'''Balanced clustering''' is a special case of [[Cluster analysis|clustering]] where, in the strictest sense, 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|datetitle=AugustStructural, Syntactic, and Statistical Pattern Recognition 2014|titlechapter=Balanced kK-Means for Clustering |journaldate=JointAugust Int.2014 Workshop|series=Lecture onNotes Structural,in Syntactic,Computer andScience StatisticalPattern|volume=8621|pages=32–41 Recognition|doi=10.1007/978-3-662-44415-3_4 (S+SSPR|isbn=978-3-662-44414-6 2014), LNCS 8621}}</ref> A typical algorithm is balanced [[K-means clustering|k-means]], which minimizes [[Mean squared error|mean square error (MSE)]]. Another type of balanced clustering called balance-driven clustering has a two-objective cost function that minimizes both the imbalance and the MSE. Typical cost functions are ratio cut<ref>{{Cite journal|last=L. Hagen and A. B. Kahng|date=1992|title=New spectral methods for ratio cut partitioning and clustering|journal=IEEE Transactions on Computer-Aided Design|volume=11 |issue=9 |pages=1074–1085 |doi=10.1109/43.159993 }}</ref> and Ncut.<ref>{{Cite journal|author=J. Shi and J. Malik|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|volume=22|issue=8|pages=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.
== Software ==
There exists implementations for balanced k-means<ref>{{Cite web |urllast=http://csM.uef I.fi/sipu/soft/Balanced Malinen and P.zip Fränti |title=Balanced k-Means implementation |lasturl=Mhttps://cs. Iuef. Malinen and Pfi/sipu/soft/Balanced.zip Fränti|publisher=University of Eastern Finland}}</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|publisher=University of Pennsylvania}}</ref>
