update on decision trees

doc/src/DecisionTrees/DecisionTrees.do.txt

@@ -443,7 +443,41 @@ than is the classification error rate.
 If our targets are the outcome of a classification process that takes for example 
 $k=1,2,\dots,K$ values, the only thing we need to think of is to set up the splitting criteria for each node.
 
- 
+We define a PDF $p_{mk}$  that represents the number of observations of a class $k$ in a region $R_m$ with $N_m$ observations. We represent this likelihood function in terms of the proportion $I(y_i=k)$  of observations of this class in the region $R_m$ as
+!bt
+\[
+p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i=k).
+\]
+!et 
+
+We let $p_{mk}$ represent the majority class of observations in region $m$. The three most common ways of splitting a node are given by 
+* Misclassification error 
+!bt
+\[
+p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i\ne k) = 1-p_{mk}.
+\]
+!et 
+* Gini index $g$
+!bt
+\[
+g = \sum_{k=1}^K p_{mk}(1-p_{mk}).
+\]
+!et 
+* Information entropy or just entropy $s$
+!bt
+\[
+s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
+\]
+!et 
+
+
+!split
+===== Entropy and the ID3 algorithm =====
+
+
+!split
+===== Writing your own code for a classification tree =====
+
 
 !split
 =====  Back to moons again =====

doc/src/ODENN/odenn.do.txt

@@ -1,4 +1,5 @@
 TITLE: Data Analysis and Machine Learning: Using Neural networks to solve ODEs and PDEs
+AUTHOR: Kristine Baluka Hein at Department of Informatics, University of Oslo, Norway
 DATE: today
 
 !split