Cut other stats

mini_proj/report/waldo.tex

@@ -252,41 +252,12 @@
 		\subsection{Performance Metrics}\label{performance-metrics}
 
 		To evaluate the performance of the models, we record the time taken by
-		each model to train, based on the training data and statistics about the
-		predictions the models make on the test data. These prediction
-		statistics include:
-
-		\begin{itemize}
-		\item
-		\textbf{Accuracy:}
-		\[a = \dfrac{|correct\ predictions|}{|predictions|} = \dfrac{tp + tn}{tp + tn + fp + fn}\]
-		\item
-		\textbf{Precision:}
-		\[p = \dfrac{|Waldo\ predicted\ as\ Waldo|}{|predicted\ as\ Waldo|} = \dfrac{tp}{tp + fp}\]
-		\item
-		\textbf{Recall:}
-		\[r = \dfrac{|Waldo\ predicted\ as\ Waldo|}{|actually\ Waldo|} = \dfrac{tp}{tp + fn}\]
-		\item
-		\textbf{F1 Measure:} \[f1 = \dfrac{2pr}{p + r}\] where \(tp\) is the
-		number of true positives, \(tn\) is the number of true negatives,
-		\(fp\) is the number of false positives, and \(tp\) is the number of
-		false negatives.
-		\end{itemize}
-
-		\emph{Accuracy} is a common performance metric used in Machine Learning,
-		however in classification problems where the training data is heavily biased
-		toward one category, sometimes a model will learn to optimize its accuracy
-		by classifying all instances as one category. I.e. the classifier will
-		classify all images that do not contain Waldo as not containing Waldo, but
-		will also classify all images containing Waldo as not containing Waldo. Thus
-		we use, other metrics to measure performance as well. \\
-
-		\emph{Precision} returns the percentage of classifications of Waldo that are
-		actually Waldo. \emph{Recall} returns the percentage of Waldos that were
-		actually predicted as Waldo. In the case of a classifier that classifies all
-		things as Waldo, the recall would be 0. \emph{F1-Measure} returns a
-		combination of precision and recall that heavily penalizes classifiers that
-		perform poorly in either precision or recall.
+		each model to train, based on the training data and the accuracy with which
+    the model makes predictions. We calculate accuracy as
+		\(a = \frac{|correct\ predictions|}{|predictions|} = \frac{tp + tn}{tp + tn + fp + fn}\)
+		where \(tp\) is the number of true positives, \(tn\) is the number of true
+    negatives, \(fp\) is the number of false positives, and \(tp\) is the number
+    of false negatives.
 
 		\section{Results} \label{sec:results}
 
@@ -322,7 +293,11 @@
 				network and traditional machine learning technique}
 			\label{tab:results}
 		\end{table}
-
+    
+    We can see by the results that Deep Neural Networks outperform our benchmark
+    classification models, although the time required to train these networks is
+    significantly greater.
+    
 		\section{Conclusion} \label{sec:conclusion}
 
 		Image from the ``Where's Waldo?'' puzzle books are ideal images to test