title: Why is a feature good for distinguishing a cluster?
body: <p>Let us supposed that we are trying to rank the importance of each feature of the dataset for each given cluster, in a clustering task. What are the characteristics that we should measure in the feature for considering it good for characterizing a given cluster?</p>
  
  <p>I am looking for a more analytical characterization of these features. For example, if a feature f have a high standard deviation in the whole dataset, but a small standard deviation within a cluster c, does this means that this feature is important for distinguishing the cluster c?</p>