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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

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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.

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  • $\begingroup$ How do we know if a pair is placed in a cluster by chance or it belongs to the cluster legitimately. How does the function decide the expected value? I have read that rand index is similarity in clusters/ total observations and the kappa statistic utility to cater for chance metric is integrated in Rand to improve the statistic. So, the problem is how do we know if what decides the random occurence? $\endgroup$
    – KHAN irfan
    Commented Jun 9, 2017 at 3:38
  • $\begingroup$ Expected value is by random permutation of labels. $\endgroup$ Commented Jun 9, 2017 at 6:47

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