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The Rand index counts pairs of points that two partitions agree about, but even random labellings agree on many pairs. The adjusted version subtracts the expected agreement and rescales, so a random clustering scores about 0, a perfect match scores 1, and systematically worse-than-random assignments go negative. That correction is what makes ARI comparable across different numbers of clusters.
Adjusted Rand index
ARI = (index - expected index) / (max index - expected index)
Because the expected agreement is subtracted. A partition that splits genuine groups apart more than chance would gives a value below zero.
No. It compares pairwise co-membership, so it works when the predicted clustering has more or fewer groups than the reference labels.