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Relative Closeness & Merge of Sub-Clusters

  • Relative closeness between a pair of clusters Ci and Cj : the absolute closeness between Ci and Cj normalized w.r.t. the internal closeness of the two clusters Ci and Cj 
    \[RC(C_{i},C_{j})=\frac{\bar{S}_{EC_{[C_{i},C_{j}}]}}{\frac{|C_{i}|}{|C_{i}|+|C_{j}|}\bar{S}_{EC_{C_{i}}}+\frac{|C_{j}|}{|C_{i}|+|C_{j}|}\bar{S}_{EC_{C_{j}}}}\]
    \[\bar{S}_{EC_{C_{i}}} and \bar{S}_{EC_{C_{i}}}\]
    are the average weights of the edges that belong in the min-cut bisector of clusters Ci and Cj , respectively, and
    \[\bar{S}_{EC_{C_{i},C_{j}}}\]
    is the average weight of the edges that connect vertices in Ci to vertices in Cj
    • Merge Sub-Clusters:
      • Merges only those pairs of clusters whose RI and RC are both above some user-specified thresholds
      • Merge those maximizing the function that combines RI and RC

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