update

doc/src/week45/week45.do.txt

@@ -428,7 +428,7 @@ p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i\ne k) = 1-p_{mk}.
 * Gini index $g$
 !bt
 \[
-g = \sum_{k=1}^K p_{mk}(1-p_{mk}).
+g = \sum_{k\ne k'} p_{mk}p_{mk'}=\sum_{k=1}^K p_{mk}(1-p_{mk}).
 \]
 !et 
 * Information entropy or just entropy $s$
@@ -439,6 +439,30 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 !et 
 
 
+!split
+===== Gini Index?Coefficient/Impurity =====
+
+The Gini index $g$ gives us the degree of probability of a specific
+variable that is wrongly classified.
+ 
+It takes values $g \in [0,1]$, 
+o $g=0$ means a *pure* case where all elements belong to one class only.
+o A value $g=1$ means that all elements are randomly distributed across various classes.
+o A  value $g=0.5$ means that the elements in a node are uniformly distributed across classes. 
+
+It favors binary splitting.
+
+!split
+===== Why binary split? =====
+
+It is custom to split to a tree uising binary splits. The reason is
+that multiway splits fragment the data too quickly, leaving
+insufficient data at the next level down.  Multiway splits can be
+achieved by a series of binary split and this is normally preferred.
+
+
+
+
 !split
 ===== Visualizing the Tree, Classification =====
 !bc pycod