title: What makes the distance measure in k-medoid "better" than k-means?
body: <p>I am reading about the difference between k-means clustering and k-medoid clustering.</p>
  
  <p>Supposedly there is an advantage to using the pairwise distance measure in the k-medoid algorithm, instead of the more familiar sum of squared Euclidean distance-type metric to evaluate variance that we find with k-means.  And apparently this different distance metric somehow reduces noise and outliers.</p>
  
  <p>I have seen this claim but I have yet to see any good reasoning as to the mathematics behind this claim.  </p>
  
  <p>What makes the pairwise distance measure commonly used in k-medoid better?  More exactly, how does the lack of a squared term allow k-medoids to have the desirable properties associated with the concept of taking a median?</p>