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Daniel Stanley Tan edited Computing_this_within_class_variance__.tex
over 8 years ago
Commit id: b334885c78cd4905468616ccc689b87b523c8e7b
deletions | additions
diff --git a/Computing_this_within_class_variance__.tex b/Computing_this_within_class_variance__.tex
index be888a2..0736756 100644
--- a/Computing_this_within_class_variance__.tex
+++ b/Computing_this_within_class_variance__.tex
...
\end{align}
where \sigma^2 is the combined variance and \mu is the combined mean. Notice that the between-class variance is simply the weighted variance of the cluster means themselves around the overall mean. Substituting $\mu = n_B(T)\mu_B(T)+n_O(T)\mu_O(T)$ and simplifying, we get
$$\sigma^2_{\text{Between}}(T) =
n_B(T)n_O(T)[\mu_B(T)-\mu_O(T)]^2$ n_B(T)n_O(T)[\mu_B(T)-\mu_O(T)]^2$$