Code in Appendix

.gitignore

@@ -8,6 +8,7 @@
 *.bbl
 *.tdo
 *.blg
+*.lof
 TeX/auto/*
 main-blx.bib
 
@@ -31,3 +32,5 @@ main-blx.bib
 # no plot data
 *.csv
 *.mean
+
+*Plots_*

TF/Main.scala

@@ -0,0 +1,76 @@
+import breeze.stats.distributions.Uniform
+import breeze.stats.distributions.Gaussian
+import scala.language.postfixOps
+
+object Activation {
+  def apply(x: Double): Double = math.max(0, x)
+
+  def d(x: Double): Double = if (x > 0) 1 else 0
+}
+
+class RSNN(val n: Int, val gamma: Double = 0.001) {
+  val g = Uniform(-10, 10)
+  val g_1 = Uniform(-5, 5)//scala.math.exp(1))
+  val g_3 = Gaussian(0, 5)
+
+  val xis = g.sample(n)
+  val vs = g_3.sample(n)
+  val bs = xis zip vs map {case(xi, v) => xi * v}
+  //val vs = g_1.sample(n)
+  //val bs = g.sample(n)
+
+  def computeL1(x: Double) = (bs zip vs) map { case (b, v) => Activation(b + v * x) }
+
+  def computeL2(l1: Seq[Double], ws: Seq[Double]): Double =
+    (l1 zip ws) map { case (l, w) => w * l } sum
+
+  def output(ws: Seq[Double])(x: Double): Double = computeL2(computeL1(x), ws)
+
+  def learn(data: Seq[(Double, Double)], ws: Seq[Double], lambda: Double, gamma: Double): Seq[Double] = {
+    // data: N \times 2
+    // ws: n \times 1
+
+    lazy val deltas = data.map {
+      case (x, y) =>
+        val l1 = computeL1(x) // n
+        val out = computeL2(l1, ws) // 1
+        (l1 zip ws) map {case (l1, w) => (l1 * 2 * (out - y) + lambda * 2 * w)  * gamma * -1} // n
+    }
+    // deltas: N × n
+
+    deltas.foldRight(ws)(
+      (delta, ws) => // delta: n
+        ws zip (delta) map { case (w, d) => w + d } // n
+    )// map (w => w - lambda * gamma * 2 * w)
+
+  }
+
+  def train(data: Seq[(Double, Double)], iter: Int, lambda: Double, gamma: Double = gamma): (Seq[Double], Double => Double)= {
+    val ws = (1 to iter).foldRight((1 to n).map(_ => 0.0) :Seq[Double])((i, w) => {
+      println(s"Training iteration $i")
+      println(w.sum/w.length)
+      learn(data, w, lambda, gamma / 10)
+    })
+    (ws, output(ws))
+  }
+}
+
+object Main {
+
+  def main(args: Array[String]): Unit = {
+    val nn = new RSNN(10, gamma = 0.0001)
+    val data = (1 to 100) map (_ * 0.01) map (t => (t, math.sin(t)))
+    val (ws, evaluate) = nn.train(data, iter = 1000, lambda = 0.8)
+
+    val results = data.map(_._1).map(evaluate(_))
+    data zip results foreach {
+      println(_)
+    }
+  }
+
+}
+
+object EqSeq {
+  def apply(left: Double, right: Double, steps: Int): Seq[Double] =
+    (0 to steps) map (_ * (right - left) / steps + left)
+}

TF/cnn.py

@@ -149,8 +149,8 @@ if __name__ == '__main__':
 
     ############################
     # in between layers
-    start_ratio_list = [[0.4, 0.5], [0.4, 0.8], [0.4,0.8], [0.4, 0.5], [0.4, 0.8],[0.4,0.8]]
-    end_ratio_list = [[0.4, 0.5], [0.4, 0.8], [0.4,0.8], [0.4, 0.5], [0.4, 0.8],[0.4,0.8]]
+    start_ratio_list = [[0.4, 0.5], [0.4, 0.8], [0.4,0.5], [0.4, 0.8], [0.4, 0.5],[0.4,0.8]]
+    end_ratio_list = [[0.4, 0.5], [0.4, 0.8], [0.4,0.5], [0.4, 0.8], [0.4, 0.5],[0.4,0.8]]
     patch_size_list = [(3, 3), (3, 3), (2, 2), (3,3), (3, 3), (2, 2)]
     ind_bgn_list = range(len(patch_size_list))
     text_list = ['Conv.', 'Conv.', 'Max-pool.', 'Conv.', 'Conv.', 'Max-pool.']
@@ -211,7 +211,7 @@ if __name__ == '__main__':
    # plt.show()
     fig.set_size_inches(8, 2.5)
 
-    fig_dir = '/home/tobi/Masterarbeit/TeX/Plots/Data/'
+    fig_dir = '/home/tobi/Masterarbeit/TeX/Figures/Data/'
     fig_ext = '.pdf'
-    fig.savefig(os.path.join(fig_dir, 'cnn_fashion_fig' + fig_ext),
+    fig.savefig(os.path.join(fig_dir, 'cnn_fashion_fig1' + fig_ext),
                 bbox_inches='tight', pad_inches=0)

TF/scratch.scala

@@ -0,0 +1,52 @@
+import breeze.plot._
+import breeze.plot.DomainFunction._
+import breeze.linalg._
+import breeze.stats.distributions.Gaussian
+
+val nn = new RSNN(5000, 0.0000001)
+
+val g = Gaussian(0, 0.3)
+
+//val data = EqSeq(-math.Pi, math.Pi, 15) map (t => (t, math.sin(t)+ g.sample(1).last))
+val (ws, evaluate) = nn.train(data, iter = 100000, lambda = (1.0/20) / 5 * (nn.n * 8) * 1)
+
+val f = Figure()
+val p = f.subplot(0)
+val x = linspace(-5, 5)
+val y =  x.map(evaluate)
+//print_data(nn, x, y, 3)
+p += plot(x, y)
+p += scatter(data.map(_._1), data.map(_._2), x => 0.1)
+f.saveas("lines.png")
+
+
+val x_i = data map {case (x,y) => x}
+val y_i = data map {case (x,y) => y}
+
+def print_data(nn: RSNN, x: DenseVector[Double], y: DenseVector[Double], tlambda: Double): Unit = {
+  val n = nn.n
+  reflect.io.File("C:/Users/tobia/Documents/Studium/Masterarbeit/Outputs/scala_out_d_1.csv").appendAll(s"x_n_$n"+s"_tl_$tlambda;" + x.toArray.mkString(";") + "\n")
+  reflect.io.File("C:/Users/tobia/Documents/Studium/Masterarbeit/Outputs/scala_out_d_1.csv").appendAll(s"y_n_$n"+s"_tl_$tlambda;" + y.toArray.mkString(";") + "\n")
+}
+reflect.io.File("C:/Users/tobia/Documents/Studium/Masterarbeit/Outputs/data_sin_d.csv").appendAll(x_i.mkString(";") + "\n")
+reflect.io.File("C:/Users/tobia/Documents/Studium/Masterarbeit/Outputs/data_sin_d.csv").appendAll(y_i.mkString(";") + "\n")
+
+
+reflect.io.File("C:/Users/tobia/Documents/Studium/Masterarbeit/Outputs/vals1.csv").appendAll(x.toArray.mkString(";") + "\n")
+reflect.io.File("C:/Users/tobia/Documents/Studium/Masterarbeit/Outputs/vals1.csv").appendAll(y.toArray.mkString(";") + "\n")
+
+for(j <- List(0.1, 1, 3)) {
+  for (i <- 3 until 4) {
+    val nn = new RSNN((5 * math.pow(10, i)).asInstanceOf[Int], 0.0000001)
+    val (ws, evaluate) = nn.train(data, iter = 100000, lambda = (1.0 / 20) / 5 * (nn.n * 8) * j)
+
+    val x = linspace(-5, 5)
+    val y = x.map(evaluate)
+    print_data(nn, x, y, j)
+  }
+}
+
+val x_i = Seq(-3.141592653589793,-2.722713633111154,-2.303834612632515,-1.8849555921538759,-1.4660765716752369,-1.0471975511965979,-0.6283185307179586,-0.2094395102393194,0.2094395102393194,0.6283185307179586,1.0471975511965974,1.4660765716752362,1.8849555921538759,2.3038346126325155,2.7227136331111543,3.1415926535897922)
+val y_i = Seq(0.0802212608585366,-0.3759376368887911,-1.3264180339054117,-0.8971334213504949,-0.7724344034354425,-0.9501497164520739,-0.6224628757084738,-0.35622668982623207,-0.18377660088356823,0.7836770998126841,0.5874762732054489,1.0696991264956026,1.1297065441952743,0.7587275382323738,-0.030547103790458163,0.044327111895927106)
+
+val data = x_i zip y_i

