ClusterNMI: Normalized Mutual Information [Strehl et al., 2003]

In FCPS: Fundamental Clustering Problems Suite

Normalized Mutual Information [Strehl et al., 2003]

Description

Mutual information measures the amount of information that two clusterings share: the higher the MI, the more information shared, indicating a higher similarity between the two clusterings [Cover and Thomas, 1991].

Usage

ClusterNMI(Cls1, Cls2,Variant="max")

Arguments

Cls1	1:n numerical vector of numbers defining the classification as the main output of the first clustering or trial for the n cases of data. It has k unique numbers representing the arbitrary labels of the clustering.
Cls2	1:n numerical vector of numbers defining the classification as the main output of the second clustering algorithm trial for the n cases of data. It has p unique numbers representing the arbitrary labels of the clustering.
Variant	Optional, string, default "max", alternatives are ifferent variants of NMI: ("min", "sqrt", "sum", "joint")

Details

Normalized mutual information scales the result to a fixed range [0, 1], where 0 indicates no mutual information (completely independent clusterings) and 1 indicates perfect correlation (the clusterings are identical). It is normalized by the entropy of both the true labels and the cluster assignments, which makes it more interpretable and less sensitive to the number of clusters. NMI is often used when you have prior knowledge about the number of clusters or when comparing different clustering results.

Value

value of normalized mutual information

Author(s)

Michael Thrun (Wrapper only)

References

[Strehl et al., 2003] Strehl, Alexander; Ghosh, Joydeep: Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions, The Journal of Machine Learning Research, Vol. 3, pp. 583–617. doi:10.1162/153244303321897735, 2003

[Cover and Thomas, 1991] Cover, T, and Thomas, J.A.: Elements of Information Theory. Wiley, 1991.

Examples

data(Hepta)
#compare to baseline
Cls2=kmeansClustering(Hepta$Data,7,Type = "Steinley")$Cls
ClusterNMI(Hepta$Cls,Cls2)
#compare different solutions
Cls3=kmeansClustering(Hepta$Data,5)$Cls
ClusterNMI(Cls3,Cls2)

FCPS documentation built on Nov. 5, 2025, 7:44 p.m.