Optimising sum-of-squares measures for clustering multisets defined over a metric space

Clustering is the problem of dividing a dataset into subsets, called clusters, which are both homogeneous and well-separated. Many criteria have been devised which simultaneously measure both of these properties. Two such criteria are centroid-distance, used by the popular k-means algorithm, and the complete sum of all intra-cluster distances squared, which we call all-squares. This paper compares these two criteria in the context of clustering multisets which are defined over a metric space.