Dear Marián,

in general, I see no problem in doing a cluster analysis on correlated data. Cluster analysis is for exploring patterns in the sample, and correlatedness of variables can be one meaningful pattern. Anyway, you may input your data set into a principal components analysis which gives you two orthogonal variables holding the same information, and you can cluster based on them - the result should be the same with Euclidean distances. The optimal choice of clustering algorithm, distance measure and number of clusters depends on the purpose of the classification. There is really no universal "best".

Cheers,

Attila

Attila Lengyel Thank you very much.

Dear Marián,

I think it makes sense to do it. Because the correlation is not perfect, and correlations usually only give evidence of linear dependencies of the data but not higher-order ones.

One thing that could be studied would be to use a distance metric that accounts for the correlation, the Mahalanobis distance metric is a metric that might be interesting to look at in this case: https://www.machinelearningplus.com/statistics/mahalanobis-distance/

Another possibility would be to perform a PCA as it would give you a set of orthogonal features without having to drop one of the two correlated features and then performing a clustering algorithm like a kmeans or hierarchcial on the transformed dataset and an easy norm like the Euclidean one as the distances will not be distorted by correlations due to the PCA transform.

I think that the choice of metric and linkaeg is more fudnamental than the clustering itself. The type of linkage of your clustering would be up to your expertise. There is always the Ward method though.

Best regards and hope this helps!

Asier

Asier Rabasco Meneghetti

Dear Asier.

Thank you very much for your answer. At the same time, I very much appreciate your professional answer and concretization.

Dear Marián,

In case your variables are both correlated, and form multiple clusters in Eucledian space, it would still be interesting to see whether correlation is consistent across clusters, or whether there are clusters where the correlation is higher or lower than in others..

Best of luck,

Danilo

Danilo Djekic Thank you very much.

Dear Marián,

have you ever considered the Simpson paradox? Maybe your correlation is high because a clustering structure exists, but not a linear one among all the data. Anyway, since you have only two variables, you can see clusters using a scatterplot. Visual exploration is always a good companion! :-)

Dear colleague Antonio Irpino

Thank you very much for your contribution. It is a very interesting source of additional information for me and has broadened my overview.

HOW DO I DETERMINE WHICH CORRELATION TYPE TO USE WHEN PERFORMING CLUSTER ANALYSIS?

Feride Bacanli this depends on your data, the first thing to do would be to see if you have linear relationships between the data features. If you have that, Pearson correlation would be the way to go (or Spearman if there are outliers that you cannot drop because they are important for your model).

If there is a non-linear but monotonic (like an exponential growth) relationship between variables, Spearman would be the way to go and can include the linear case. However, it might be that you have non-monotonic relationships (maybe some of the features show a parabolic relationship), it might be a good idea to transform the features to get a linear relationship between them or make separate clusterings for different regions of the conflictive feature where it becomes linear/monotonic.

But again, it depends on the kind of data you have. The most direct way to see it is to visualise the data and get a sense of what you are doing.