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Cluster


The term "cluster" denotes a collection of objects grouped by a specified relation, and its precise meaning depends on context.

In percolation theory, a cluster is a connected component of occupied sites or bonds. For a square point lattice with nearest-neighbor adjacency, it is a group of filled cells connected through vertical or horizontal neighbors.

In cluster analysis, a cluster is a group of data elements that are comparatively close according to a chosen distance or dissimilarity measure. In cluster sampling, a cluster is a group of population units that may be selected and observed together.

In a cluster algebra, a cluster is an n-tuple of algebraically independent cluster variables belonging to one seed.


See also

Cluster Algebra, Cluster Analysis, Cluster Perimeter, Cluster Sampling, Percolation Theory, s-Cluster, s-Run

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References

Cochran, W. G. Sampling Techniques, 3rd ed. New York: Wiley, 1977.Fomin, S. and Zelevinsky, A. "Cluster Algebras I: Foundations." J. Amer. Math. Soc. 15, 497-529, 2002. https://doi.org/10.1090/S0894-0347-01-00385-X.Kaufman, L. and Rousseeuw, P. J. Finding Groups in Data: An Introduction to Cluster Analysis. New York: Wiley, 1990.Stauffer, D. and Aharony, A. Introduction to Percolation Theory, 2nd ed. London, England: Taylor & Francis, 1992.

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Cluster

Cite this as:

Weisstein, Eric W. "Cluster." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Cluster.html

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