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Bachelor-Final-Presentation: Added first draft

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\subsection{Merged Symbols}
\begin{frame}[fragile]{Merged symbols (MER error)}
\begin{table}[ht]
\centering
\begin{tabular}{lc|lc}
\toprule
\multicolumn{2}{c}{Base symbol} & \multicolumn{2}{c}{equivalent symbols}\\
\LaTeX & Rendered & \LaTeX & Rendered \\\midrule
\verb+\sum+ & $\sum$ & \verb+$\Sigma$+ & $\Sigma$\\
\verb+\prod+ & $\prod$ & \verb+$\Pi$+ & $\Pi$\\
~ & ~ & \verb+$\sqcap$+ & $\sqcap$\\
\verb+\coprod+ & $\coprod$ & \verb+$\amalg$+ & $\amalg$\\
~ & ~ & \verb+$\sqcup$+ & $\sqcup$\\
\verb+\perp+ & $\perp$ & \verb+$\bot$+ & $\bot$\\
\verb+\models+ & $\models$ & \verb+$\vDash$+ & $\vDash$\\
\verb+|+ & | & \verb+\mid+ & $\mid$ \\
\verb+\Delta+ & $\Delta$ & \verb+$\triangle$+ & $\triangle$\\
~ & ~ & \verb+$\vartriangle$+ & $\vartriangle$\\
\bottomrule
\end{tabular}
\end{table}
\end{frame}
\begin{frame}[fragile]{Merged symbols (MER error)}
\begin{table}[ht]
\centering
\begin{tabular}{lc|lc}
\toprule
\multicolumn{2}{c}{Base symbol} & \multicolumn{2}{c}{equivalent symbols}\\
\LaTeX & Rendered & \LaTeX & Rendered \\\midrule
\verb+\|+ & $\|$ & \verb+$\parallel$+ & $\parallel$\\
\verb+\ohm+ & $\Omega$ & \verb+$\Omega$+ & $\Omega$\\
\verb+\setminus+ & $\setminus$ & \verb+$\backslash$+ & $\backslash$\\
\verb+\checked+ & {\mbox {\wasyfamily \char 8}} & \verb+$\checkmark$+ & $\checkmark$\\
\verb+\&+ & $\&$ & \verb+$\with$+ & $\&$\\
\verb+\#+ & $\#$ & \verb+$\sharp$+ & $\sharp$\\
\verb+\S+ & $\S$ & \verb+$\mathsection$+ & $\mathsection$\\
\verb+\nabla+ & $\nabla$ & \verb+\triangledown+ & $\triangledown$\\
\verb+\lhd+ & $\lhd$ & \verb+$\triangleleft$+ & $\triangleleft$\\
~ & ~ & \verb+$\vartriangleleft$+ & $\vartriangleleft$\\
\verb+\oiint+ & $\oiint$ & \verb+$\varoiint$+ & $\varoiint$\\
\bottomrule
\end{tabular}
\end{table}
\end{frame}
\begin{frame}[fragile]{Merged symbols (MER error)}
\begin{table}[ht]
\centering
\begin{tabular}{lc|lc}
\toprule
\multicolumn{2}{c}{Base symbol} & \multicolumn{2}{c}{equivalent symbols}\\
\LaTeX & Rendered & \LaTeX & Rendered \\\midrule
\verb+\mathbb{R}+ & $\mathbb{R}$ & \verb+$\mathds{R}$+ & $\mathds{R}$\\
\verb+\mathbb{Q}+ & $\mathbb{Q}$ & \verb+\mathds{Q}+ & $\mathds{Q}$\\
\verb+\mathbb{Z}+ & $\mathbb{Z}$ & \verb+\mathds{Z}+ & $\mathds{Z}$\\
\verb+\mathcal{A}+ & $\mathcal{A}$ & \verb+\mathscr{A}+ & $\mathscr{A}$\\
\verb+\mathcal{D}+ & $\mathcal{D}$ & \verb+\mathscr{D}+ & $\mathscr{D}$\\
\verb+\mathcal{N}+ & $\mathcal{N}$ & \verb+\mathscr{N}+ & $\mathscr{N}$\\
