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'''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 book|last=M. I. Malinen and P. Fränti|title=Structural, Syntactic, and Statistical Pattern Recognition |chapter=Balanced K-Means for Clustering |date=August 2014 |series=Lecture Notes in Computer Science |volume=8621|pages=32–41 |doi=10.1007/978-3-662-44415-3_4 |isbn=978-3-662-44414-6 }}</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.<ref>{{cite journal |last1=de Ramos |first1=D. C. |last2=Ferreira |first2=L. R. |last3=Santos |first3=M. M. D. |last4=Teixeira |first4=E. L. S. |last5=Yoshioka |first5=L. R. |last6=Justo |first6=J. F. |last7=Malik |first7=A. W. |title=Evaluation of Cluster Algorithms for Radar-Based Object Recognition in Autonomous and Assisted Driving |journal=Sensors |date=2024 |volume=24 |issue=22 |page=7219 |doi=10.3390/s24227219|doi-access=free }}</ref> It is then preferred that each car delivers to an equal number of locations.
== Software ==
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