Hecht-Nielsen, R., Neurocomputing, (1990), Addison-Wesley Reading, MA
[14] Johnson, R.A.; Wichern, D.W., Applied multivariate statistical analysis, (2002), Prentice-Hall New Jersey
[15] Kiang, M.Y., Extending the Kohonen self-organizing map networks for clustering analysis, Computational statistics & data analysis, 38, 2, 161-180, (2001) · Zbl 1095.62509
[16] Kohonen, T., Self-organization and associative memory, (1989), Springer-Verlag New York · Zbl 0528.68062
[17] Kohonen, T., Self-organizing maps, (1995), Springer-Verlag Berlin
[18] Kosko, B., Neural networks and fuzzy systems, (1992), Prentice-Hall Englewood Cliffs, NJ
[19] Krishnamurthy, A.K.; Ahalt, S.C.; Melton, D.E.; Chen, P., Neural networks for vector quantization of speech and images, IEEE journal on selected areas in communications, 8, 1449-1457, (1990)
[20] Mangiameli, P.; Chen, S.K.; West, D., A comparison of SOM neural network and hierarchical clustering methods, European journal of operational research, 93, 2, 402-417, (1996) · Zbl 0912.90209
[21] McCulloch, W.S.; Pitts, W., A logical calculus of the ideas immanent in nervous activity, Bulletin of mathematical biophysics, 5, 1, 115-133, (1943) · Zbl 0063.03860
[22] Milligan, G.W.; Cooper, M.C., An examination of the effect of six types of error perturbation on fifteen clustering algorithms, Psychometrika, 45, 3, 159-179, (1980)
[23] Milligan, G.W., An algorithm for generating artificial test clusters, Psychometrika, 50, 1, 123-127, (1985)
[24] Rosenblatt, F., The perceptron: A probabilistic model for information storage and organization in the brain, Psychology review, 65, 1, 386-408, (1958)
[25] Roubens, M., Fuzzy clustering algorithms and their cluster validity, European journal of operational research, 10, 294-301, (1982) · Zbl 0485.62055
[26] SAS, 1999. SAS/STAT User’s Guide (version 8.01). SAS Institute, Cary, NC.
[27] Schreer, J.F.; O’Hara, R.J.H.; Kovacs, K.M., Classification of dive profiles: A comparison of statistical clustering techniques and unsupervised artificial neural networks, Journal of agriculture biological and environmental statistics, 3, 4, 383-404, (1998)
[28] Susanto, S.; Kennedy, R.D.; Price, J.H., A new fuzzy c-means and assignment technique based cell formation algorithm to perform part-type clusters and machine-type clusters separately, Production planning and control, 10, 4, 375-388, (1999)
[29] Zhang, D.-Q.; Chen, S.-C., Clustering incomplete data using kernel-based fuzzy c-means algorithm, Neural processing letters, 18, 3, 155-162, (2003)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.