TeX/Appendix_code.tex

@@ -0,0 +1,189 @@
+  \section{Code...}
+  \begin{itemize}
+    \item Code for randomized shallow neural network
+    \item Code for keras
+  \end{itemize}
+
+  \clearpage
+  \begin{lstfloat}
+\begin{lstlisting}[language=iPython]
+import breeze.stats.distributions.Uniform
+import breeze.stats.distributions.Gaussian
+import scala.language.postfixOps
+
+object Activation {
+  def apply(x: Double): Double = math.max(0, x)
+
+  def d(x: Double): Double = if (x > 0) 1 else 0
+}
+
+class RSNN(val n: Int, val gamma: Double = 0.001) {
+    val g_unif = Uniform(-10, 10)
+    val g_gauss = Gaussian(0, 5)
+
+    val xis = g_unif.sample(n)
+    val vs = g_gauss.sample(n)
+    val bs = xis zip vs map {case(xi, v) => xi * v}
+
+    def computeL1(x: Double) = (bs zip vs) map {
+        case (b, v) => Activation(b + v * x) }
+  
+    def computeL2(l1: Seq[Double], ws: Seq[Double]): Double =
+        (l1 zip ws) map { case (l, w) => w * l } sum
+  
+    def output(ws: Seq[Double])(x: Double): Double =
+        computeL2(computeL1(x), ws)
+  
+    def learn(data: Seq[(Double, Double)], ws: Seq[Double],
+        lamb: Double, gamma: Double): Seq[Double] = {
+    
+        lazy val deltas = data.map {
+            case (x, y) =>
+                val l1 = computeL1(x)
+                val out = computeL2(l1, ws)
+                (l1 zip ws) map {case (l1, w) => (l1 * 2 * (out - y) +
+                    lam * 2 * w)  * gamma * -1}
+        }
+  
+        deltas.foldRight(ws)(
+            (delta, ws) => ws zip (delta) map { case (w, d) => w + d })  
+    }
+
+    def train(data: Seq[(Double, Double)], iter: Int, lam: Double,
+        gamma: Double = gamma): (Seq[Double], Double => Double)= {
+      
+        val ws = (1 to iter).foldRight((1 to n).map(
+            _ => 0.0) :Seq[Double])((i, w) => {
+            println(s"Training iteration $i")
+            println(w.sum/w.length)
+            learn(data, w, lam, gamma / 10)
+        })
+        (ws, output(ws))
+    }
+}
+\end{lstlisting}
+\caption{Scala code used to build and train the ridge penalized
+  randomized shallow neural network in .... The parameter \textit{lam}
+in the train function represents the $\lambda$ parameter in the error
+function. The parameters \textit{n} and \textit{gamma} set the number
+of hidden nodes and the stepsize for training.}
+\label{lst:rsnn}
+\end{lstfloat}
+\clearpage
+
+\begin{lstlisting}[language=iPython]
+import tensorflow as tf
+import numpy as np
+from tensorflow.keras.callbacks import CSVLogger
+from tensorflow.keras.preprocessing.image import ImageDataGenerator
+
+mnist = tf.keras.datasets.mnist
+
+(x_train, y_train), (x_test, y_test) = mnist.load_data()
+x_train = x_train.reshape(x_train.shape[0], 28, 28, 1)
+x_train = x_train / 255.0
+x_test = x_test.reshape(x_test.shape[0], 28, 28, 1)
+x_test = x_test / 255.0
+
+y_train = tf.keras.utils.to_categorical(y_train)
+y_test = tf.keras.utils.to_categorical(y_test)
+
+model = tf.keras.models.Sequential()
+model.add(tf.keras.layers.Conv2D(24,kernel_size=5,padding='same',
+    activation='relu',input_shape=(28,28,1)))
+model.add(tf.keras.layers.MaxPool2D())
+model.add(tf.keras.layers.Conv2D(64,kernel_size=5,padding='same',
+    activation='relu'))
+model.add(tf.keras.layers.MaxPool2D(padding='same'))
+model.add(tf.keras.layers.Flatten())
+model.add(tf.keras.layers.Dense(256, activation='relu'))
+model.add(tf.keras.layers.Dropout(0.2))
+model.add(tf.keras.layers.Dense(10, activation='softmax'))
+model.compile(optimizer='adam', loss="categorical_crossentropy",
+    metrics=["accuracy"])
+
+datagen = ImageDataGenerator(
+    rotation_range = 30,
+    zoom_range = 0.15,
+    width_shift_range=2,
+    height_shift_range=2,
+    shear_range = 1)
+
+csv_logger = CSVLogger(<Target File>)
+    
+history = model.fit(datagen.flow(x_train, y_train, batch_size=50),
+validation_data=(x_test, y_test),
+    epochs=125, callbacks=[csv_logger],
+    steps_per_epoch = x_train.shape[0]//50) 
+
+\end{lstlisting}
+\clearpage
+\begin{lstlisting}[language=iPython]
+import tensorflow as tf
+import numpy as np
+from tensorflow.keras.callbacks import CSVLogger
+from tensorflow.keras.preprocessing.image import ImageDataGenerator
+mnist = tf.keras.datasets.fashion_mnist
+
+(x_train, y_train), (x_test, y_test) = mnist.load_data()
+x_train = x_train.reshape(x_train.shape[0], 28, 28, 1)
+x_test = x_test.reshape(x_test.shape[0], 28, 28, 1)
+x_train, x_test = x_train / 255.0, x_test / 255.0
+
+y_train = tf.keras.utils.to_categorical(y_train)
+y_test = tf.keras.utils.to_categorical(y_test)
+
+model = tf.keras.Sequential()
+model.add(tf.keras.layers.Conv2D(filters = 32, kernel_size = (3, 3),
+    activation='relu', input_shape = (28, 28, 1), padding='same'))
+model.add(tf.keras.layers.Conv2D(filters = 32, kernel_size = (2, 2), activation='relu', padding = 'same'))
+model.add(tf.keras.layers.MaxPool2D(strides=(2,2)))
+model.add(tf.keras.layers.Conv2D(filters = 64, kernel_size = (3, 3), activation='relu', padding='same'))
+model.add(tf.keras.layers.Conv2D(filters = 64, kernel_size = (3, 3), activation='relu', padding='same'))
+model.add(tf.keras.layers.MaxPool2D(strides=(2,2)))
+model.add(tf.keras.layers.Flatten())
+model.add(tf.keras.layers.Dense(256, activation='relu'))
+model.add(tf.keras.layers.Dropout(0.2))
+model.add(tf.keras.layers.Dense(10, activation='softmax'))
+
+model.compile(optimizer=tf.keras.optimizers.Adam(lr = 1e-3), loss="categorical_crossentropy", metrics=["accuracy"])
+
+datagen = ImageDataGenerator(
+    rotation_range = 15,
+    zoom_range = 0.1,
+    width_shift_range=2,
+    height_shift_range=2,
+    shear_range = 0.5,
+    fill_mode = 'constant',
+    cval = 0)
+        
+    csv_logger = CSVLogger(<Target File>)
+    
+    history = model.fit(datagen.flow(x_train, y_train, batch_size=30),
+        steps_per_epoch=2000,
+        validation_data=(x_test, y_test),
+        epochs=125, callbacks=[csv_logger],
+        shuffle=True)
+
+\end{lstlisting}
+\clearpage
+\begin{lstlisting}[language=iPython]
+def get_random_sample(a, b, number_of_samples=10):
+    x = []
+    y = []
+    for category_number in range(0,10):
+    # get all samples of a category
+        train_data_category = a[b==category_number]
+        # pick a number of random samples from the category
+        train_data_category = train_data_category[np.random.randint(
+            train_data_category.shape[0], size=number_of_samples), :]
+        x.extend(train_data_category)
+        y.append([category_number]*number_of_samples)
+
+        return (np.asarray(x).reshape(-1, 28, 28, 1),
+            np.asarray(y).reshape(10*number_of_samples,1))
+\end{lstlisting}
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% End:

TeX/Figures/RN_vs_RS.tex

@@ -131,11 +131,12 @@ plot coordinates {
     Ridge Penalized Neural Network compared to Regression Spline,
     with them being trained on $\text{data}_A$ in a), b), c) and on
     $\text{data}_B$ in d), e), f).
-    The Parameters of each are given above.
+    The Parameters of each are given above. The implementation of the
+    network in Scala is given in Listing~\ref{lst:rsnn}
   }
   \label{fig:rn_vs_rs}
 \end{figure}
 %%% Local Variables:
 %%% mode: latex
-%%% TeX-master:
+%%% TeX-master: "main"
 %%% End:

TeX/Figures/mnist.tex

@@ -1,34 +1,34 @@
 \begin{figure}[h]
     \centering
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist0.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist0.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist1.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist1.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist2.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist2.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist3.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist3.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist4.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist4.pdf}
   \end{subfigure}\\
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist5.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist5.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist6.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist6.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist7.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist7.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist8.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist8.pdf}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist9.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist9.pdf}
   \end{subfigure}
   \caption[MNIST data set]{The MNIST data set contains 70.000 images of preprocessed handwritten
     digits. Of these images 60.000 are used as training images, while

TeX/Figures/pfg_test.tex

@@ -177,12 +177,12 @@ plot coordinates {
 \begin{center}
   \begin{figure}[h]
     \centering
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist0.pdf}
+  \begin{subfigure}{\textwidth}
+    \includegraphics[width=\textwidth]{Data/cnn_fashion_fig.pdf}
     \caption{original\\image}
   \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist_gen_zoom.pdf}
+  \begin{subfigure}{\textwidth}
+    \includegraphics[width=\textwidth]{Data/cnn_fashion_fig1.pdf}
     \caption{random\\zoom}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}