\verb+\mathcal{R}+ & $\mathcal{R}$ & \verb+\mathscr{R}+ & $\mathscr{R}$\\
\verb+\propto+ & $\propto$ & \verb+$\varpropto$+ & $\varpropto$\\
\bottomrule
\end{tabular}
\end{table}
\end{frame}
\subsection{Evaluation}
\begin{frame}{Experiments}
\textbf{Preprocessing:} Scaling, shifting and linear interpolation\\
\textbf{Features:} Coordinates of 80 points (4 strokes with 20 points each)\\
\textbf{Learning:} MLP, 1000 epochs, LR $\eta=0.1$, Momentum $\alpha=0.1$
\begin{table}[h]
\centering
\begin{tabular}{clrrr}
\toprule
\multirow{2}{*}{System} & \multirow{2}{*}{Topology} & \multicolumn{3}{c}{Classification error}\\
& & TOP1 & TOP3 & MER \\\midrule
$B_1$ & 160:500:369 & $\SI{23.34}{\percent}$ & $\SI{6.80}{\percent}$ & $\SI{6.64}{\percent}$ \\
$B_2$ & 160:500:500:369 & \underline{$\SI{21.51}{\percent}$} & $\SI{5.75}{\percent}$ & $\SI{5.67}{\percent}$ \\
$B_3$ & 160:500:500:500:369 & $\SI{21.93}{\percent}$ & \underline{$\SI{5.74}{\percent}$} & \underline{$\SI{5.64}{\percent}$} \\
$B_4$ & 160:500:500:500:500:369 & $\SI{23.88}{\percent}$ & $\SI{6.12}{\percent}$ & $\SI{6.04}{\percent}$ \\
\bottomrule
\end{tabular}
\caption{Baseline systems with three different classification error measures.
All errors were measured on the test set.}
\label{table:baseline-systems}
\end{table}
\end{frame}
\subsection{Complex classifier}
\begin{frame}{Complex classifier}
\textbf{Preprocessing:} Connect strokes, scale, shift and linear interpolation\\
\textbf{Features:} Coordinates of 80 points (4 strokes with 20 points each), re-curvature per stroke, ink, stroke count, aspect ratio\\
\textbf{Learning:} MLP, 1000 epochs, LR $\eta=0.1$, Momentum $\alpha=0.1$
\begin{table}[htb]
\centering
\begin{tabular}{lrrrrrr}
\toprule
\multirow{2}{*}{System} & \multicolumn{3}{c}{Classification error}\\
& TOP1 & change & TOP3 & change & MER & change \\\midrule
$B_{1,c}$ & $\SI{20.96}{\percent}$ & $\SI{-2.38}{\percent}$ & $\SI{5.24}{\percent}$ & $\SI{-1.56}{\percent}$ & $\SI{5.13}{\percent}$ & $\SI{-1.51}{\percent}$ \\
$B_{2,c}$ & $\SI{20.10}{\percent}$ & $\SI{-1.41}{\percent}$ & $\SI{4.44}{\percent}$ & $\SI{-1.31}{\percent}$ & $\SI{4.36}{\percent}$ & $\SI{-1.31}{\percent}$ \\
$B_{3,c}$ & $\SI{21.51}{\percent}$ & $\SI{-0.42}{\percent}$ & $\SI{4.89}{\percent}$ & $\SI{-0.85}{\percent}$ & $\SI{4.80}{\percent}$ & $\SI{-0.84}{\percent}$ \\
$B_{4,c}$ & $\SI{00.00}{\percent}$ & $\SI{-0.00}{\percent}$ & $\SI{0.00}{\percent}$ & $\SI{-0.00}{\percent}$ & $\SI{0.00}{\percent}$ & $\SI{-0.00}{\percent}$ \\
\bottomrule
\end{tabular}
\caption{Error rates of the complex recognizer systems.}
\label{table:complex-recognizer-systems-evaluation}
\end{table}
\end{frame}