update

doc/src/week45/week45.do.txt

@@ -440,7 +440,7 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 
 
 !split
-===== Gini Index?Coefficient/Impurity =====
+===== Gini Index (or Coefficient or Impurity) =====
 
 The Gini index $g$ gives us the degree of probability of a specific
 variable that is wrongly classified.
@@ -453,7 +453,7 @@ o A  value $g=0.5$ means that the elements in a node are uniformly distributed a
 It favors binary splitting.
 
 !split
-===== Why binary split? =====
+===== Why binary splits? =====
 
 It is custom to split to a tree uising binary splits. The reason is
 that multiway splits fragment the data too quickly, leaving
@@ -461,6 +461,61 @@ insufficient data at the next level down.  Multiway splits can be
 achieved by a series of binary split and this is normally preferred.
 
 
+!split
+===== Computing a Tree using the Gini Index =====
+
+Consider the following example with attributes/features and two
+possible outcomes (classes)  for each attribute.  Assume we wish to find some
+correlations between the average grade of a student as function of the
+number of hours studied and hours slept. We want also to correlate the
+grade in a given course with the general trend, whether the students
+recently has gotten grades below average or above.
+
+We have three features/attributes
+o Trend of average grades before present course, classified as either below  or above  the average grade of the whole class  
+o The number of hours studies, classified again as either higher (more than 3 hours per day) or lower . Here we have used a standard for one $ECTS$ which is scaled to 25-30 hours of work for a semester which lasts 18 weeks, with 15 weeks of lectures and 3 weeks for exams, assuming a total of 30 ECTS per semester. 
+o The number of hours slept as high for more than $8$ hours and below  for less than 8 hours of sleep, classified again as either high or low
+o The final grade whether it is above or below average
+
+
+!split
+=====  The Table =====
+
+|---------------------------------------------------|
+| Grade Trend | Hours slept | Hours Studied | Grade |
+|---------------------------------------------------|
+
+
+
+!split
+===== Computing the various Gini Indices =====
+
+In computations we will translate all classes into numbers. Being
+these binary classes, they can easily be split into ones and zeros.
+
+!bblock Gini index for Average trend
+
+!eblock
+
+
+!split
+===== Computing the various Gini Indices, Hours slept =====
+
+
+!bblock Gini index for hour slept
+
+!eblock
+
+
+!split
+===== Computing the various Gini Indices, Hours studied =====
+
+
+!bblock Gini index for hour studied
+
+!eblock
+
+
 
 
 !split