I performed a categorical clustering with some selected UCI datasets. I one-hot encoded the features, then directly used Binomial Mixture Model and KModes using this one-hot encoded data. On the otherhand, I preprocessed the one-hot encoded datasets further by using Gower's distance and fed the output into a hierarchical clustering with compete linkage. In my experiment I used the Elbow method to determine the optimal number of clusters for each clustering method.
My expectation was that ARI (Adjusted Rand Index)and NMI (Normalized Mutual Information) will always be greater than FMI (Folkes-Mallows Index), but turns out that FMI is almost always giving higher values than ARI and NMI, based on my readings ARI and NMI are the two accepted "standard" metrics for clustering. But in this case I am starting to doubt if ARI and NMI should be considered as the "standards", at least for my experiments.
My question would be when to use, and not to use, FMI, ARI and NMI. It is obvious in my case that ARI and NMI are showing that the clustering results are bad, but is contradicting the result of FMI.
