Other Coefficients for Comparing Partitions
Although we strongly recommend the use of Wallace to compare partitions, there are several other coefficients that have been used. Here we summarize the most relevant. All the coefficients presented can be calculated using this website but they are not calculated by default.
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Jaccard Index
The Jaccard index (also known as Jaccard similarity coefficient) between partitions A and B is defined as the size of the intersection divided by the size of the union of the sample sets:
where a, b, c and d are the entries in the mismatch matrix.
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Fowlkes and Mallows
Another method for comparing clusters was proposed by Fowlkes and Mallows (1983) as an alternative for Rand index. The Fowlkes and Mallows index can be defined as
Actually, the Wallace coefficient was derived from this index (Wallace, 1983) and therefore it can be rewritten as
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Mirkin Metric
This coefficient assumes null value for identical clusterings and positive values otherwise. It corresponds to the Hamming distance between the binary vector representation of each partition.
It provides an alternative adjusted form of Rand index. However, unlike Hubert and Arabie's adjusted Rand (Hubert, 1985) it doesn't provide a correction for chance agreement. Meila (2005) also proposed a bounded version of this index:
