Synonyms
CLARA (Clustering LARge Applications); CLARANS (Clustering large applications based upon randomized search); K-means partition; PAM (Partitioning Around Medoids)
Definitions
K-Means
Given an integer k and a set of objects S = {p1, p2,…,pn} in Euclidian space, the problem of k-means clustering is to find a set of centre points (means) P = {c1, c2,…,ck}, |P| = k in the space, such that S can be partitioned into k corresponding clusters C1, C2,…,Ck, by assigning each object in S to the closest centre ci. The sum of square error criterion (SEC) measure, defined as \( {\displaystyle {\sum}_{i=1}^k{\displaystyle \sum_{p\in {C}_i}\Big|p-{c}_i}}\Big|{}^2 \), is minimized.
K-Medoids
Given an integer k and a set of objects S = {p1, p2, …, pn} in Euclidian space, the problem of k-medoids clustering is to find a set of objects as medoids P = {o1, o2,…,ok}, |P| = k in the space, such that S can be partitioned into k corresponding clusters C1, C2,…,Ck, by assigning each object in Sto the...
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Kaufman L, Rousseeuw PJ. Finding groups in data: an introduction to cluster analysis. New York: Wiley; 1990.
MacQueen J. Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematics, Statistics and Probabilities; 1967. p. 281–97.
Ng RT, Han J. Efficient and effective clustering methods for spatial data mining. In: Proceedings of the 20th International Conference on Very Large Databases; 1994. p. 144–55.
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Li, X. (2018). K-Means and K-Medoids. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_545
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_545
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