'''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, and Statistical Pattern Recognition (S+SSPR|volume=8621|pages=32–41 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.▼
{{Userspace draft|source=ArticleWizard|date=March 2016}}
'''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=Balanced k-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>.
== References ==
<references />
<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags, these references will then appear here automatically --><references /><!--- Categories --->
{{cite journal |doi=10.1134/S1064226917120105 |title=On Balanced Clustering (Indices, Models, Examples) |year=2017 |last1=Levin |first1=M. Sh. |journal=Journal of Communications Technology and Electronics |volume=62 |issue=12 |pages=1506–1515 |s2cid=255277095 }}
[[Category:ArticlesClustering created via the Article Wizardcriteria]]
== Balanced clustering ==
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