Clustering is the partitioning of a data set into subsets or clusters, so that the degree of association is strong between members of the same cluster and weak between members of different clusters according to some defined distance measure.
Several methods of performing cluster analysis exist:
Partitional clustering
Hierarchical clustering.
HISTORY
See classification and data analysis.
MATHEMATICAL ASPECTS
To carry out cluster analysis on a set of n objects, we need to define a distance between the objects (or more generally a measure of the similarity between the objects) that need to be classified. The existence of some kind of structure within the set of objects is assumed.
To carry out a hierarchical classification of a set E of objects \( { \{x_1,x_2,\ldots,x_n\} } \), it is necessary to define a distance associated with E that can be used to obtain a distance table between the objects of E. Similarly, a distance must also be defined for any subsets of E.
One approach to...
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REFERENCES
Celeux, G., Diday, E., Govaert, G., Lechevallier, Y., Ralambondrainy, H.: Classification automatique des données—aspects statistiques et informatiques. Dunod, Paris (1989)
Everitt, B.S.: Cluster Analysis. Halstead, London (1974)
Gordon, A.D.: Classification. Methods for the Exploratory Analysis of Multivariate Data. Chapman & Hall, London (1981)
Jambu, M., Lebeaux, M.O.: Classification automatique pour l'analyse de données. Dunod, Paris (1978)
Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)
Lerman, L.C.: Classification et analyse ordinale des données. Dunod, Paris (1981)
Tomassone, R., Daudin, J.J., Danzart, M., Masson, J.P.: Discrimination et classement. Masson, Paris (1988)
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(2008). Cluster Analysis. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_60
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DOI: https://doi.org/10.1007/978-0-387-32833-1_60
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