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302 lines
11 KiB
TeX
302 lines
11 KiB
TeX
\documentclass[a4paper, 12pt, draft=true]{article}
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\usepackage{pgfplots}
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\usepackage{filecontents}
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\usepackage{subcaption}
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\usepackage{adjustbox}
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\usepackage{xcolor}
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\usepackage{tabu}
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\usepackage{showframe}
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\usepackage{graphicx}
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\usepackage{titlecaps}
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\usetikzlibrary{calc, 3d}
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\usepgfplotslibrary{colorbrewer}
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\newcommand\Tstrut{\rule{0pt}{2.6ex}} % = `top' strut
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\newcommand\Bstrut{\rule[-0.9ex]{0pt}{0pt}} % = `bottom' strut
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\begin{document}
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\pgfplotsset{
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compat=1.11,
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legend image code/.code={
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\draw[mark repeat=2,mark phase=2]
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plot coordinates {
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(0cm,0cm)
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(0.3cm,0cm) %% default is (0.3cm,0cm)
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(0.6cm,0cm) %% default is (0.6cm,0cm)
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};%
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}
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}
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\begin{figure}
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\begin{subfigure}[h]{\textwidth}
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\begin{tikzpicture}
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\begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
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/pgf/number format/precision=3},tick style = {draw = none}, width = \textwidth,
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height = 0.35\textwidth, legend style={at={(0.9825,0.0175)},anchor=south east},
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ylabel = {Test Accuracy}, cycle
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list/Dark2, every axis plot/.append style={line width
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=1.25pt}]
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% \addplot [dashed] table
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% [x=epoch, y=accuracy, col sep=comma, mark = none]
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% {Data/adam_datagen_full.log};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_1.mean};
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% \addplot [dashed] table
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% [x=epoch, y=accuracy, col sep=comma, mark = none]
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% {Data/adam_datagen_dropout_02_full.log};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_datagen_1.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_datagen_dropout_02_1.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_dropout_02_1.mean};
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\addlegendentry{\footnotesize{G.}}
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\addlegendentry{\footnotesize{G. + D. 0.2}}
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\addlegendentry{\footnotesize{G. + D. 0.4}}
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\addlegendentry{\footnotesize{D. 0.2}}
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\addlegendentry{\footnotesize{D. 0.4}}
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\addlegendentry{\footnotesize{Default}}
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\end{axis}
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\end{tikzpicture}
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\caption{1 sample per class}
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\vspace{0.25cm}
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\end{subfigure}
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\begin{subfigure}[h]{\textwidth}
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\begin{tikzpicture}
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\begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
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/pgf/number format/precision=3},tick style = {draw = none}, width = \textwidth,
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height = 0.35\textwidth, legend style={at={(0.9825,0.0175)},anchor=south east},
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ylabel = {Test Accuracy}, cycle
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list/Dark2, every axis plot/.append style={line width
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=1.25pt}]
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_dropout_00_10.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_dropout_02_10.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_datagen_dropout_00_10.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_datagen_dropout_02_10.mean};
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\addlegendentry{\footnotesize{G.}}
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\addlegendentry{\footnotesize{G. + D. 0.2}}
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\addlegendentry{\footnotesize{G. + D. 0.4}}
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\addlegendentry{\footnotesize{D. 0.2}}
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\addlegendentry{\footnotesize{D. 0.4}}
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\addlegendentry{\footnotesize{Default}}
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\end{axis}
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\end{tikzpicture}
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\caption{10 samples per class}
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\end{subfigure}
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\begin{subfigure}[h]{\textwidth}
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\begin{tikzpicture}
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\begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
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/pgf/number format/precision=3},tick style = {draw = none}, width = 0.9875\textwidth,
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height = 0.35\textwidth, legend style={at={(0.9825,0.0175)},anchor=south east},
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xlabel = {epoch}, ylabel = {Test Accuracy}, cycle
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list/Dark2, every axis plot/.append style={line width
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=1.25pt}, ymin = {0.92}]
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_dropout_00_100.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_dropout_02_100.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_datagen_dropout_00_100.mean};
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\addplot table
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[x=epoch, y=val_accuracy, col sep=comma, mark = none]
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{Data/adam_datagen_dropout_02_100.mean};
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\addlegendentry{\footnotesize{G.}}
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\addlegendentry{\footnotesize{G. + D. 0.2}}
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\addlegendentry{\footnotesize{G. + D. 0.4}}
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\addlegendentry{\footnotesize{D. 0.2}}
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\addlegendentry{\footnotesize{D. 0.4}}
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\addlegendentry{\footnotesize{Default}}
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\end{axis}
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\end{tikzpicture}
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\caption{100 samples per class}
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\vspace{.25cm}
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\end{subfigure}
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\caption{Accuracy for the net given in ... with Dropout (D.),
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data generation (G.), a combination, or neither (Default) implemented and trained
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with \textsc{Adam}. For each epoch the 60.000 training samples
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were used, or for data generation 10.000 steps with each using
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batches of 60 generated data points. For each configuration the
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model was trained 5 times and the average accuracies at each epoch
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are given in (a). Mean, maximum and minimum values of accuracy on
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the test and training set are given in (b).}
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\end{figure}
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\begin{table}
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\centering