TeX/Figures/test.tex

@@ -11,9 +11,15 @@
 \definecolor{ipython_red}{RGB}{186, 33, 33}
 \definecolor{ipython_green}{RGB}{0, 128, 0}
 \definecolor{ipython_cyan}{RGB}{64, 128, 128}
-\definecolor{ipython_purple}{RGB}{170, 34, 255}
+\definecolor{ipython_purple}{RGB}{110, 64, 130}
 
 \usepackage{listings}
+\usepackage{float}
+
+\newfloat{lstfloat}{htbp}{lop}
+\floatname{lstfloat}{Listing}
+\def\lstfloatautorefname{Listing}
+
 \lstset{
     breaklines=true,
     %
@@ -38,10 +44,11 @@
 %% modified by me (should not have empty lines)
 %%
 \lstdefinelanguage{iPython}{
-    morekeywords={access,and,break,class,continue,def,del,elif,else,except,exec,finally,for,from,global,if,import,in,is,lambda,not,or,pass,print,raise,return,try,while},%
+  morekeywords={access,and,break,class,continue,def,del,elif,else,except,exec,finally,for,from,global,if,import,
+    in,is,lambda,not,or,pass,print,raise,return,try,while},%
     %
     % Built-ins
-    morekeywords=[2]{abs,all,any,basestring,bin,bool,bytearray,callable,chr,classmethod,cmp,compile,complex,delattr,dict,dir,divmod,enumerate,eval,execfile,file,filter,float,format,frozenset,getattr,globals,hasattr,hash,help,hex,id,input,int,isinstance,issubclass,iter,len,list,locals,long,map,max,memoryview,min,next,object,oct,open,ord,pow,property,range,raw_input,reduce,reload,repr,reversed,round,set,setattr,slice,sorted,staticmethod,str,sum,super,tuple,type,unichr,unicode,vars,xrange,zip,apply,buffer,coerce,intern},%
+    morekeywords=[2]{abs,all,any,basestring,bin,bool,bytearray,callable,chr,classmethod,cmp,compile,complex,delattr,dict,dir,divmod,enumerate,eval,execfile,file,filter,float,format,frozenset,getattr,globals,hasattr,hash,help,hex,id,input,int,isinstance,issubclass,iter,len,list,locals,long,map,max,memoryview,min,next,object,oct,open,ord,pow,property,range,raw_input,reduce,reload,repr,reversed,round,set,setattr,slice,sorted,staticmethod,str,sum,super,tuple,type,unichr,unicode,vars,xrange,zip,apply,buffer,coerce,intern,val},%
     %
     sensitive=true,%
     morecomment=[l]\#,%
@@ -91,7 +98,7 @@
      {?}{{{\color{ipython_purple}?}}}1,
     %
     identifierstyle=\color{black}\ttfamily,
-    commentstyle=\color{ipython_cyan}\ttfamily,
+    commentstyle=\color{ipython_red}\ttfamily,
     stringstyle=\color{ipython_red}\ttfamily,
     keepspaces=true,
     showspaces=false,
@@ -109,9 +116,80 @@
     %   extendedchars=true,
     basicstyle=\scriptsize,
     keywordstyle=\color{ipython_green}\ttfamily,
+    morekeywords = [3]{Int, Double},
+    morekeywords = [2]{foldRight, case},
+    keywordstyle = [3]{\color{ipython_purple}\ttfamily},
+    keywordstyle = [2]{\color{ipython_cyan}\ttfamily},
 }
 
+
 \begin{document}
+
+\begin{lstfloat}
+\begin{lstlisting}[language=iPython]
+import breeze.stats.distributions.Uniform
+import breeze.stats.distributions.Gaussian
+import scala.language.postfixOps
+
+object Activation {
+  def apply(x: Double): Double = math.max(0, x)
+
+  def d(x: Double): Double = if (x > 0) 1 else 0
+}
+
+class RSNN(val n: Int, val gamma: Double = 0.001) {
+    val g_unif = Uniform(-10, 10)
+    val g_gauss = Gaussian(0, 5)
+
+    val xis = g_unif.sample(n)
+    val vs = g_gauss.sample(n)
+    val bs = xis zip vs map {case(xi, v) => xi * v}
+
+    def computeL1(x: Double) = (bs zip vs) map {
+        case (b, v) => Activation(b + v * x) }
+  
+    def computeL2(l1: Seq[Double], ws: Seq[Double]): Double =
+        (l1 zip ws) map { case (l, w) => w * l } sum
+  
+    def output(ws: Seq[Double])(x: Double): Double =
+        computeL2(computeL1(x), ws)
+  
+    def learn(data: Seq[(Double, Double)], ws: Seq[Double],
+        lamb: Double, gamma: Double): Seq[Double] = {
+    
+        lazy val deltas = data.map {
+            case (x, y) =>
+                val l1 = computeL1(x) // n
+                val out = computeL2(l1, ws) // 1
+                (l1 zip ws) map {case (l1, w) => (l1 * 2 * (out - y) +
+                    lam * 2 * w)  * gamma * -1}
+        }
+  
+        deltas.foldRight(ws)(
+            (delta, ws) => ws zip (delta) map { case (w, d) => w + d })  
+    }
+
+    def train(data: Seq[(Double, Double)], iter: Int, lam: Double,
+        gamma: Double = gamma): (Seq[Double], Double => Double)= {
+      
+        val ws = (1 to iter).foldRight((1 to n).map(
+            _ => 0.0) :Seq[Double])((i, w) => {
+            println(s"Training iteration $i")
+            println(w.sum/w.length)
+            learn(data, w, lam, gamma / 10)
+        })
+        (ws, output(ws))
+    }
+}
+\end{lstlisting}
+\caption{Scala code used to build and train the ridge penalized
+  randomized shallow neural network in .... The parameter \textit{lam}
+in the train function represents the $\lambda$ parameter in the error
+function. The parameters \textit{n} and \textit{gamma} set the number
+of hidden nodes and the stepsize for training.}
+\end{lstfloat}
+\clearpage
+
 \begin{lstlisting}[language=iPython]
 import tensorflow as tf
 import numpy as np
@@ -136,7 +214,7 @@ model.add(tf.keras.layers.Conv2D(64,kernel_size=5,padding='same',activation='rel
 model.add(tf.keras.layers.MaxPool2D(padding='same'))
 model.add(tf.keras.layers.Flatten())
 model.add(tf.keras.layers.Dense(256, activation='relu'))
-model.add(tf.keras.layers.Dropout(j))
+model.add(tf.keras.layers.Dropout(0.2))
 model.add(tf.keras.layers.Dense(10, activation='softmax'))
 model.compile(optimizer='adam', loss="categorical_crossentropy",
     metrics=["accuracy"])
@@ -150,10 +228,59 @@ datagen = ImageDataGenerator(
 
 csv_logger = CSVLogger(<Target File>)
     
-history = model.fit(datagen.flow(x_train_, y_train_, batch_size=50),
-    validation_data=(x_test, y_test), epochs=125,
-    callbacks=[csv_logger],
-    steps_per_epoch = x_train_.shape[0]//50) 
+history = model.fit(datagen.flow(x_train, y_train, batch_size=50),
+validation_data=(x_test, y_test),
+    epochs=125, callbacks=[csv_logger],
+    steps_per_epoch = x_train.shape[0]//50) 
+
+\end{lstlisting}
+\clearpage
+\begin{lstlisting}[language=iPython]
+import tensorflow as tf
+import numpy as np
+from tensorflow.keras.callbacks import CSVLogger
+from tensorflow.keras.preprocessing.image import ImageDataGenerator
+mnist = tf.keras.datasets.fashion_mnist
+
+(x_train, y_train), (x_test, y_test) = mnist.load_data()
+x_train = x_train.reshape(x_train.shape[0], 28, 28, 1)
+x_test = x_test.reshape(x_test.shape[0], 28, 28, 1)
+x_train, x_test = x_train / 255.0, x_test / 255.0
+
+y_train = tf.keras.utils.to_categorical(y_train)
+y_test = tf.keras.utils.to_categorical(y_test)
+
+model = tf.keras.Sequential()
+model.add(tf.keras.layers.Conv2D(filters = 32, kernel_size = (3, 3), activation='relu',
+    input_shape = (28, 28, 1), padding='same'))
+model.add(tf.keras.layers.Conv2D(filters = 32, kernel_size = (2, 2), activation='relu', padding = 'same'))
+model.add(tf.keras.layers.MaxPool2D(strides=(2,2)))
+model.add(tf.keras.layers.Conv2D(filters = 64, kernel_size = (3, 3), activation='relu', padding='same'))
+model.add(tf.keras.layers.Conv2D(filters = 64, kernel_size = (3, 3), activation='relu', padding='same'))
+model.add(tf.keras.layers.MaxPool2D(strides=(2,2)))
+model.add(tf.keras.layers.Flatten())
+model.add(tf.keras.layers.Dense(256, activation='relu'))
+model.add(tf.keras.layers.Dropout(0.2))
+model.add(tf.keras.layers.Dense(10, activation='softmax'))
+
+model.compile(optimizer=tf.keras.optimizers.Adam(lr = 1e-3), loss="categorical_crossentropy", metrics=["accuracy"])
+
+datagen = ImageDataGenerator(
+    rotation_range = 15,
+    zoom_range = 0.1,
+    width_shift_range=2,
+    height_shift_range=2,
+    shear_range = 0.5,
+    fill_mode = 'constant',
+    cval = 0)
+        
+    csv_logger = CSVLogger(<Target File>)
+    
+    history = model.fit(datagen.flow(x_train, y_train, batch_size=30),
+        steps_per_epoch=2000,
+        validation_data=(x_test, y_test),
+        epochs=125, callbacks=[csv_logger],
+        shuffle=True)
 
