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145 lines
6.6 KiB
TeX
145 lines
6.6 KiB
TeX
\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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(0.075cm,0cm) %% default is (0.3cm,0cm)
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(0.15cm,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}[b]{0.48\textwidth}
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\begin{subfigure}[b]{\textwidth}
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\begin{adjustbox}{width=\textwidth, height=0.25\textheight}
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\begin{tikzpicture}
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\begin{axis}[
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ytick = {-1, 0, 1, 2},
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yticklabels = {$-1$, $\phantom{-0.}0$, $1$, $2$},
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restrict x to domain=-4:4, enlarge x limits = {0.1}]
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\addplot table [x=x, y=y, col sep=comma, only marks,
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forget plot] {Figures/Data/sin_6.csv};
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\addplot [black, line width=2pt] table [x=x, y=y, col
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sep=comma, mark=none] {Figures/Data/matlab_0.csv};
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\addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_0.0,
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y=y_n_5000_tl_0.0, col sep=comma, mark=none] {Figures/Data/scala_out_sin.csv};
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\addlegendentry{$f_1^{*, 0.1}$};
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\addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
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\end{axis}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{$\lambda = 0.1$}
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\end{subfigure}\\
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\begin{subfigure}[b]{\textwidth}
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\begin{adjustbox}{width=\textwidth, height=0.25\textheight}
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\begin{tikzpicture}
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\begin{axis}[restrict x to domain=-4:4, enlarge x limits = {0.1}]
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\addplot table [x=x, y=y, col sep=comma, only marks,
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forget plot] {Figures/Data/sin_6.csv};
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\addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Figures/Data/matlab_1.csv};
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\addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_1.0,
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y=y_n_5000_tl_1.0, col sep=comma, mark=none] {Figures/Data/scala_out_sin.csv};
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\addlegendentry{$f_1^{*, 1.0}$};
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\addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
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\end{axis}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{$\lambda = 1.0$}
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\end{subfigure}\\
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\begin{subfigure}[b]{\textwidth}
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\begin{adjustbox}{width=\textwidth, height=0.25\textheight}
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\begin{tikzpicture}
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\begin{axis}[restrict x to domain=-4:4, enlarge x limits = {0.1}]
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\addplot table [x=x, y=y, col sep=comma, only marks,
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forget plot] {Figures/Data/sin_6.csv};
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\addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Figures/Data/matlab_3.csv};
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\addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_3.0,
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y=y_n_5000_tl_3.0, col sep=comma, mark=none] {Figures/Data/scala_out_sin.csv};
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\addlegendentry{$f_1^{*, 3.0}$};
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\addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
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\end{axis}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{$\lambda = 3.0$}
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\end{subfigure}
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\end{subfigure}
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\begin{subfigure}[b]{0.48\textwidth}
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\begin{subfigure}[b]{\textwidth}
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\begin{adjustbox}{width=\textwidth, height=0.245\textheight}
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\begin{tikzpicture}
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\begin{axis}[
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ytick = {-2,-1, 0, 1, 2},
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yticklabels = {$-2$,$-1$, $\phantom{-0.}0$, $1$, $2$},
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restrict x to domain=-4:4, enlarge x limits = {0.1}]
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\addplot table [x=x, y=y, col sep=comma, only marks,
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forget plot] {Figures/Data/data_sin_d_t.csv};
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\addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Figures/Data/matlab_sin_d_01.csv};
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\addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_0.1,
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y=y_n_5000_tl_0.1, col sep=comma, mark=none] {Figures/Data/scala_out_d_1_t.csv};
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\addlegendentry{$f_1^{*, 0.1}$};
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\addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
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\end{axis}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{$\lambda = 0.1$}
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\end{subfigure}\\
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\begin{subfigure}[b]{\textwidth}
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\begin{adjustbox}{width=\textwidth, height=0.25\textheight}
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\begin{tikzpicture}
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\begin{axis}[restrict x to domain=-4:4, enlarge x limits = {0.1}]
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\addplot table [x=x, y=y, col sep=comma, only marks,
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forget plot] {Figures/Data/data_sin_d_t.csv};
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\addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Figures/Data/matlab_sin_d_1.csv};
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\addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_1.0,
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y=y_n_5000_tl_1.0, col sep=comma, mark=none] {Figures/Data/scala_out_d_1_t.csv};
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\addlegendentry{$f_1^{*, 1.0}$};
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\addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda},*}$};
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\end{axis}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{$\lambda = 1.0$}
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\end{subfigure}\\
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\begin{subfigure}[b]{\textwidth}
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\begin{adjustbox}{width=\textwidth, height=0.25\textheight}
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\begin{tikzpicture}
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\begin{axis}[restrict x to domain=-4:4, enlarge x limits = {0.1}]
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\addplot table [x=x, y=y, col sep=comma, only marks,
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forget plot] {Figures/Data/data_sin_d_t.csv};
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\addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Figures/Data/matlab_sin_d_3.csv};
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\addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_3.0,
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y=y_n_5000_tl_3.0, col sep=comma, mark=none] {Figures/Data/scala_out_d_1_t.csv};
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\addlegendentry{$f_1^{*, 3.0}$};
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\addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
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\end{axis}
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\end{tikzpicture}
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\end{adjustbox}
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\caption{$\lambda = 3.0$}
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\end{subfigure}
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\end{subfigure}
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\caption[Comparison of Shallow Neural Networks and Regression
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Splines] {% In these Figures the behaviour stated in ... is
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% visualized
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% in two exaples. For $(a), (b), (c)$ six values of sinus equidistantly
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% spaced on $[-\pi, \pi]$ have been used as training data. For
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% $(d),(e),(f)$ 15 equidistand values have been used, where
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% $y_i^{train} = \sin(x_i^{train}) + \varepsilon_i$ and
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% $\varepsilon_i \sim \mathcal{N}(0, 0.3)$. For
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% $\mathcal{RN}_w^{\tilde{\lambda, *}}$ the random weights are
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% distributed as follows
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% \begin{align*}
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% \xi_k &\sim
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% \end{align*}
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Ridge Penalized Neural Network compared to Regression Spline,
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with them being trained on $\text{data}_A$ in a), b), c) and on
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$\text{data}_B$ in d), e), f).
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The Parameters of each are given above. The implementation of the
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network in Scala is given in Listing~\ref{lst:rsnn}
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}
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\label{fig:rn_vs_rs}
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\end{figure}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "main"
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%%% End:
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