Abstract
Neural Network models are commonly used for cluster analysis in engineering, computational neuroscience, and the biological sciences, although they are rarely used in the social sciences. In this study we compare the classification capabilities of the 1-dimensional Kohonen neural network with two partitioning (Hartigan and Späthk-means) and three hierarchical (Ward's, complete linkage, and average linkage) cluster methods in 2,580 data sets with known cluster structure. Overall, the performance of the Kohonen networks was similar to, or better than, the performance of the other methods.
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References
American Psychological Association. (1992).PsycINFO users manual. Washington, DC: Author.
Anderson, J. A. (1995).An introduction to neural networks. Cambridge, MA: the MIT Press.
Angéniol, B., de la Croix Vaubois, G., & Texier, J. Y. (1988). Self-organizing feature maps and the traveling salesman problem.Neural Networks, 1, 289–293.
Atiya, Amir F. (1990). An unsupervised learning technique for artificial neural networks.Neural Networks, 3, 707–7111.
Balakrishan, P. V., Cooper, M. C., Jacob, V. S., & Lewis, P. A. (1994). A study of the classification capabilities of neural networks using unsupervised learning: A comparison withK-Means clustering.Psychometrika, 59, 509–525.
Bayne, C. K., Beauchamp, J. J., Begovich, C. L., & Kane, V. E. (1980). Monte Carlo comparisons of selected clustering procedures.Pattern Recognition, 12, 51–62.
Blashfield, R. K. (1976). Mixture model tests of cluster analysis: Accuracy of four agglomerative hierarchical methods.Psychological Bulletin, 83, 377–388.
Blashfield, R. K., & Aldenderfer, M. S. (1988). The methods and problems of cluster analysis. In J. Nesselroade & R. B. Cattell (Eds.),Handbook of multivariate experimental psychology (2nd ed., pp. 447–474). New York: Plenum Press.
Chen, S. K., Mangiameli, P., & West, D. (1995). The comparative ability of self-organizing neural networks to define cluster structure.Omega International Journal of Management Science, 23, 271–279.
Cheng, R., & Milligan, G. W. (1995). Mapping influence regions in hierarchical clustering.Multivariate Behavioral Research, 30, 547–576.
Childress, M. (1981).Statistics for evaluating classifications: A new view. Paper presented at the meeting of the Classification Society Annual Meeting.
Churchland, P. S., & Sejnowski, T. J. (1992).The computational brain. Cambridge, MA: The MIT Press.
Cohen, J. (1960). A coefficient of agreement for nominal scales.Educational and Psychological Measurement, 20, 37–46.
Cormack, R. M. (1971). A review of classification.Journal of the Royal Statistical Society, Series A, 134, 321–367.
Darken, C., & Moody, J. (1990). Fast adaptive k-means clustering: Some empirical results.Proceedings of the International Joint Conference on Neural Networks, II, 233–238.
Donoghue, J. R. (1995). The effects of within-group covariance structure on recovery in cluster analysis: I. The bivariate case.Multivariate Behavioral Research, 30, 227–254.
Downton, M., & Brennan, T. (1980).Comparing classifications: An evaluation of several coefficients of partition agreement. Paper presented at the Classification Society Annual Meeting.
Everitt, B. (1993).Cluster analysis (3rd ed.). New York: Halsted Press.
Fowlkes, E. B., & Mallows, C. L. (1980).A new measure of similarity between two hierarchical clusterings and its use in studying hierarchical clustering methods. Paper presented at the meeting of the Classification Society Annual Meeting.
Hartigan, J. A. (1975).Clustering algorithms. New York: Wiley.
Hartigan, J. A., & Wong, M. A. (1979). A k-means clustering algorithm.Applied Statistics, 28, 100–108.
Haykin, S. S. (1994).Neural networks: A comprehensive foundation. New York: Macmillan.
Hays, D. L. (1973).Statistics for the social sciences (2nd ed.). New York: Holt, Rhinehart & Winston.
Hebb, D. O. (1949).The organization of behavior. New York: Wiley.
Hubel, D. H., & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in the cat's visual cortex.Journal of Physiology (London), 160, 106–154.
Hubel, D. H, & Wiesel, T. N. (1977). Functional architecture of macaque visual cortex.Proceedings of the Royal Society of London, Series B, 198, 1–59.
Hubert, L., & Arabie, P. (1985). Comparing partitions.Journal of Classification, 2, 193–218.
INSPEC, Institution of Electrical Engineers. (1991).INSPEC user manual. Stevenage, Herts., U. K.: Autor.
Kinderman, A. J., & Monahan, J. F. (1977). Computer generation of random variables using the ratio of uniform deviates.ACM Transactions on Mathematical Software, 3, 257–260.
Kohonen, T. (1995).Self-organizing maps. Berlin, Heidelberg, New York: Springer.
Kohonen, T., Kangas, J., & Laaksonen, J. (1995).SOM_PAK: The Self-Organizing MAP Program Package, Version 3.1 [Computer program]. Helsinki University of Technology, Laboratory of Computer and Information Science, Rakentajanaukio 2 C, SF-02150 Espoo, Finland. (Available by anonymous ftp from cochlea.hut.fi: 130.233.168.48)
Kuiper, F. K., & Fisher, L. (1975). A Monte Carlo comparison of six clustering procedures.Biometrics, 31, 777–783.
McCulloch, W. S., & Pitts, W. H. (1943). A logical calculus of ideas immanent in nervous activity.Bulletin of Mathematical Biophysics, 5, 115–133.
Milligan, G. W. (1980). An examination of the effect of six types of error perturbation on fifteen clustering algorithms.Psychometrika, 45, 325–342.
Milligan, G. W. (1981). A review of Monte Carlo tests of cluster analysis.Multivariate Behavioral Research, 16, 379–407.
Milligan, G. W. (1983). Characteristics of four external criterion measures. In J. Felsenstein (Ed.),Numerical taxonomy. Berlin: Germany: Springer-Verlag.
Milligan, G. W. (1985). An algorithm for generating artificial test clusters.Psychometrika, 50, 123–127.
Milligan, G. W., & Cooper, M. C. (1987). Methodology review: Clustering methods.Applied Psychological Measurement, 11(4), 329–354.
Milligan, G. W., & Schilling, D. A. (1985). Asymptotic and finite-sample characteristics of four external criterion measures.Multivariate Behavioral Research, 20, 97–109.
Morey, L. (1981).The measurement of classification agreement: An adjustment to the Rand Index for chance agreement. Paper presented at the meeting of the Classification Society Annual Meeting.
Murtagh, F., & Hernández-Pajares, M. (1995). The Kohonen self-organizing map method: An assessment.Journal of Classification, 12, 165–190.
NeuralWare. (1991).Neuralworks Professional II/Plus [software manual]. Pittsburgh, PA: Author.
Pal, N. R., Bezdek, J. C., & Tsao, E. C-K. (1993). Generalized clustering networks and Kohonen's self-organizing scheme.IEEE Transactions on Neural Networks, 4, 549–557.
Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods.Journal of the American Statistical Association, 66, 846–850.
Ripley, B. D. (1993). Statistical aspects of neural networks. In O. E. Bandorff-Nielsen, J. L. Jensen, & W. S. Kendall (Eds.),Network and chaos—Statistical and probabilistic aspects (pp. 40–123). London: Chapman and Hall.
Rumelhart, D. E., McClelland, J. L., & the PDP Research Group (1987).Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundations. Cambridge, MA: MIT Press.
Scheibler, D., & Schneider, W. (1985). Monte Carlo tests of the accuracy of cluster analysis algorithms: A comparison of hierarchical and nonhierarchical methods.Multivariate Behavioral Research, 20, 283–304.
Smith, M. (1993).Neural networks for statistical modeling. New York, NY: Van Nostrand Reinhold.
Sokal, R., & Michener, C. D. (1958). A statistical method for evaluating systematic relationships.University of Kansas Scientific Bulletin, 38, 1409–1438.
Späth, H. (1985).Cluster dissection and analysis: Theory, Fortran examples. New York: Ellis Horwood.
StatSci. (1993).S-Plus for Windows users manual. Seattle, WA: Statistical Sciences, Inc.
Vinod, V. V., Chaudhury, S., Mukherjee, J., & Ghose, S. (1994). A connectionist approach for clustering with applications in image analysis.IEEE Transactions on Systems, Man, & Cybernetics, 3, 365–384.
Waller, N. G., Underhill, J. M., & Kaiser, H. A. (1996).A method for generating simulated plasmodes and artifical test clusters with user-defined shape, size, and orientation. Manuscript submitted for publication.
Ward, J. H. (1963). Hierarchical grouping to optimize an objective function.Journal of the American Statistical Association, 58, 236–244.
Wothke, W. (1993). Nonpositive definite matrices in structural modeling. In K. A. Bollen & J. S. Long (Eds.),Testing structural equation models (pp. 256–293). Newbury Park: SAGE.
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Waller, N.G., Kaiser, H.A., Illian, J.B. et al. A comparison of the classification capabilities of the 1-dimensional kohonen neural network with two pratitioning and three hierarchical cluster analysis algorithms. Psychometrika 63, 5–22 (1998). https://doi.org/10.1007/BF02295433
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DOI: https://doi.org/10.1007/BF02295433