 \end{lstlisting}
 \begin{lstlisting}[language=iPython]
@@ -172,4 +299,5 @@ def get_random_sample(a, b, number_of_samples=10):
         return (np.asarray(x).reshape(-1, 28, 28, 1),
             np.asarray(y).reshape(10*number_of_samples,1))
 \end{lstlisting}
+
 \end{document} 

TeX/Plots/Data/data_sin_d_t.csv

@@ -1,17 +0,0 @@
-x,y
--3.141592653589793,0.0802212608585366
--2.722713633111154,-0.3759376368887911
--2.303834612632515,-1.3264180339054117
--1.8849555921538759,-0.8971334213504949
--1.4660765716752369,-0.7724344034354425
--1.0471975511965979,-0.9501497164520739
--0.6283185307179586,-0.6224628757084738
--0.2094395102393194,-0.35622668982623207
-0.2094395102393194,-0.18377660088356823
-0.6283185307179586,0.7836770998126841
-1.0471975511965974,0.5874762732054489
-1.4660765716752362,1.0696991264956026
-1.8849555921538759,1.1297065441952743
-2.3038346126325155,0.7587275382323738
-2.7227136331111543,-0.030547103790458163
-3.1415926535897922,0.044327111895927106

TeX/Plots/Data/min_max.txt

@@ -1,58 +0,0 @@
-datagen_dropout_02_1
-test
-0.6604& 0.5175& 0.60136& 0.002348447
-
-datagen_dropout_00_1
-test
-0.6704& 0.4878& 0.58621& 0.003600539
-
-dropout_02_1
-test
-0.5312& 0.4224& 0.47137& 0.001175149
-
-default_1
-test
-0.5633& 0.3230& 0.45702& 0.004021449
-
-datagen_dropout_02_10
-test
-0.9441& 0.9061& 0.92322& 0.00015
-train
-1& 0.97& 0.989& 1e-04
-
-datagen_dropout_00_10
-test
-0.931& 0.9018& 0.9185& 6e-05
-train
-1& 0.97& 0.99& 0.00013
-
-dropout_02_10
-test
-0.9423& 0.9081& 0.92696& 0.00013
-train
-1& 0.99& 0.992& 2e-05
-
-default_10
-test
-0.8585& 0.8148& 0.83771& 0.00027
-train
-1& 1& 1& 0
-
-datagen_dropout_02_100
-test
-0.9805& 0.9727& 0.97826& 0
-train
-
-datagen_dropout_00_100
-test
-0.981& 0.9702& 0.9769& 1e-05
-train
-
-dropout_02_100
-test
-0.9796& 0.9719& 0.97703& 1e-05
-train
-
-default_100
-test
-0.9637& 0.9506& 0.95823& 2e-05

TeX/Plots/Data/scala_out_d_1_t.csv

@@ -1,101 +0,0 @@
-x_n_5000_tl_0.1,y_n_5000_tl_0.1,x_n_5000_tl_1.0,y_n_5000_tl_1.0,x_n_5000_tl_3.0,y_n_5000_tl_3.0
--5.0,1.794615305950707,-5.0,0.3982406589003759,-5.0,-0.4811539502118497
--4.898989898989899,1.6984389486364895,-4.898989898989899,0.35719218031912614,-4.898989898989899,-0.48887996302459025
--4.797979797979798,1.6014200743009022,-4.797979797979798,0.3160182633093358,-4.797979797979798,-0.4966732473871599
--4.696969696969697,1.5040575427157106,-4.696969696969697,0.27464978660531225,-4.696969696969697,-0.5045073579233731
--4.595959595959596,1.4061194142774731,-4.595959595959596,0.23293440418365288,-4.595959595959596,-0.5123589845230747
--4.494949494949495,1.3072651356075136,-4.494949494949495,0.19100397829173557,-4.494949494949495,-0.5202738824510786
--4.393939393939394,1.2078259346207492,-4.393939393939394,0.1488314515422353,-4.393939393939394,-0.5282281154332915
--4.292929292929293,1.1079271590765678,-4.292929292929293,0.10646618526238515,-4.292929292929293,-0.536250283913464
--4.191919191919192,1.0073183089866045,-4.191919191919192,0.0637511521454329,-4.191919191919192,-0.5443068679044686
--4.090909090909091,0.9064682044248323,-4.090909090909091,0.020965778107027506,-4.090909090909091,-0.5524049731989601
--3.9898989898989896,0.805095064694333,-3.9898989898989896,-0.02200882631350869,-3.9898989898989896,-0.5605562335116703
--3.888888888888889,0.7032463151196859,-3.888888888888889,-0.06548644224881082,-3.888888888888889,-0.5687680272492979
--3.787878787878788,0.6007843964001714,-3.787878787878788,-0.10914135786185346,-3.787878787878788,-0.5770307386196555
--3.686868686868687,0.4978572358270573,-3.686868686868687,-0.15292201515712506,-3.686868686868687,-0.5853131654059709
--3.5858585858585856,0.39465522349482535,-3.5858585858585856,-0.19694472820060063,-3.5858585858585856,-0.593636189078738
--3.484848484848485,0.29091175104318323,-3.484848484848485,-0.24139115547918963,-3.484848484848485,-0.6019914655156898
--3.383838383838384,0.1868284306918275,-3.383838383838384,-0.28617728400089926,-3.383838383838384,-0.6103823599700093
--3.282828282828283,0.0817944681090728,-3.282828282828283,-0.33119615483860937,-3.282828282828283,-0.6188088888423856
--3.1818181818181817,-0.023670753859105602,-3.1818181818181817,-0.3764480559542342,-3.1818181818181817,-0.6272515625106694
--3.080808080808081,-0.1299349094939808,-3.080808080808081,-0.42202262988259276,-3.080808080808081,-0.6357221532633648
--2.9797979797979797,-0.2360705715363967,-2.9797979797979797,-0.467584017465408,-2.9797979797979797,-0.6440454918766952
--2.878787878787879,-0.34125419448980393,-2.878787878787879,-0.5126079284225549,-2.878787878787879,-0.65203614244987
--2.7777777777777777,-0.443504036212927,-2.7777777777777777,-0.5569084060463078,-2.7777777777777777,-0.6594896031012563
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--2.5757575757575757,-0.6363089624800997,-2.5757575757575757,-0.6396725440402657,-2.5757575757575757,-0.6715398637661353
--2.474747474747475,-0.725241414197713,-2.474747474747475,-0.6753456416248385,-2.474747474747475,-0.674565545688341
--2.3737373737373737,-0.8010191169999671,-2.3737373737373737,-0.7066964605752718,-2.3737373737373737,-0.6765307025278043
--2.272727272727273,-0.8626605255789729,-2.272727272727273,-0.7348121862404637,-2.272727272727273,-0.6766187567521622
--2.1717171717171717,-0.911435840482434,-2.1717171717171717,-0.7592451818361001,-2.1717171717171717,-0.6747200340049733
--2.070707070707071,-0.9518228090965052,-2.070707070707071,-0.7755022118880182,-2.070707070707071,-0.6711535886166349
--1.9696969696969697,-0.9791642715505677,-1.9696969696969697,-0.7889078495544403,-1.9696969696969697,-0.6653309071624213
--1.868686868686869,-0.9959505678135467,-1.868686868686869,-0.7978655263590677,-1.868686868686869,-0.6574048849245917
--1.7676767676767677,-1.0042572630521163,-1.7676767676767677,-0.8024926242661324,-1.7676767676767677,-0.6465258005011485
--1.6666666666666665,-1.0031374573437621,-1.6666666666666665,-0.8024786300118695,-1.6666666666666665,-0.6326231142587367
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TeX/Plots/Data/scala_out_sin.csv

@@ -1,101 +0,0 @@
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TeX/Plots/Data/sin_6.csv

@@ -1,7 +0,0 @@
-x,y
--3.14159265358979 , -1.22464679914735e-16
--1.88495559215388 , -0.951056516295154
--0.628318530717959 , -0.587785252292473
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TeX/Plots/Data/sin_conv.csv

