Merge branch 'master' of github.com:Dekker1/ResearchMethods

mini_proj/report/waldo.tex

@@ -24,11 +24,23 @@
 
 	\begin{document}
 		\title{What is Waldo?}
-		\author{Kelvin Davis \and Jip J. Dekker\and Anthony Silvestere}
+		\author{Kelvin Davis \and Jip J. Dekker \and Anthony Silvestere}
 		\maketitle
 
 		\begin{abstract}
-
+%
+		The famous brand of picture puzzles ``Where's Waldo?'' relates well to many
+		unsolved image classification problem. This offers us the opportunity to
+		test different image classification methods on a data set that is both small
+		enough to compute in a reasonable time span and easy for humans to
+		understand. In this report we compare the well known machine learning
+		methods Naive Bayes, Support Vector Machines, $k$-Nearest Neighbors, and
+		Random Forest against the Neural Network Architectures LeNet, Fully
+		Convolutional Neural Networks, and Fully Convolutional Neural Networks.
+		\todo{I don't like this big summation but I think it is the important
+		information}
+		Our comparison shows that \todo{...}
+%
 		\end{abstract}
 
 		\section{Introduction}
@@ -106,7 +118,17 @@
 
 		\paragraph{Naive Bayes Classifier}
 
-		\cite{naivebayes}
+		\cite{naivebayes} is a classification method according to Bayes' theorem,
+		shown in \Cref{eq:bayes}. Bayes' theorem allows us to calculate the
+		probability of an event taking into account prior knowledge of conditions of
+		the event in question. In classification this allows us to calculate the
+		probability that a new instance has a certain class based its features. We
+		then assign the class that has the highest probability.
+
+		\begin{equation}
+			\label{eq:bayes}
+			P(A\mid B)=\frac {P(B\mid A)\,P(A)}{P(B)}
+		\end{equation}
 
 		\paragraph{$k$-Nearest Neighbors}