I am unable to understand what is the adjusted term in ARI. The expected index term in the ARI is from a prior. Kindly explain
The adjustment is simply
(Rand index - Expected value)/(Optimal value - Expected value)
The purpose is to scale it in an interpretable way. 0 is "as good as random", less than 0 is worse, and close to 1 is good.
The problem with the non adjusted Rand index is that a random result on certain data sets can achieve a high score otherwise.