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TeX/Plots/RN_vs_RS.tex

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-\pgfplotsset{
-compat=1.11,
-legend image code/.code={
-\draw[mark repeat=2,mark phase=2]
-plot coordinates {
-(0cm,0cm)
-(0.075cm,0cm)        %% default is (0.3cm,0cm)
-(0.15cm,0cm)         %% default is (0.6cm,0cm)
-};%
-}
-}
-\begin{figure}
-  \begin{subfigure}[b]{0.5\textwidth}
-    \begin{subfigure}[b]{\textwidth}
-      \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-        \begin{tikzpicture}
-          \begin{axis}[
-        ytick = {-1, 0, 1, 2},
-        yticklabels = {$-1$, $\phantom{-0.}0$, $1$, $2$},]
-            \addplot table [x=x, y=y, col sep=comma, only marks,
-            forget plot] {Plots/Data/sin_6.csv};
-            \addplot [black, line width=2pt] table [x=x, y=y, col
-            sep=comma, mark=none] {Plots/Data/matlab_0.csv};
-            \addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_0.0,
-            y=y_n_5000_tl_0.0, col sep=comma, mark=none] {Plots/Data/scala_out_sin.csv};
-            \addlegendentry{$f_1^{*, 0.1}$};
-            \addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
-          \end{axis}
-        \end{tikzpicture}
-      \end{adjustbox}
-      \caption{$\lambda = 0.1$}
-    \end{subfigure}\\
-    \begin{subfigure}[b]{\textwidth}
-      \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-        \begin{tikzpicture}
-          \begin{axis}
-            \addplot table [x=x, y=y, col sep=comma, only marks,
-            forget plot] {Plots/Data/sin_6.csv};
-            \addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Plots/Data/matlab_1.csv};
-            \addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_1.0,
-            y=y_n_5000_tl_1.0, col sep=comma, mark=none] {Plots/Data/scala_out_sin.csv};
-            \addlegendentry{$f_1^{*, 1.0}$};
-            \addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
-          \end{axis}
-        \end{tikzpicture}
-      \end{adjustbox}
-      \caption{$\lambda = 1.0$}
-    \end{subfigure}\\
-    \begin{subfigure}[b]{\textwidth}
-      \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-        \begin{tikzpicture}
-          \begin{axis}
-            \addplot table [x=x, y=y, col sep=comma, only marks,
-            forget plot] {Plots/Data/sin_6.csv};
-            \addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Plots/Data/matlab_3.csv};
-            \addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_3.0,
-            y=y_n_5000_tl_3.0, col sep=comma, mark=none] {Plots/Data/scala_out_sin.csv};
-            \addlegendentry{$f_1^{*, 3.0}$};
-            \addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
-          \end{axis}
-        \end{tikzpicture}
-      \end{adjustbox}
-      \caption{$\lambda = 3.0$}
-    \end{subfigure}
-  \end{subfigure}
-  \begin{subfigure}[b]{0.5\textwidth}
-    \begin{subfigure}[b]{\textwidth}
-      \begin{adjustbox}{width=\textwidth, height=0.245\textheight}
-        \begin{tikzpicture}
-          \begin{axis}[
-        ytick = {-2,-1, 0, 1, 2},
-        yticklabels = {$-2$,$-1$, $\phantom{-0.}0$, $1$, $2$},]
-            \addplot table [x=x, y=y, col sep=comma, only marks,
-            forget plot] {Plots/Data/data_sin_d_t.csv};
-            \addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Plots/Data/matlab_sin_d_01.csv};
-            \addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_0.1,
-            y=y_n_5000_tl_0.1, col sep=comma, mark=none] {Plots/Data/scala_out_d_1_t.csv};
-            \addlegendentry{$f_1^{*, 0.1}$};
-            \addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
-          \end{axis}
-        \end{tikzpicture}
-      \end{adjustbox}
-      \caption{$\lambda = 0.1$}
-    \end{subfigure}\\
-    \begin{subfigure}[b]{\textwidth}
-      \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-        \begin{tikzpicture}
-          \begin{axis}
-            \addplot table [x=x, y=y, col sep=comma, only marks,
-            forget plot] {Plots/Data/data_sin_d_t.csv};
-            \addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Plots/Data/matlab_sin_d_1.csv};
-            \addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_1.0,
-            y=y_n_5000_tl_1.0, col sep=comma, mark=none] {Plots/Data/scala_out_d_1_t.csv};
-            \addlegendentry{$f_1^{*, 1.0}$};
-            \addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda},*}$};
-          \end{axis}
-        \end{tikzpicture}
-      \end{adjustbox}
-      \caption{$\lambda = 1.0$}
-    \end{subfigure}\\
-    \begin{subfigure}[b]{\textwidth}
-      \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-        \begin{tikzpicture}
-          \begin{axis}
-            \addplot table [x=x, y=y, col sep=comma, only marks,
-            forget plot] {Plots/Data/data_sin_d_t.csv};
-            \addplot [black, line width=2pt] table [x=x, y=y, col sep=comma, mark=none] {Plots/Data/matlab_sin_d_3.csv};
-            \addplot [red, line width = 1.5pt, dashed] table [x=x_n_5000_tl_3.0,
-            y=y_n_5000_tl_3.0, col sep=comma, mark=none] {Plots/Data/scala_out_d_1_t.csv};
-            \addlegendentry{$f_1^{*, 3.0}$};
-            \addlegendentry{$\mathcal{RN}_w^{\tilde{\lambda}}$};
-          \end{axis}
-        \end{tikzpicture}
-      \end{adjustbox}
-      \caption{$\lambda = 3.0$}
-    \end{subfigure}
-  \end{subfigure}
-  \caption[Comparison of shallow neural networks and regression
-  splines]{% In these Figures the behaviour stated in ... is
-           % visualized 
-    % in two exaples. For $(a), (b), (c)$ six values of sinus equidistantly
-    % spaced on $[-\pi, \pi]$ have been used as training data. For
-    % $(d),(e),(f)$ 15 equidistand values have been used, where
-    % $y_i^{train} = \sin(x_i^{train}) + \varepsilon_i$ and
-    % $\varepsilon_i \sim \mathcal{N}(0, 0.3)$. For
-    % $\mathcal{RN}_w^{\tilde{\lambda, *}}$ the random weights are
-    % distributed as follows
-    % \begin{align*}
-    %   \xi_k &\sim
-    % \end{align*}
-    Ridge Penalized Neural Network compared to Regression Spline,
-    with them being trained on $\text{data}_A$ in a), b), c) and on
-    $\text{data}_B$ in d), e), f).
-    The Parameters of each are given above.
-  }
-  \label{fig:rn_vs_rs}
-\end{figure}
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master:
-%%% End:

TeX/Plots/SGD_vs_GD.tex

@@ -1,93 +0,0 @@
-\pgfplotsset{
-compat=1.11,
-legend image code/.code={
-\draw[mark repeat=2,mark phase=2]
-plot coordinates {
-(0cm,0cm)
-(0.0cm,0cm)        %% default is (0.3cm,0cm)
-(0.0cm,0cm)         %% default is (0.6cm,0cm)
-};%
-}
-}
-\begin{figure}
-  \begin{subfigure}[h!]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[tick style = {draw = none}, width = \textwidth,
-        height = 0.6\textwidth,
-        xtick = {1, 3, 5,7,9,11,13,15,17,19},
-        xticklabels = {$2$, $4$, $6$, $8$,
-          $10$,$12$,$14$,$16$,$18$,$20$},
-        xlabel = {training epoch}, ylabel = {classification accuracy}]
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma] {Plots/Data/GD_01.log};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma] {Plots/Data/GD_05.log};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma] {Plots/Data/GD_1.log};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma]
-        {Plots/Data/SGD_01_b32.log};
-        
-         \addlegendentry{GD$_{0.01}$}
-        \addlegendentry{GD$_{0.05}$}
-        \addlegendentry{GD$_{0.1}$}
-        \addlegendentry{SGD$_{0.01}$}
-      \end{axis}
-    \end{tikzpicture}
-    %\caption{Classification accuracy}
-  \end{subfigure}
-  \begin{subfigure}[b]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[tick style = {draw = none}, width = \textwidth,
-        height = 0.6\textwidth,
-        ytick = {0, 1, 2, 3, 4},
-        yticklabels = {$0$, $1$, $\phantom{0.}2$, $3$, $4$},
-        xtick = {1, 3, 5,7,9,11,13,15,17,19},
-        xticklabels = {$2$, $4$, $6$, $8$,
-          $10$,$12$,$14$,$16$,$18$,$20$},
-        xlabel = {training epoch}, ylabel = {error measure\vphantom{fy}}]
-        \addplot table
-        [x=epoch, y=val_loss, col sep=comma] {Plots/Data/GD_01.log};
-        \addplot table
-        [x=epoch, y=val_loss, col sep=comma] {Plots/Data/GD_05.log};
-        \addplot table
-        [x=epoch, y=val_loss, col sep=comma] {Plots/Data/GD_1.log};
-        \addplot table
-        [x=epoch, y=val_loss, col sep=comma] {Plots/Data/SGD_01_b32.log};
-        
-        \addlegendentry{GD$_{0.01}$}
-        \addlegendentry{GD$_{0.05}$}
-        \addlegendentry{GD$_{0.1}$}
-        \addlegendentry{SGD$_{0.01}$}
-        
-      \end{axis}
-    \end{tikzpicture}
-    \caption{Performance metrics during training}
-  \end{subfigure}
-  % \\~\\
-  \caption[Performance comparison of SDG and GD]{The neural network given in ?? trained with different
-    algorithms on the MNIST handwritten digits data set. For gradient
-    descent the learning rated 0.01, 0.05 and 0.1 are (GD$_{\cdot}$). For
-    stochastic gradient descend a batch size of 32 and learning rate
-    of 0.01 is used (SDG$_{0.01}$).}
-  \label{fig:sgd_vs_gd}
-\end{figure}
-
-\begin{table}[h]
-  \begin{tabu} to \textwidth {@{}  *4{X[c]}c*4{X[c]} @{}}
-    \multicolumn{4}{c}{Classification Accuracy}
-    &~&\multicolumn{4}{c}{Error Measure}
-    \\\cline{1-4}\cline{6-9}
-    GD$_{0.01}$&GD$_{0.05}$&GD$_{0.1}$&SGD$_{0.01}$&&GD$_{0.01}$&GD$_{0.05}$&GD$_{0.1}$&SGD$_{0.01}$
-    \\\cline{1-4}\cline{6-9}
-    \multicolumn{9}{c}{test}\\
-    0.265&0.633&0.203&0.989&&2.267&1.947&3.91&0.032
-  \end{tabu}
-  \caption{Performance metrics of the networks trained in
-    Figure~\ref{fig:sgd_vs_gd} after 20 training epochs.}
-  \label{table:sgd_vs_gd}
-\end{table}
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/Plots/_region_.tex

