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159 lines
No EOL
9.8 KiB
TeX
159 lines
No EOL
9.8 KiB
TeX
\subsection{Evaluation}
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\begin{frame}{Baseline Systems}
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\textbf{Preprocessing:} Scaling, shifting and linear interpolation\\
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\textbf{Features:} Coordinates of 80 points (4 strokes with 20 points each)\\
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\textbf{Learning:} MLP, 1000 epochs, LR $\eta=0.1$, Momentum $\alpha=0.1$
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\begin{table}[h]
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\centering
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\begin{tabular}{clrrr}
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\toprule
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\multirow{2}{*}{System} & \multirow{2}{*}{Topology} & \multicolumn{3}{c}{Classification error}\\
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& & TOP1 & TOP3 & MER \\\midrule
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$B_1$ & 160:500:369 & $\SI{23.34}{\percent}$ & $\SI{6.80}{\percent}$ & $\SI{6.64}{\percent}$ \\
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$B_2$ & 160:500:500:369 & \underline{$\SI{21.51}{\percent}$} & $\SI{5.75}{\percent}$ & $\SI{5.67}{\percent}$ \\
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$B_3$ & 160:500:500:500:369 & $\SI{21.93}{\percent}$ & \underline{$\SI{5.74}{\percent}$} & \underline{$\SI{5.64}{\percent}$} \\
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% $B_4$ & 160:500:500:500:500:369 & $\SI{23.88}{\percent}$ & $\SI{6.12}{\percent}$ & $\SI{6.04}{\percent}$ \\
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\bottomrule
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\end{tabular}
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\caption{Baseline systems with three different classification error measures.
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All errors were measured on the test set.}
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\label{table:baseline-systems}
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\end{table}
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\end{frame}
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\subsection{Merged Symbols}
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\begin{frame}[fragile]{Merged symbols (MER error)}
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\begin{table}[ht]
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\centering
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\begin{tabular}{lc|lc}
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\toprule
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\multicolumn{2}{c}{Base symbol} & \multicolumn{2}{c}{equivalent symbols}\\
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\LaTeX & Rendered & \LaTeX & Rendered \\\midrule
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\verb+\sum+ & $\sum$ & \verb+$\Sigma$+ & $\Sigma$\\
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\verb+\prod+ & $\prod$ & \verb+$\Pi$+ & $\Pi$\\
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~ & ~ & \verb+$\sqcap$+ & $\sqcap$\\
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\verb+\coprod+ & $\coprod$ & \verb+$\amalg$+ & $\amalg$\\
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~ & ~ & \verb+$\sqcup$+ & $\sqcup$\\
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\verb+\perp+ & $\perp$ & \verb+$\bot$+ & $\bot$\\
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\verb+\models+ & $\models$ & \verb+$\vDash$+ & $\vDash$\\
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\verb+|+ & | & \verb+\mid+ & $\mid$ \\
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\verb+\Delta+ & $\Delta$ & \verb+$\triangle$+ & $\triangle$\\
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~ & ~ & \verb+$\vartriangle$+ & $\vartriangle$\\
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\bottomrule
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\end{tabular}
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\end{table}
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\end{frame}
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\begin{frame}[fragile]{Merged symbols (MER error)}
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\begin{table}[ht]
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\centering
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\begin{tabular}{lc|lc}
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\toprule
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\multicolumn{2}{c}{Base symbol} & \multicolumn{2}{c}{equivalent symbols}\\
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\LaTeX & Rendered & \LaTeX & Rendered \\\midrule
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\verb+\|+ & $\|$ & \verb+$\parallel$+ & $\parallel$\\
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\verb+\ohm+ & $\Omega$ & \verb+$\Omega$+ & $\Omega$\\
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\verb+\setminus+ & $\setminus$ & \verb+$\backslash$+ & $\backslash$\\
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\verb+\checked+ & {\mbox {\wasyfamily \char 8}} & \verb+$\checkmark$+ & $\checkmark$\\
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\verb+\&+ & $\&$ & \verb+$\with$+ & $\&$\\
