exercise-classification: Fixed a wrong midpoint used in the calculati…

…on of Information Gain and Gini Index
FAU-CS6 · Jun 13, 2024 · 4a0f63a · 4a0f63a
1 parent a0be7ac
commit 4a0f63a
Showing 1 changed file with 5 additions and 5 deletions.
diff --git a/exercise/4-Classification.tex b/exercise/4-Classification.tex
@@ -144,7 +144,7 @@ \subsection*{Task 1: Information Gain}
 						                                                        & = 0                                                                                                                                                                                                                                     \\
 					                        \end{alignat*}
 
-					                  \item \textbf{Split point $25,5$:}
+					                  \item \textbf{Split point $25,0$:}
 
 					                        \begin{alignat*}{2}
 						                        \text{Info}\OfAttribute{Age}(D) & = \sum_{j=1}^v \frac{|D\OfAttribute{Age$,j$}|}{|D\OfAttribute{Age}|} \text{Info}(D_{A\OfAttribute{Age$,j$}})                                                                                                                            \\
@@ -159,7 +159,7 @@ \subsection*{Task 1: Information Gain}
 
 				                  \end{enumerate}
 
-				                  Therefore, the Information Gain for the attribute \textit{Age} is $0,817$ (if we split at $25,5$).
+				                  Therefore, the Information Gain for the attribute \textit{Age} is $0,817$ (if we split at $25,0$).
 
 				            \item \textbf{Attribute \textit{Major}:}
 
@@ -599,10 +599,10 @@ \subsection*{Task 2: Gini Index}
 						                                                              & = 0,5 - 0,5                                                                                                                                                                                                                               \\
 						                                                              & = 0                                                                                                                                                                                                                                       \\
 					                        \end{alignat*}
-					                  \item \textbf{Split point $25,5$:}
+					                  \item \textbf{Split point $25,0$:}
 
 					                        \begin{alignat*}{2}
-						                        \text{Gini}\OfAttribute{Age}(D)       & = \frac{|D\OfSpecificValue{Age}{$\leq$}{25,5}|}{|D\OfAttribute{Age}|} \text{Gini}(D\OfSpecificValue{Age}{$\leq$}{25,5}) + \frac{|D\OfSpecificValue{Age}{$>$}{25,5}|}{|D\OfAttribute{Age}|} \text{Gini}(D\OfSpecificValue{Age}{$>$}{25,5}) \\
+						                        \text{Gini}\OfAttribute{Age}(D)       & = \frac{|D\OfSpecificValue{Age}{$\leq$}{25,0}|}{|D\OfAttribute{Age}|} \text{Gini}(D\OfSpecificValue{Age}{$\leq$}{25,0}) + \frac{|D\OfSpecificValue{Age}{$>$}{25,0}|}{|D\OfAttribute{Age}|} \text{Gini}(D\OfSpecificValue{Age}{$>$}{25,0}) \\
 						                                                              & = \frac{3}{6} \left(1 - \left(\frac{2}{3}\right)^2 - \left(\frac{1}{3}\right)^2\right) + \frac{3}{6} \left(1 - \left(\frac{1}{3}\right)^2 - \left(\frac{2}{3}\right)^2\right)                                                             \\
 						                                                              & = \frac{3}{6} \cdot 0,4444 + \frac{3}{6} \cdot 0,4444                                                                                                                                                                                     \\
 						                                                              & = 0,4444                                                                                                                                                                                                                                  \\
@@ -612,7 +612,7 @@ \subsection*{Task 2: Gini Index}
 					                        \end{alignat*}
 				                  \end{enumerate}
 
-				                  The best split point is $25,5$ since its Gini Index is the lowest ($0,4444$) and therefore the reduction of impurity ($0,0556$) is the highest.
+				                  The best split point is $25,0$ since its Gini Index is the lowest ($0,4444$) and therefore the reduction of impurity ($0,0556$) is the highest.
 
 				            \item \textbf{Attribute \textit{Major}:}