My goal is to analyse how some variables play a part in clustering a group of individuals, i.e. what are the deterministic factors that differentiate one cluster from another. Besides manually analysing the distribution of variables in each cluster, I was thinking about using classification techniques like random forest on the dataset, using the clusters as a pseudo response, which might give some idea of variable importance. However I am not sure if this is a sensible thing to do, and there seem to be no such discussion anywhere.

  • $\begingroup$ What meaning do you put in "covariates" here? We usually speak of covariates in the context of regression or anova where independent variables correlatate. $\endgroup$ – ttnphns Sep 5 '17 at 7:47
  • $\begingroup$ nah I just meant variables, I'll edit it then, just to prevent confusion $\endgroup$ – shavendy Sep 5 '17 at 9:20
  • $\begingroup$ Since you've created groups, such as clusters, you are in the right to do any subsequent analysis you wish, with them. You should only keep in mind that since you maximized differences between the groups in your data (and not obtained them as random samples from a clustered population) you shouldn't perform significance testing. Any other analysis is welcome - if you see it reasonable to do. $\endgroup$ – ttnphns Sep 5 '17 at 9:35

I think any method to study variable importance is worth a try. This could be as simple as the correlation between features and binary indicator variables for each cluster, or as complex as a random forest.

Often people don't do such an analysis, and then won't realize that (e.g., because of inappropriate preprocessing) their clusters only depend on a single variable. So in particular, you should also check which variables do not have an impact.

  • $\begingroup$ right I see. Variable importance does give some interesting results and help with the post-clustering analysis so these methods are definitely worth trying. Thank you! $\endgroup$ – shavendy Sep 13 '17 at 9:54

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