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I have a data set n=175 and for 2 different clustering (A and B) I have 5 and 6 clusters. The table for similarity of clusterings is below. First I calculated the Rand Index both manually with Excel and with "cluster_similarity" function in R and I got 63,4%. Than I calculated the Adjusted Rand index both with Excel and "adjustedRandIndex" function in R. I got 0,003 even not %3. Why is this big difference? I am very confused, I was planning to use Rand Index for my paper work but I am afraid if I have to use the adjsuted one. There are some zeros and ones in the table, may be those are problem.

n=175 for both clustering A and clustering B

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Always use the adjusted rand index. There is no reason to use the non-adjusted version.

Assuming you have a data set of 100 objects. 90 are type A. 10 are type B in the first clustering. For the second clustering, pick 90 random objects, and label them A, and the remaining 10 B. A typical confusion matrix will look like this:

81 19
19 1

and have a Rand index of somewhere around 0.95 - this looks pretty good. But the labels were given randomly, it must not be good! The adjusted rand index of this solution should be close to 0.

Thus:

  1. A high Rand index may be due to label distribution. A value of 0.95 can still be random!
  2. Adjusted rand values near 0 do indicate random results; values less than 0 even worse-than-guessing.
  3. Always prefer adjusted Rand to regular Rand index!

In the example of your question, the clusterings are as similar as random labels.

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  • $\begingroup$ Thank You. Do you have any idea about finding the similarity of these clusterings using that matrix. There are many indexes I know but I am not good in R so I could not calculate them. Rand Index and adjusted one was really easy to calculate. $\endgroup$
    – Emrah Bilgiç
    Commented Aug 21, 2016 at 12:46
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    $\begingroup$ ARI and NMI are the two important ones. I can't help you with R. It's slow and the syntax is madness $\endgroup$
    – Has QUIT--Anony-Mousse
    Commented Aug 21, 2016 at 14:34
  • $\begingroup$ I also calculated Variation of Information which is 2,89 and NMI which is 0,05. But I could not understand how to interpret them. Still my clusterings are dissimilar? $\endgroup$
    – Emrah Bilgiç
    Commented Aug 22, 2016 at 8:06
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    $\begingroup$ VI no idea. Probably > 1 is bad (high variation). NMI close to 0: not similar. So I would say all indexes say no agreement. $\endgroup$
    – Has QUIT--Anony-Mousse
    Commented Aug 22, 2016 at 8:20

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