Balanced clustering: Difference between revisions

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'''Balanced clustering'''

Balanced clustering is a special case of [[Cluster analysis|clustering]], where in the strictest.sense, the cluster sizes are constrained to <math>\lfloor {n\over k}\rfloor</math> or <math>\lceil{n \over k}\rceil</math>, where <math>n</math> is the number of points and <math>k</math> is the number of clusters.<ref>{{Cite journal|last=M. I. Malinen and P. Fränti|first=|date=August 2014|title=Balanced k-Means for Clustering|url=|journal=Joint Int. Workshop on Structural, Syntactic, and Statistical Pattern Recognition (S+SSPR 2014), LNCS 8621|doi=|pmid=|access-date=}}</ref> This type of balanced clustering is called balance-constrained clustering. Typical algorithm is Balanced k-Means, which minimizes mean square error (MSE). There is also another type of balanced clustering, it is called balance-driven clustering. In it the cost function is two-objective that minimizes both inbalanceimbalance and MSE. Typical cost functions are Ratio cut<ref>{{Cite journal|last=L. Hagen and A. B. Kahng|first=|date=1992|title=New spectral methods for ratio cut partitioning and clustering|url=|journal=IEEE Transactions on Computer-Aided Design|doi=|pmid=|access-date=}}</ref> and Ncut.<ref>{{Cite journal|last=J. Shi and J. Malik|first=|date=2000|title=Normalized cuts and image segmentation|url=|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|doi=|pmid=|access-date=}}</ref>

== Software ==