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Intra- and Inter-cluster distance

Large difference between Intra-cluster distance and Inter-cluster distance.

Inter-cluster distance measured by within-cluster sum of squares. Measures cluster "compactness".

For one cluster $r$:

D_r &=& \sum_i \sum_j \vert\vert x_i - x_j \vert\vert ^2 \\
&=& 2n_r \sum_i \vert\vert x_i - \overline{x} \vert\vert^2

For all $k$ clusters:

\begin{displaymath}W_k = \sum_{r = 1}^k \frac{1}{2 n_r} D_r \end{displaymath}

Maureen Hillenmeyer 2006-05-09