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Say clustering was performed. My concern is to understand what characterizes certain cluster. Which variables differ most for a certain cluster? Are there any methods for performing such kind of analysis?
For example, say I have 50 variables and 10 clusters. The desired result would sound like: for a cluster 1 variables 5, 16, 23, 42 and 49 contribute to the biggest difference from other clusters.
You can always assume that the clusters are classes and train a classifier on that.
A decision tree classifier comes to my mind, as it will often produce a "human readable" classification tree.
An interesting topic to look into is Fuzzy clustering.
The idea behind fuzzy clustering is that a cluster can have elements that are more "typical" than others and therefore have a higher membership within that cluster than other members which are less "typical".
For example, a Robin would have a high value (say 0.9) for its membership in the Birds cluster, while a Penguin would have a low value (say 0.4) for its membership in the Birds cluster.
With 50 data items (and 10 clusters!) to cluster a good inference might be difficult to obtain.
A good book to read on Fuzzy Clustering and Fuzzy Logic is the following Fuzzy Sets and Fuzzy Logic: Theory and Applications by Bo and Klir, although it is a bit dated.
