I need an approach to assign weights to variables based on the cluster. I am not trying to learn the clusters, as I already have them, but I would just like to now understand how "important" each variable is to the cluster. Is there any way of determining weights per variable per cluster?
I thought I could use a multi-class classifier and learn the variable importance and use them as weights, but these weights would then be global across all clusters, and not cluster specific.
In another attempt, I could probably do something like a logistic regression one-versus all, and use the coefficients there as weights. But I'm wondering if this even makes sense.
Any idea on how to learn how important features are to clusters?