Balanced clustering

Balanced clustering is a special case of clustering where, in the strictest sense, cluster sizes are constrained to $\lfloor {n \over k}\rfloor$ or $\lceil {n \over k}\rceil$ , where $n$ is the number of points and $k$ is the number of clusters.^[1] A typical algorithm is balanced k-means, which minimizes 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^[2] and Ncut.^[3]

Software

There exists implementations for balanced k-means^[4] and Ncut^[5]

References

^ M. I. Malinen and P. Fränti (August 2014). "Balanced k-Means for Clustering". Joint Int. Workshop on Structural, Syntactic, and Statistical Pattern Recognition (S+SSPR 2014), LNCS 8621.
^ L. Hagen and A. B. Kahng (1992). "New spectral methods for ratio cut partitioning and clustering". IEEE Transactions on Computer-Aided Design.
^ J. Shi and J. Malik (2000). "Normalized cuts and image segmentation". IEEE Transactions on Pattern Analysis and Machine Intelligence. doi:10.1109/34.868688.
^ M. I. Malinen and P. Fränti. "Balanced k-Means implementation". University of Eastern Finland.
^ T. Cour, S. Yu and J. Shi. "Ncut implementation". University of Pennsylvania.

[1] M. I. Malinen and P. Fränti (August 2014). "Balanced k-Means for Clustering". Joint Int. Workshop on Structural, Syntactic, and Statistical Pattern Recognition (S+SSPR 2014), LNCS 8621.

[2] L. Hagen and A. B. Kahng (1992). "New spectral methods for ratio cut partitioning and clustering". IEEE Transactions on Computer-Aided Design.

[3] J. Shi and J. Malik (2000). "Normalized cuts and image segmentation". IEEE Transactions on Pattern Analysis and Machine Intelligence. doi:10.1109/34.868688.

[4] M. I. Malinen and P. Fränti. "Balanced k-Means implementation". University of Eastern Finland.

[5] T. Cour, S. Yu and J. Shi. "Ncut implementation". University of Pennsylvania.

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