Comparing partitions. (English) Zbl 0587.62128

Hubert, Lawrence; Arabie, Phipps

Classification as a tool of research, Proc. 9th Annu. Meet. Classif. Soc. F.R.G., Karlsruhe/Ger. 1985, 209-215 (1986).

[For the entire collection see Zbl 0583.00029.]
The Rand index for comparing two partitions of an object set is briefly reviewed and then reinterpreted as a task of comparing two proximity measures. The latter framework suggests a number of alternative measures of partition correspondence and includes several indices familiar in the statistical literature for assessing association in contingency tables.
Finally, using object triples rather than object pairs, an alternative statistic is suggested that has several desirable properties: it is corrected for chance, bounded between \(\pm 1\), and has a clear probabilistic interpretation with respect to the given data.

MSC:

62H30	Classification and discrimination; cluster analysis (statistical aspects)
62H17	Contingency tables
62H20	Measures of association (correlation, canonical correlation, etc.)

Keywords:

comparing partitions; Rand index; proximity measures; alternative measures of partition correspondence; object triples

Citations:

Zbl 0583.00029