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 normal distribution
.
Then, we run again the k-means
and we obtain perfect clusters
.
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 log-transformed
variables?
Clearly, my example is related to log-transformation but we can talk about z-score
or 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.