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Partitioning Algorithms: Basic Concept

  • 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

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