Abstract
Let us consider the problem of finding clusters in a heterogeneous, high-dimensional setting. Usually a (global) cluster analysis model is applied to reach this aim. As a result, often ten or more clusters are detected in a heterogeneous data set. The idea of this paper is to perform subsequent local cluster analyses. Here the following two main questions arise. Is it possible to improve the stability of some of the clusters? Are there new clusters that are not yet detected by global clustering? The paper presents a methodology for such an iterative clustering that can be a useful tool in discovering stable and meaningful clusters. The proposed methodology is used successfully in the field of archaeometry. Here, without loss of generality, it is applied to hierarchical cluster analysis. The improvements of local cluster analysis will be illustrated by means of multivariate graphics.
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References
BANFIELD, J.D. and RAFTERY, A.E. (1993): Model-Based Gaussian and non-Gaussian Clustering. Biometrics, 49, 803–821.
HENNIG, C. (2004): A General Robustness and Stability Theory for Cluster Analysis. Preprint, 7,, Universität Hamburg.
HUBERT, L.J. and ARABIE, P. (1985): Comparing Partitions. Journal of Classification, 2, 193–218.
JAIN, A. K. and DUBES, R. C. (1988): Algorithms for Clustering Data. Prentice Hall, Englewood.
MUCHA, H.-J. (1992): Clusteranalyse mit Mikrocomputern. Akademie Verlag, Berlin.
MUCHA, H.-J. (2004): Automatic Validation of Hierarchical Clustering. In: J. Antoch (Ed.): Proceedings in Computational Statistics, COMPSTAT 2004, 16th Symposium. Physica-Verlag, Heidelberg, 1535–1542.
MUCHA, H.-J., BARTEL, H.-G., and DOLATA, J. (2005): Model-based Cluster Analysis of Roman Bricks and Tiles from Worms and Rheinzabern. In: C. Weihs and W. Gaul, W. (Eds.): Classification-The Ubiquitous Challenge, Springer, Heidelberg, 317–324.
MUCHA, H.-J. and HAIMERL, E. (2005): Automatic Validation of Hierarchical Cluster Analysis with Application in Dialectometry. In: C. Weihs and W. Gaul, W. (Eds.): Classification-The Ubiquitous Challenge, Springer, Heidelberg, 513–520.
PRIEBE, C. E., MARCHETTE, D. J., PARK, Y., WEGMAN, E. J., SOLKA, J. L., SOCOLINSKY, D. A., KARAKOS, D., CHURCH, K. W., GUGLIELMI, R., COIFMAN, R. R., LIN, D., HEALY, D. M., JACOBS, M. Q., and TSAO, A. (2004): Iterative Denoising for Cross-Corpus Discovery. In: J. Antoch (Ed.): Proceedings in Computational Statistics, COMPSTAT 2004, 16th Symposium. Physica-Verlag, Heidelberg, 381–392.
SCHWARZ, A. and ARMINGER, G. (2005): Credit Scoring Using Global and Local Statistical Models. In: C. Weihs and W. Gaul, W. (Eds.): Classification-The Ubiquitous Challenge, Springer, Heidelberg, 442–449.
UNDERHILL, L.G. and PEISACH, M. (1985): Correspondence analysis and its application in multielement trace analysis. J. Trace and microprobe techniques 3(1 and 2), 41–65.
WARD, J.H. (1963): Hierarchical Grouping Methods to Optimise an Objective Function. JASA, 58, 235–244.
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Mucha, HJ. (2006). Finding Meaningful and Stable Clusters Using Local Cluster Analysis. In: Batagelj, V., Bock, HH., Ferligoj, A., Žiberna, A. (eds) Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34416-0_12
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DOI: https://doi.org/10.1007/3-540-34416-0_12
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