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WGA Algorithm

WGA = $\frac{d_b}{k_1d_{1}+k_2d_{2}+\alpha}$

Alpha is used to make sure that division by zero never happens.

$n_i$ is the total number of items in group i.

t is the number of pairings with a group.

$t_i = (n_i-1)+(n_i-2)+...+(n_i-(n_i-1))$ = $\frac{n_i(n_i-1)}{2}$

$k_1=\frac{t_1}{t_1+t_2}$

$k_2=\frac{t_2}{t_1+t_2}$

$d_i$ is the average Euclidean distance among all sample pairs within the group.

$d_i = \sqrt{ (v_1 - v_2)^2 + (v_1 - v_3)^2 + ... + (v_1 - v_{n_i})^2 + (v_2 - v_3)^2 + ... + (v_2 - v_{n_i})^2 + ... + (v_{n_{i-1}} - v_{n_i})^2 } $

$d_i = \sqrt{ \sum\limits_{i=1}^{n_i-1} \sum\limits_{j=i+1}^{n_i} (v_i - v_j)^2 }$

$d_b = | mean_1 - mean_2 |$

WGA = $ \frac{d_b}{k_1d_{1}+k_2d_{2}+\alpha}$
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Topic revision: r12 - 12 Sep 2005, ColeBeck
 

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