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\verb+\#+ & $\#$ & \verb+$\sharp$+ & $\sharp$\\
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\verb+\S+ & $\S$ & \verb+$\mathsection$+ & $\mathsection$\\
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\verb+\nabla+ & $\nabla$ & \verb+\triangledown+ & $\triangledown$\\
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\verb+\lhd+ & $\lhd$ & \verb+$\triangleleft$+ & $\triangleleft$\\
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~ & ~ & \verb+$\vartriangleleft$+ & $\vartriangleleft$\\
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\verb+\oiint+ & $\oiint$ & \verb+$\varoiint$+ & $\varoiint$\\
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\bottomrule
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\end{tabular}
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\end{table}
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\end{frame}
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\begin{frame}[fragile]{Merged symbols (MER error)}
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\begin{table}[ht]
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\centering
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\begin{tabular}{lc|lc}
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\toprule
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\multicolumn{2}{c}{Base symbol} & \multicolumn{2}{c}{equivalent symbols}\\
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\LaTeX & Rendered & \LaTeX & Rendered \\\midrule
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\verb+\mathbb{R}+ & $\mathbb{R}$ & \verb+$\mathds{R}$+ & $\mathds{R}$\\
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\verb+\mathbb{Q}+ & $\mathbb{Q}$ & \verb+\mathds{Q}+ & $\mathds{Q}$\\
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\verb+\mathbb{Z}+ & $\mathbb{Z}$ & \verb+\mathds{Z}+ & $\mathds{Z}$\\
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\verb+\mathcal{A}+ & $\mathcal{A}$ & \verb+\mathscr{A}+ & $\mathscr{A}$\\
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\verb+\mathcal{D}+ & $\mathcal{D}$ & \verb+\mathscr{D}+ & $\mathscr{D}$\\
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\verb+\mathcal{N}+ & $\mathcal{N}$ & \verb+\mathscr{N}+ & $\mathscr{N}$\\
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\verb+\mathcal{R}+ & $\mathcal{R}$ & \verb+\mathscr{R}+ & $\mathscr{R}$\\
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\verb+\propto+ & $\propto$ & \verb+$\varpropto$+ & $\varpropto$\\
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\bottomrule
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\end{tabular}
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\end{table}
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\end{frame}
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\subsection{Evaluation}
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\begin{frame}{Preprocessing: Connect strokes}
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\begin{table}[h]
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\centering
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\begin{tabular}{lrrrrrr}
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\toprule
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\multirow{2}{*}{System} & \multicolumn{6}{c}{Classification error}\\
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\cmidrule(l){2-7}
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& TOP1 & change & TOP3 & change & MER & change \\\midrule
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$B_{1,\theta = \SI{5}{\pixel}}$ & $\SI{23.27}{\percent}$ & $\SI{-0.07}{\percent}$ & $\SI{6.50}{\percent}$ & $\SI{-0.30}{\percent}$ & $\SI{6.37}{\percent}$ & $\SI{-0.27}{\percent}$ \\
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$B_{2,\theta = \SI{5}{\pixel}}$ & $\SI{21.20}{\percent}$ & $\SI{-0.31}{\percent}$ & $\SI{5.59}{\percent}$ & $\SI{-0.16}{\percent}$ & $\SI{5.50}{\percent}$ & $\SI{-0.17}{\percent}$ \\
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$B_{3,\theta = \SI{5}{\pixel}}$ & $\SI{21.80}{\percent}$ & $\SI{-0.13}{\percent}$ & $\SI{5.54}{\percent}$ & $\SI{-0.20}{\percent}$ & $\SI{5.47}{\percent}$ & $\SI{-0.17}{\percent}$ \\\midrule
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$B_{1,\theta = \SI{10}{\pixel}}$& $\SI{23.17}{\percent}$ & $\SI{-0.17}{\percent}$ & $\SI{6.61}{\percent}$ & $\SI{-0.19}{\percent}$ & $\SI{6.47}{\percent}$ & $\SI{-0.17}{\percent}$ \\
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$B_{2,\theta = \SI{10}{\pixel}}$& \underline{$\SI{20.97}{\percent}$} & $\SI{-0.54}{\percent}$ & $\SI{5.43}{\percent}$ & $\SI{-0.32}{\percent}$ & $\SI{5.34}{\percent}$ & $\SI{-0.33}{\percent}$ \\
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$B_{3,\theta = \SI{10}{\pixel}}$& $\SI{21.34}{\percent}$ & $\SI{-0.59}{\percent}$ & \underline{$\SI{5.42}{\percent}$} & $\SI{-0.32}{\percent}$ & \underline{$\SI{5.33}{\percent}$} & $\SI{-0.31}{\percent}$ \\\midrule
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$B_{1,\theta = \SI{20}{\pixel}}$& $\SI{22.81}{\percent}$ & $\SI{-0.53}{\percent}$ & $\SI{6.28}{\percent}$ & $\SI{-0.52}{\percent}$ & $\SI{6.19}{\percent}$ & $\SI{-0.45}{\percent}$ \\
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$B_{2,\theta = \SI{20}{\pixel}}$& $\SI{21.61}{\percent}$ & $\SI{+0.10}{\percent}$ & $\SI{5.79}{\percent}$ & $\SI{+0.04}{\percent}$ & $\SI{5.69}{\percent}$ & $\SI{+0.02}{\percent}$ \\