@@ -1,71 +0,0 @@
-\message{ !name(pfg_test.tex)}\documentclass{article}
-\usepackage{pgfplots}
-\usepackage{filecontents}
-\usepackage{subcaption}
-\usepackage{adjustbox}
-\usepackage{xcolor}
-\usepackage{graphicx}
-\usetikzlibrary{calc, 3d}
-
-\begin{document}
-
-\message{ !name(pfg_test.tex) !offset(6) }
-
-      \end{axis}
-    \end{tikzpicture}
-  \end{adjustbox}
-  \caption{True position (\textcolor{red}{red}), distorted data (black)}
-\end{figure}
-\begin{center}
-\begin{figure}[h]
-  \begin{subfigure}{0.49\textwidth}
-    \includegraphics[width=\textwidth]{Data/klammern.jpg}
-    \caption{Original Picure}
-  \end{subfigure}
-  \begin{subfigure}{0.49\textwidth}
-    \includegraphics[width=\textwidth]{Data/image_conv4.png}
-    \caption{test}
-  \end{subfigure}
-  \begin{subfigure}{0.49\textwidth}
-    \includegraphics[width=\textwidth]{Data/image_conv5.png}
-    \caption{test}
-  \end{subfigure}
-  \begin{subfigure}{0.49\textwidth}
-    \includegraphics[width=\textwidth]{Data/image_conv6.png}
-    \caption{test}
-  \end{subfigure}
-\end{figure}
-\end{center}
-
-\begin{figure}
-  \begin{adjustbox}{width=\textwidth}
-    \begin{tikzpicture}  
-      \begin{scope}[x = (0:1cm), y=(90:1cm), z=(15:-0.5cm)]
-        \node[canvas is xy plane at z=0, transform shape] at (0,0)
-        {\includegraphics[width=5cm]{Data/klammern_r.jpg}};
-        \node[canvas is xy plane at z=2, transform shape] at (0,-0.2)
-        {\includegraphics[width=5cm]{Data/klammern_g.jpg}};
-        \node[canvas is xy plane at z=4, transform shape] at (0,-0.4)
-        {\includegraphics[width=5cm]{Data/klammern_b.jpg}};
-        \node[canvas is xy plane at z=4, transform shape] at (-8,-0.2)
-        {\includegraphics[width=5.3cm]{Data/klammern_rgb.jpg}};
-      \end{scope}
-    \end{tikzpicture}
-  \end{adjustbox}
-  \caption{On the right the red, green and blue chanels of the picture
-    are displayed. In order to better visualize the color channes the
-    black and white picture of each channel has been colored in the
-    respective color. Combining the layers results in the image on the
-    left}
-\end{figure}
-
-
-
-\message{ !name(pfg_test.tex) !offset(3) }
-
-\end{document}
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End:

TeX/Plots/fashion_mnist.tex

@@ -1,53 +0,0 @@
-\begin{figure}[h]
-    \centering
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist0.pdf}
-    \caption{T-shirt/top}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist1.pdf}
-    \caption{Trousers}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist2.pdf}
-    \caption{Pullover}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist3.pdf}
-    \caption{Dress}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist4.pdf}
-    \caption{Coat}
-  \end{subfigure}\\
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist5.pdf}
-    \caption{Sandal}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist6.pdf}
-    \caption{Shirt}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist7.pdf}
-    \caption{Sneaker}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist8.pdf}
-    \caption{Bag}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/fashion_mnist9.pdf}
-    \caption{Ankle boot}
-  \end{subfigure}
-  \caption[Fashion MNIST data set]{The fashtion MNIST data set contains 70.000 images of
-    preprocessed product images from Zalando, which are categorized as
-    T-shirt/top, Trouser, Pullover, Dress, Coat, Sandal, Shirt,
-    Sneaker, Bag, Ankle boot. Of these images 60.000 are used as training images, while
-    the rest are used to validate the models trained.}
-  \label{fig:MNIST}
-\end{figure}
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/Plots/gen_dropout.tex

@@ -1,82 +0,0 @@
-\pgfplotsset{
-compat=1.11,
-legend image code/.code={
-\draw[mark repeat=2,mark phase=2]
-plot coordinates {
-(0cm,0cm)
-(0.15cm,0cm)        %% default is (0.3cm,0cm)
-(0.3cm,0cm)         %% default is (0.6cm,0cm)
-};%
-}
-}
-\begin{figure}
-  \begin{subfigure}[h]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
-                     /pgf/number format/precision=3},tick style = {draw = none}, width = \textwidth,
-        height = 0.6\textwidth, ymin = 0.988, legend style={at={(0.9825,0.0175)},anchor=south east},
-        xlabel = {epoch}, ylabel = {Classification Accuracy}, cycle
-        list/Dark2, every axis plot/.append style={line width =1.25pt}]
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_full_mean.log};  
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_02_full_mean.log}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_04_full_mean.log};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_02_full_mean.log}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_04_full_mean.log}; 
-        \addplot [dashed] table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_full_mean.log}; 
-        
-        \addlegendentry{\footnotesize{G.}}
-        \addlegendentry{\footnotesize{G. + D. 0.2}}
-        \addlegendentry{\footnotesize{G. + D. 0.4}}
-        \addlegendentry{\footnotesize{D. 0.2}}
-        \addlegendentry{\footnotesize{D. 0.4}}
-        \addlegendentry{\footnotesize{Default}}
-      \end{axis}
-    \end{tikzpicture}
-    \caption{Classification accuracy}
-    \vspace{.25cm}
-  \end{subfigure}
-  \begin{subfigure}[h]{1.0\linewidth}
-    \begin{tabu} to \textwidth {@{}lc*5{X[c]}@{}}
-      \Tstrut \Bstrut & \textsc{\,Adam\,} & D. 0.2 & D. 0.4 & G. &G.+D.\,0.2 & G.+D.\,0.4 \\
-      \hline           
-      \multicolumn{7}{c}{Test Accuracy}\Bstrut                       \\
-      \cline{2-7}
-      mean     \Tstrut   & 0.9914 & 0.9923 & 0.9930 & 0.9937 & 0.9938 & 0.9943 \\
-      max                & 0.9926 & 0.9930 & 0.9934 & 0.9946 & 0.9955 & 0.9956 \\
-      min                & 0.9887 & 0.9909 & 0.9922 & 0.9929 & 0.9929 & 0.9934 \\
-      \hline
-      \multicolumn{7}{c}{Training Accuracy}\Bstrut                             \\
-      \cline{2-7}
-      mean       \Tstrut & 0.9994 & 0.9991 & 0.9989 & 0.9967 & 0.9954 & 0.9926 \\
-      max                & 0.9996 & 0.9996 & 0.9992 & 0.9979 & 0.9971 & 0.9937 \\
-      min                & 0.9992 & 0.9990 & 0.9984 & 0.9947 & 0.9926 & 0.9908 \\      
-    \end{tabu}
-    \caption{Mean and maximum accuracy after 48 epochs of training.}
-    \label{fig:gen_dropout_b}
-  \end{subfigure}
-  \caption[Performance comparison of overfitting measures]{Accuracy for the net given in ... with Dropout (D.),
-    data generation (G.), a combination, or neither (Default) implemented and trained
-    with \textsc{Adam}. For each epoch the 60.000 training samples
-    were used, or for data generation 10.000 steps with each using
-    batches of 60 generated data points. For each configuration the
-    model was trained 5 times and the average accuracies at each epoch
-    are given in (a). Mean, maximum and minimum values of accuracy on
-    the test and training set are given in (b).}
-  \label{fig:gen_dropout}
-\end{figure}
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/Plots/mnist.tex

@@ -1,41 +0,0 @@
-\begin{figure}[h]
-    \centering
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist0.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist1.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist2.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist3.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist4.pdf}
-  \end{subfigure}\\
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist5.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist6.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist7.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist8.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist9.pdf}
-  \end{subfigure}
-  \caption[MNIST data set]{The MNIST data set contains 70.000 images of preprocessed handwritten
-    digits. Of these images 60.000 are used as training images, while
-    the rest are used to validate the models trained.}
-  \label{fig:MNIST}
-\end{figure}
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/Plots/pfg_test.tex