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\begin{tabu} to \textwidth {@{}l*4{X[c]}@{}}
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\Tstrut \Bstrut & \textsc{Adam} & D. 0.2 & Gen & Gen.+D. 0.2 \\
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\hline
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&
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\multicolumn{4}{c}{\titlecap{test accuracy for 1 sample}}\Bstrut \\
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\cline{2-5}
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max \Tstrut & 0.5633 & 0.5312 & 0.6704 & 0.6604 \\
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min & 0.3230 & 0.4224 & 0.4878 & 0.5175 \\
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mean & 0.4570 & 0.4714 & 0.5862 & 0.6014 \\
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var & 0.0040 & 0.0012 & 0.0036 & 0.0023 \\
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\hline
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&
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\multicolumn{4}{c}{\titlecap{test accuracy for 10 samples}}\Bstrut \\
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\cline{2-5}
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max \Tstrut & 0.8585 & 0.9423 & 0.9310 & 0.9441 \\
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min & 0.8148 & 0.9081 & 0.9018 & 0.9061 \\
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mean & 0.8377 & 0.9270 & 0.9185 & 0.9232 \\
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var & 2.7e-4 & 1.3e-4 & 6e-05 & 1.5e-4 \\
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\hline
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&
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\multicolumn{4}{c}{\titlecap{test accuracy for 100 samples}}\Bstrut \\
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\cline{2-5}
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max & 0.9637 & 0.9796 & 0.9810 & 0.9805 \\
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min & 0.9506 & 0.9719 & 0.9702 & 0.9727 \\
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mean & 0.9582 & 0.9770 & 0.9769 & 0.9783 \\
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var & 2e-05 & 1e-05 & 1e-05 & 0 \\
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\hline
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\end{tabu}
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\caption{Values of the test accuracy of the model trained 10 times
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of random training sets containing 1, 10 and 100 data points per
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class.}
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\end{table}
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\begin{center}
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\begin{figure}[h]
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\centering
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist0.pdf}
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\caption{original\\image}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist_gen_zoom.pdf}
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\caption{random\\zoom}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist_gen_shear.pdf}
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\caption{random\\shear}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist_gen_rotation.pdf}
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\caption{random\\rotation}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist_gen_shift.pdf}
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\caption{random\\positional shift}
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\end{subfigure}\\
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist5.pdf}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist6.pdf}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist7.pdf}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist8.pdf}
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\end{subfigure}
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\begin{subfigure}{0.19\textwidth}
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\includegraphics[width=\textwidth]{Data/mnist9.pdf}
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\end{subfigure}
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\caption{The MNIST data set contains 70.000 images of preprocessed handwritten
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digits. Of these images 60.000 are used as training images, while
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the rest are used to validate the models trained.}
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\end{figure}
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\end{center}
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\begin{figure}
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\begin{adjustbox}{width=\textwidth}
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\begin{tikzpicture}
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\begin{scope}[x = (0:1cm), y=(90:1cm), z=(15:-0.5cm)]
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\node[canvas is xy plane at z=0, transform shape] at (0,0)
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{\includegraphics[width=5cm]{Data/klammern_r.jpg}};
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\node[canvas is xy plane at z=2, transform shape] at (0,-0.2)
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{\includegraphics[width=5cm]{Data/klammern_g.jpg}};
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\node[canvas is xy plane at z=4, transform shape] at (0,-0.4)
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{\includegraphics[width=5cm]{Data/klammern_b.jpg}};
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\node[canvas is xy plane at z=4, transform shape] at (-8,-0.2)
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{\includegraphics[width=5.3cm]{Data/klammern_rgb.jpg}};
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\end{scope}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{On the right the red, green and blue chanels of the picture
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are displayed. In order to better visualize the color channes the
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black and white picture of each channel has been colored in the
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respective color. Combining the layers results in the image on the
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left}
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\end{figure}
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\begin{figure}
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\centering
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\begin{subfigure}{.45\linewidth}
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\centering
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\begin{tikzpicture}
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\begin{axis}[enlargelimits=false, ymin=0, ymax = 1, width=\textwidth]
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\addplot [domain=-5:5, samples=101,unbounded coords=jump]{1/(1+exp(-x)};
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\begin{subfigure}{.45\linewidth}
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\centering
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\begin{tikzpicture}
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\begin{axis}[enlargelimits=false, width=\textwidth]
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\addplot[domain=-5:5, samples=100]{tanh(x)};
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\begin{subfigure}{.45\linewidth}
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\centering
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\begin{tikzpicture}
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\begin{axis}[enlargelimits=false, width=\textwidth,
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ytick={0,2,4},yticklabels={\hphantom{4.}0,2,4}, ymin=-1]
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\addplot[domain=-5:5, samples=100]{max(0,x)};
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\begin{subfigure}{.45\linewidth}
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\centering
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\begin{tikzpicture}
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\begin{axis}[enlargelimits=false, width=\textwidth, ymin=-1,
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ytick={0,2,4},yticklabels={$\hphantom{-5.}0$,2,4}]
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\addplot[domain=-5:5, samples=100]{max(0,x)+ 0.1*min(0,x)};
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\end{figure}
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\begin{tikzpicture}
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\begin{axis}[enlargelimits=false]
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\addplot [domain=-5:5, samples=101,unbounded coords=jump]{1/(1+exp(-x)};
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\addplot[domain=-5:5, samples=100]{tanh(x)};
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\addplot[domain=-5:5, samples=100]{max(0,x)};
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\end{axis}
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\end{tikzpicture}
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\begin{tikzpicture}
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\begin{axis}[enlargelimits=false]
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\addplot[domain=-2*pi:2*pi, samples=100]{cos(deg(x))};
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\end{axis}
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\end{tikzpicture}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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