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$B_{3,\theta = \SI{20}{\pixel}}$& $\SI{21.71}{\percent}$ & $\SI{-0.22}{\percent}$ & $\SI{5.55}{\percent}$ & $\SI{-0.19}{\percent}$ & $\SI{5.45}{\percent}$ & $\SI{-0.19}{\percent}$ \\
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\bottomrule
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\end{tabular}
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\caption{Models $B_1$--$B_4$ with additionally applied stroke
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connect algorithm.}
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\label{table:stroke-connect-evaluation}
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\end{table}
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\end{frame}
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\begin{frame}{Learning: Supervised layer-wise pretraining}
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\begin{table}[tb]
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\centering
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\begin{tabular}{lrrrrrr}
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\toprule
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\multirow{2}{*}{System}& \multicolumn{6}{c}{Classification error}\\
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\cmidrule(l){2-7}
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& TOP1 & change & TOP3 & change & MER & change \\\midrule
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$B_1$ & $\SI{23.34}{\percent}$ & & $\SI{6.80}{\percent}$ & & $\SI{6.64}{\percent}$ & \\%chktex 8
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$B_{2,p}$ & $\SI{19.89}{\percent}$ & $\SI{-1.62}{\percent}$ & $\SI{4.76}{\percent}$ & $\SI{-0.99}{\percent}$ & $\SI{4.68}{\percent}$ & $\SI{-0.99}{\percent}$\\
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$B_{3,p}$ & \underline{$\SI{19.43}{\percent}$} & $\SI{-2.50}{\percent}$ & \underline{$\SI{4.64}{\percent}$} & $\SI{-1.10}{\percent}$ & \underline{$\SI{4.54}{\percent}$} & $\SI{-1.10}{\percent}$\\
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% $B_{4,p}$ (pretrained) & $\SI{19.63}{\percent}$ & $\SI{-4.25}{\percent}$ & $\SI{4.66}{\percent}$ & $\SI{-1.46}{\percent}$ & $\SI{4.55}{\percent}$ & $\SI{-1.49}{\percent}$\\
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\bottomrule
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\end{tabular}
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\caption{Supervised layer-wise pretraining, 1000 epochs per layer}
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\label{table:pretraining-copy-before}
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\end{table}
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\end{frame}
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\definecolor{light-gray}{gray}{0.70}
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\subsection{Optimized classifier}
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\begin{frame}{Optimized classifier}
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\textbf{Preprocessing:} Connect strokes{\color{light-gray}, scale, shift and linear interpolation}\\
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\textbf{Features:} {\color{light-gray}Coordinates of 80 points (4 strokes with 20 points each),} re-curvature per stroke, ink, stroke count, aspect ratio\\
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\textbf{Learning:} {\color{light-gray}MLP, 1000 epochs, LR $\eta=0.1$, Momentum $\alpha=0.1$,} supervised layer-wise pretraining
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\begin{table}[htb]
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\centering
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\begin{tabular}{lrrrrrr}
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\toprule
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\multirow{2}{*}{System} & \multicolumn{6}{c}{Classification error}\\
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\cmidrule(l){2-7}
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& TOP1 & change & TOP3 & change & MER & change \\\midrule
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$B_{1,c}$ & $\SI{20.96}{\percent}$ & $\SI{-2.38}{\percent}$ & $\SI{5.24}{\percent}$ & $\SI{-1.56}{\percent}$ & $\SI{5.13}{\percent}$ & $\SI{-1.51}{\percent}$ \\
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$B_{2,c}$ & $\SI{18.26}{\percent}$ & $\SI{-3.25}{\percent}$ & $\SI{4.07}{\percent}$ & $\SI{-1.68}{\percent}$ & \underline{$\SI{3.98}{\percent}$} & $\SI{-1.69}{\percent}$ \\
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$B_{3,c}$ & \underline{$\SI{18.19}{\percent}$} & $\SI{-3.74}{\percent}$ & \underline{$\SI{4.06}{\percent}$} & $\SI{-1.68}{\percent}$ & $\SI{3.99}{\percent}$ & $\SI{-1.65}{\percent}$ \\
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% $B_{4,c}$ & $\SI{18.57}{\percent}$ & $\SI{-5.31}{\percent}$ & $\SI{4.25}{\percent}$ & $\SI{-1.87}{\percent}$ & $\SI{4.18}{\percent}$ & $\SI{-1.86}{\percent}$ \\
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\bottomrule
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\end{tabular}
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\caption{Error rates of the complex recognizer systems.}
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\label{table:complex-recognizer-systems-evaluation}
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\end{table}
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\end{frame} |