'''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 journalbook|last=M. I. Malinen and P. Fränti|firsttitle=|date=AugustStructural, Syntactic, and Statistical Pattern Recognition 2014|titlechapter=Balanced kK-Means for Clustering |urldate=August 2014 |journalseries=JointLecture Int.Notes Workshopin onComputer Structural,Science Syntactic, andStatistical Pattern Recognition|volume=8621|pages=32–41 (S+SSPR 2014), LNCS 8621|doi=10.1007/978-3-662-44415-3_4 |pmidisbn=|access978-date=3-662-44414-6 }}</ref> ThisA typetypical of balanced clusteringalgorithm is calledbalanced balance[[K-constrainedmeans clustering. Typical algorithm is Balanced |k-Meansmeans]], which minimizes [[Mean squared error|mean square error (MSE)]]. There is also anotherAnother type of balanced clustering, it is called balance-driven clustering.Inhas ita thetwo-objective cost function is two-objective that minimizes both inbalancethe imbalance and the MSE. Typical cost functions are Ratioratio 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|doivolume=11 |pmidissue=9 |access-datepages=1074–1085 |doi=10.1109/43.159993 }}</ref> and Ncut.<ref>{{Cite journal|lastauthor=J. Shi and J. Malik|first=|date=2000|title=Normalized cuts and image segmentation|url=https://repository.upenn.edu/cis_papers/107|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|doivolume=22|pmidissue=8|access-datepages=888–905|doi=10.1109/34.868688}}</ref> Balanced clustering can be used for example in scenarios where freight has to be delivered to <math>n</math> locations with <math>k</math> cars. It is then preferred that each car delivers to an equal number of locations.▼
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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 inbalance 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 ==
There exists implementations for Balancedbalanced k-Meansmeans<ref>{{Cite web|url=http://cs.uef.fi/sipu/soft/Balanced.zip|title=Balancedk-Means implementation|last=M. I. Malinen and P. Fränti |firsttitle=Balanced k-Means implementation |date=|websiteurl=https://cs.uef.fi/sipu/soft/Balanced.zip |publisher=University of Eastern Finland|access-date=}}</ref> and Ncut<ref>{{Cite web|url=http://www.cis.upenn.edu/~jshi/software/|title=Ncut implementation|last=T. Cour, S. Yu and J. Shi|first=|date=|website=|publisher=University of Pennsylvania|access-date=}}</ref>
