Current Slide

• Partitioning method: Partitioning a database D of n objects into a set of k clusters, such that the sum of squared distances is minimized (where ci is the centroid or medoid of cluster Ci)

\[E=\sum_{i=1}^{k}\sum_{p\epsilon C_{i}}(d(p,c_{i}))^{2}\]

• Given k, find a partition of k clusters that optimizes the chosen partitioning criterion
• Global optimal: exhaustively enumerate all partitions
• Heuristic methods: k-means and k-medoids algorithms
• k-means (MacQueen’67, Lloyd’57/’82): Each cluster is represented by the center of the cluster
• k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster