Assessing Clustering Quality

A measure for the quality of a solution given the true clustering should be devised. Let T be the ``true'' solution and S the solution we wish to measure. Denote by n₁₁ the number of pairs of elements that are in the same cluster in both S and T. Denote by n₀₁ the number of pairs that are in the same cluster only in S, and by n₁₀ the number of pairs that are in the same cluster only in T. We define the Minkowski Score to be:

$$D_M(T,S)=\sqrt{\frac{n_{01}+n_{10}}{n_{11}+n_{10}}}$$

In this case the optimum score is 0, with lower scores being ``better''. An alternative is the Jaccard Score:

$$D_J(T,S)=\frac{n_{11}}{n_{11}+n_{10}+n_{01}}$$

Here the optimum score is 1, with greater scores being ``better''.