since some time I have a question to which I have not found the proper answer yet.
My doubt concerns the interpretation of the results of a
clustering algorithm which was run on features to which a
log-transformation was applied.
Specifically, let's assume we want to run a
k-means algorithm on 3 interval variables. Unfortunately, these three interval variables are extremely bad distributed and the k-means gives the worst result we have ever seen.
However, let's imagine that by applying a
log transformation to each variable, we obtain three incredibly perfect
Then, we run again the
k-means and we obtain perfect
Now, my doubt concerns the interpretation of this cluster obtained by running a
k-means on three
log-transformed variables: it is not clear whether our interpretation of the clusters obtained should be made on the original variables or it should be made on the
Clearly, my example is related to log-transformation but we can talk about
min-max normalization or any other kind of
transformation that we apply in order to improve the quality
distribution before running the clustering algorithm.
To clarify, what I mean by interpretation is the
profiling of the cluster, which means try to describe which are the characteristics common to the individuals belonging to that cluster.