I have a set of data (countries), and I use a clustering method (Kmeans) to create two partitions on them based on different data (diet and covid stats). So I get two groups of partitions, and I want to compare them in order to know if a clustering method will aggregate the same countries on the two sets of data.
I want to use the adjusted Rand index in order to do compute this similarity.
The problem is, when you run two clustering algorithms, you have no guarantee whatsoever that the partition labels will be the same. My two KMeans could produce the exact same partition but, for example, the first KMeans could label the cluster containing the US as "A", while the other KMeans could label it as "B". To my understanding, the Rand index needs these labels to be the same.
I cannot find an existing and reliable method in order to "normalize" group labels. Such as if I find the US in group "A" in the first clustering result, I want the US in group A in the second clustering result as well. I think I could write the algorithm myself, but it would be better to use a method that is tested and approved, if such one even exists.
Is there such a method ?