Rand index

The problem, from first principles

If you do have reference labels, you can ask how well a clustering agrees with them. Cluster ids are arbitrary names, so comparing them directly is meaningless; instead compare how both partitions treat every pair of samples: together in both, or apart in both, counts as agreement.

From theory to code

Implement rand_index(labels_a, labels_b), the fraction of sample pairs on which the two partitions agree.

Constraints

• labels_a and labels_b are one-dimensional arrays of equal length; ids can be any integers.
• A pair agrees if both partitions put it in the same cluster, or both put it in different clusters.
• Return a Python float in [0, 1]; return 1.0 when there are fewer than two samples (no pairs).

Hints

Open one at a time. Each gives away a little more than the last.