@@ -1,301 +0,0 @@
-\documentclass[a4paper, 12pt, draft=true]{article}
-\usepackage{pgfplots}
-\usepackage{filecontents}
-\usepackage{subcaption}
-\usepackage{adjustbox}
-\usepackage{xcolor}
-\usepackage{tabu}
-\usepackage{showframe}
-\usepackage{graphicx}
-\usepackage{titlecaps}
-\usetikzlibrary{calc, 3d}
-\usepgfplotslibrary{colorbrewer}
-
-\newcommand\Tstrut{\rule{0pt}{2.6ex}}         % = `top' strut
-\newcommand\Bstrut{\rule[-0.9ex]{0pt}{0pt}}   % = `bottom' strut
-
-\begin{document}
-\pgfplotsset{
-compat=1.11,
-legend image code/.code={
-\draw[mark repeat=2,mark phase=2]
-plot coordinates {
-(0cm,0cm)
-(0.3cm,0cm)        %% default is (0.3cm,0cm)
-(0.6cm,0cm)         %% default is (0.6cm,0cm)
-};%
-}
-}
-\begin{figure}
-  \begin{subfigure}[h]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
-                     /pgf/number format/precision=3},tick style = {draw = none}, width = \textwidth,
-        height = 0.35\textwidth, legend style={at={(0.9825,0.0175)},anchor=south east},
-        ylabel = {Test Accuracy}, cycle
-        list/Dark2, every axis plot/.append style={line width
-          =1.25pt}]
-        % \addplot [dashed] table
-        % [x=epoch, y=accuracy, col sep=comma, mark = none]
-        % {Data/adam_datagen_full.log};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_1.mean};  
-        % \addplot [dashed] table
-        % [x=epoch, y=accuracy, col sep=comma, mark = none]
-        % {Data/adam_datagen_dropout_02_full.log}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_datagen_1.mean}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_datagen_dropout_02_1.mean};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_dropout_02_1.mean};
-
-        
-        \addlegendentry{\footnotesize{G.}}
-        \addlegendentry{\footnotesize{G. + D. 0.2}}
-        \addlegendentry{\footnotesize{G. + D. 0.4}}
-        \addlegendentry{\footnotesize{D. 0.2}}
-        \addlegendentry{\footnotesize{D. 0.4}}
-        \addlegendentry{\footnotesize{Default}}
-      \end{axis}
-    \end{tikzpicture}
-    \caption{1 sample per class}
-    \vspace{0.25cm}
-  \end{subfigure}
-  \begin{subfigure}[h]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
-                     /pgf/number format/precision=3},tick style = {draw = none}, width = \textwidth,
-        height = 0.35\textwidth, legend style={at={(0.9825,0.0175)},anchor=south east},
-        ylabel = {Test Accuracy}, cycle
-        list/Dark2, every axis plot/.append style={line width
-          =1.25pt}]
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_dropout_00_10.mean}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_dropout_02_10.mean}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_datagen_dropout_00_10.mean}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_datagen_dropout_02_10.mean};
-
-        
-        \addlegendentry{\footnotesize{G.}}
-        \addlegendentry{\footnotesize{G. + D. 0.2}}
-        \addlegendentry{\footnotesize{G. + D. 0.4}}
-        \addlegendentry{\footnotesize{D. 0.2}}
-        \addlegendentry{\footnotesize{D. 0.4}}
-        \addlegendentry{\footnotesize{Default}}
-      \end{axis}
-    \end{tikzpicture}
-    \caption{10 samples per class}
-  \end{subfigure}
-  \begin{subfigure}[h]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
-                     /pgf/number format/precision=3},tick style = {draw = none}, width = 0.9875\textwidth,
-        height = 0.35\textwidth, legend style={at={(0.9825,0.0175)},anchor=south east},
-        xlabel = {epoch}, ylabel = {Test Accuracy}, cycle
-        list/Dark2, every axis plot/.append style={line width
-          =1.25pt}, ymin = {0.92}]
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_dropout_00_100.mean};
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_dropout_02_100.mean}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_datagen_dropout_00_100.mean}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Data/adam_datagen_dropout_02_100.mean}; 
-        
-        \addlegendentry{\footnotesize{G.}}
-        \addlegendentry{\footnotesize{G. + D. 0.2}}
-        \addlegendentry{\footnotesize{G. + D. 0.4}}
-        \addlegendentry{\footnotesize{D. 0.2}}
-        \addlegendentry{\footnotesize{D. 0.4}}
-        \addlegendentry{\footnotesize{Default}}
-      \end{axis}
-    \end{tikzpicture}
-    \caption{100 samples per class}
-    \vspace{.25cm}
-  \end{subfigure}
-  \caption{Accuracy for the net given in ... with Dropout (D.),
-    data generation (G.), a combination, or neither (Default) implemented and trained
-    with \textsc{Adam}. For each epoch the 60.000 training samples     
-    were used, or for data generation 10.000 steps with each using
-    batches of 60 generated data points. For each configuration the
-    model was trained 5 times and the average accuracies at each epoch
-    are given in (a). Mean, maximum and minimum values of accuracy on
-    the test and training set are given in (b).}
-\end{figure}
-\begin{table}
-  \centering
-  \begin{tabu} to \textwidth {@{}l*4{X[c]}@{}}
-      \Tstrut \Bstrut    & \textsc{Adam} & D. 0.2 & Gen    & Gen.+D. 0.2  \\
-      \hline           
-                         & 
-      \multicolumn{4}{c}{\titlecap{test accuracy for 1 sample}}\Bstrut    \\
-      \cline{2-5}
-       max     \Tstrut   & 0.5633        & 0.5312 & 0.6704 & 0.6604       \\
-       min               & 0.3230        & 0.4224 & 0.4878 & 0.5175       \\
-       mean              & 0.4570        & 0.4714 & 0.5862 & 0.6014       \\
-       var               & 0.0040        & 0.0012 & 0.0036 & 0.0023       \\
-      \hline
-                         & 
-      \multicolumn{4}{c}{\titlecap{test accuracy for 10 samples}}\Bstrut  \\
-      \cline{2-5}
-       max       \Tstrut & 0.8585        & 0.9423 & 0.9310 & 0.9441       \\
-       min               & 0.8148        & 0.9081 & 0.9018 & 0.9061       \\
-       mean              & 0.8377        & 0.9270 & 0.9185 & 0.9232       \\
-       var               & 2.7e-4        & 1.3e-4 & 6e-05  & 1.5e-4       \\
-      \hline
-                         & 
-      \multicolumn{4}{c}{\titlecap{test accuracy for 100 samples}}\Bstrut \\
-      \cline{2-5}
-       max               & 0.9637        & 0.9796 & 0.9810 & 0.9805       \\
-       min               & 0.9506        & 0.9719 & 0.9702 & 0.9727       \\
-       mean              & 0.9582        & 0.9770 & 0.9769 & 0.9783       \\
-       var               & 2e-05         & 1e-05  & 1e-05  & 0            \\
-      \hline
-    \end{tabu}
-    \caption{Values of the test accuracy of the model trained 10 times
-      of random training sets containing 1, 10 and 100 data points per
-      class.}
-\end{table}
-
-\begin{center}
-  \begin{figure}[h]
-    \centering
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist0.pdf}
-    \caption{original\\image}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist_gen_zoom.pdf}
-    \caption{random\\zoom}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist_gen_shear.pdf}
-    \caption{random\\shear}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist_gen_rotation.pdf}
-    \caption{random\\rotation}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist_gen_shift.pdf}
-  \caption{random\\positional shift}
-  \end{subfigure}\\
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist5.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist6.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist7.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist8.pdf}
-  \end{subfigure}
-  \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Data/mnist9.pdf}
-  \end{subfigure}
-  \caption{The MNIST data set contains 70.000 images of preprocessed handwritten
-    digits. Of these images 60.000 are used as training images, while
-    the rest are used to validate the models trained.}
-\end{figure}
-\end{center}
-
-\begin{figure}
-  \begin{adjustbox}{width=\textwidth}
-    \begin{tikzpicture}  
-      \begin{scope}[x = (0:1cm), y=(90:1cm), z=(15:-0.5cm)]
-        \node[canvas is xy plane at z=0, transform shape] at (0,0)
-        {\includegraphics[width=5cm]{Data/klammern_r.jpg}};
-        \node[canvas is xy plane at z=2, transform shape] at (0,-0.2)
-        {\includegraphics[width=5cm]{Data/klammern_g.jpg}};
-        \node[canvas is xy plane at z=4, transform shape] at (0,-0.4)
-        {\includegraphics[width=5cm]{Data/klammern_b.jpg}};
-        \node[canvas is xy plane at z=4, transform shape] at (-8,-0.2)
-        {\includegraphics[width=5.3cm]{Data/klammern_rgb.jpg}};
-      \end{scope}
-    \end{tikzpicture}
-  \end{adjustbox}
-  \caption{On the right the red, green and blue chanels of the picture
-    are displayed. In order to better visualize the color channes the
-    black and white picture of each channel has been colored in the
-    respective color. Combining the layers results in the image on the
-    left}
-\end{figure}
-
-\begin{figure}
-  \centering
-  \begin{subfigure}{.45\linewidth}
-    \centering
-    \begin{tikzpicture}
-      \begin{axis}[enlargelimits=false, ymin=0, ymax = 1, width=\textwidth]
-        \addplot [domain=-5:5, samples=101,unbounded coords=jump]{1/(1+exp(-x)};
-      \end{axis}
-    \end{tikzpicture}
-  \end{subfigure}
-  \begin{subfigure}{.45\linewidth}
-    \centering
-    \begin{tikzpicture}
-      \begin{axis}[enlargelimits=false, width=\textwidth]
-        \addplot[domain=-5:5, samples=100]{tanh(x)};
-      \end{axis}
-    \end{tikzpicture}
-  \end{subfigure}
-  \begin{subfigure}{.45\linewidth}
-    \centering
-    \begin{tikzpicture}
-      \begin{axis}[enlargelimits=false, width=\textwidth,
-        ytick={0,2,4},yticklabels={\hphantom{4.}0,2,4}, ymin=-1]
-        \addplot[domain=-5:5, samples=100]{max(0,x)};
-      \end{axis}
-    \end{tikzpicture}
-  \end{subfigure}
-  \begin{subfigure}{.45\linewidth}
-    \centering
-    \begin{tikzpicture}
-      \begin{axis}[enlargelimits=false, width=\textwidth, ymin=-1,
-        ytick={0,2,4},yticklabels={$\hphantom{-5.}0$,2,4}]
-        \addplot[domain=-5:5, samples=100]{max(0,x)+ 0.1*min(0,x)};
-      \end{axis}
-    \end{tikzpicture}
-  \end{subfigure}
-\end{figure}
-
-
-\begin{tikzpicture}
-\begin{axis}[enlargelimits=false]
-\addplot [domain=-5:5, samples=101,unbounded coords=jump]{1/(1+exp(-x)};
-\addplot[domain=-5:5, samples=100]{tanh(x)};
-\addplot[domain=-5:5, samples=100]{max(0,x)};
-\end{axis}
-\end{tikzpicture}
-
-\begin{tikzpicture}
-\begin{axis}[enlargelimits=false]
-\addplot[domain=-2*pi:2*pi, samples=100]{cos(deg(x))};
-\end{axis}
-\end{tikzpicture}
-
-\end{document}
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End:

TeX/Plots/sdg_comparison.tex

@@ -1,78 +0,0 @@
-\pgfplotsset{
-compat=1.11,
-legend image code/.code={
-\draw[mark repeat=2,mark phase=2]
-plot coordinates {
-(0cm,0cm)
-(0.0cm,0cm)        %% default is (0.3cm,0cm)
-(0.0cm,0cm)         %% default is (0.6cm,0cm)
-};%
-}
-}
-\begin{figure}
-  \begin{subfigure}[h]{\textwidth}
-    \begin{tikzpicture}
-      \begin{axis}[tick style = {draw = none}, width = \textwidth,
-        height = 0.6\textwidth, ymin = 0.92, legend style={at={(0.9825,0.75)},anchor=north east},
-        xlabel = {epoch}, ylabel = {Classification Accuracy}]
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adagrad.log}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adadelta.log}; 
-        \addplot table
-        [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam.log}; 
-        
-         \addlegendentry{\footnotesize{ADAGRAD}}
-        \addlegendentry{\footnotesize{ADADELTA}}
-        \addlegendentry{\footnotesize{ADAM}}
-        \addlegendentry{SGD$_{0.01}$}
-      \end{axis}
-    \end{tikzpicture}
-    %\caption{Classification accuracy}
-    \vspace{.25cm}
-  \end{subfigure}
-  % \begin{subfigure}[b]{\textwidth}
-  %   \begin{tikzpicture}
-  %     \begin{axis}[tick style = {draw = none}, width = \textwidth,
-  %       height = 0.6\textwidth, ymax = 0.5,
-  %       xlabel = {epoch}, ylabel = {Error Measure\vphantom{y}},ytick ={0,0.1,0.2,0.3,0.4,0.45,0.5}, yticklabels =
-  %       {0,0.1,0.2,0.3,0.4,\phantom{0.94},0.5}]
-  %       \addplot table
-  %       [x=epoch, y=val_loss, col sep=comma, mark = none] {Plots/Data/adagrad.log};
-  %       \addplot table
-  %       [x=epoch, y=val_loss, col sep=comma, mark = none] {Plots/Data/adadelta.log};
-  %       \addplot table
-  %       [x=epoch, y=val_loss, col sep=comma, mark = none] {Plots/Data/adam.log};
-        
-  %       \addlegendentry{\footnotesize{ADAGRAD}}
-  %       \addlegendentry{\footnotesize{ADADELTA}}
-  %       \addlegendentry{\footnotesize{ADAM}}
-  %       \addlegendentry{SGD$_{0.01}$}
-        
-  %     \end{axis}
-  %   \end{tikzpicture}
-  %   \caption{Performance metrics during training}
-  %   \vspace{.25cm}
-  % \end{subfigure}
-  \begin{subfigure}[b]{1.0\linewidth}
-    \begin{tabu} to \textwidth {@{}  *3{X[c]}c*3{X[c]} @{}}
-      \multicolumn{3}{c}{Classification Accuracy}
-      &~&\multicolumn{3}{c}{Error Measure}
-      \\\cline{1-3}\cline{5-7}
-      ADAGRAD&ADADELTA&ADAM&&ADAGRAD&ADADELTA&ADAM
-      \\\cline{1-3}\cline{5-7}
-      1&1&1&&1&1&1
-    \end{tabu}
-    \caption{Performace metrics after 20 epochs}
-  \end{subfigure}
-  \caption[Performance comparison of training algorithms]{Classification accuracy on the test set and ...Performance metrics of the network given in ... trained
-    with different optimization algorithms}
-  \label{fig:comp_alg}
-\end{figure}
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/Plots/sin_conv.csv

@@ -1,64 +0,0 @@
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-"42",4.1,-0.818277111064411,3.81674488816054,-0.548538951165239,3.63032709398802,-0.41285438330036
-"43",4.2,-0.871575772413588,4.47703348424544,-0.998992385231986,3.88581748102334,-0.592305016590357
-"44",4.3,-0.916165936749455,4.46179199544059,-0.969288921090897,3.96444243944485,-0.643076376622242
-"45",4.4,-0.951602073889516,4.15184730382548,-1.11987501275525,3.93838897981045,-0.743258835859858
-"46",4.5,-0.977530117665097,4.64522916494355,-0.772872365801468,4.15504805602606,-0.691414328153313
-"47",4.6,-0.993691003633465,4.68087925098283,-0.650422764094352,4.24176417425486,-0.675107584174976
-"48",4.7,-0.999923257564101,5.00475403211142,-0.922605880059771,4.41432228408005,-0.770625346502085
-"49",4.8,-0.996164608835841,4.71428836112322,-1.14280193223997,4.41279031790692,-0.861010494025717
-"50",4.9,-0.982452612624332,5.02115518218406,-0.9819618243158,4.57449352886454,-0.843786948015608
-"51",5,-0.958924274663138,4.92057344952522,-0.872931430146499,4.61418118503201,-0.836318916150308
-"52",5.1,-0.925814682327732,5.37277893732831,-0.91444926304078,4.81555148166217,-0.864686555983682
-"53",5.2,-0.883454655720153,5.19524942845082,-1.41169784739596,4.84152902094499,-1.03768305406186
-"54",5.3,-0.832267442223901,5.4432222181271,-0.726481337519931,4.98565483155961,-0.856094353978009
-"55",5.4,-0.772764487555987,4.98285013865449,-0.692803346852181,4.90897053115903,-0.838425020062396
-"56",5.5,-0.705540325570392,5.33298025214155,-0.343702005257262,5.0497327607228,-0.711573964373115
-"57",5.6,-0.631266637872321,5.49935694796791,-0.828968673188174,5.15036520204232,-0.816467931201244
-"58",5.7,-0.550685542597638,5.69204187550805,-0.481580461165225,5.26232964126231,-0.689500817105975
-"59",5.8,-0.464602179413757,5.84391772412888,-0.20453899468884,5.38069867877875,-0.564365367144995
-"60",5.9,-0.373876664830236,5.48166674139637,-0.597796931577294,5.3357436834558,-0.649913835818738
-"61",6,-0.279415498198926,5.77474590863769,-0.280234463056808,5.46956415981143,-0.524503219480344
-"62",6.1,-0.182162504272095,6.36764321572312,-0.0996286988755344,5.7169871104113,-0.422854073705143
-"63",6.2,-0.0830894028174964,6.46175133910451,-0.025702847911482,5.83540227044819,-0.355719019286555

TeX/Plots/sin_conv.tex

@@ -1,45 +0,0 @@
-\begin{figure}
-  \centering
-  \begin{subfigure}[b]{0.49\textwidth}
-    \centering
-    \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-      \begin{tikzpicture}
-        \begin{axis}[tick style = {draw = none}, xticklabel = \empty,
-          yticklabel=\empty]
-          \addplot [mark options={scale = 0.7}, mark = o] table
-          [x=x_d,y=y_d, col sep = comma] {Plots/Data/sin_conv.csv}; 
-          \addplot [red, mark=x] table [x=x_i, y=y_i, col sep=comma, color ='black'] {Plots/Data/sin_conv.csv};
-        \end{axis}
-      \end{tikzpicture}
-    \end{adjustbox}
-    \caption{True position (\textcolor{red}{red}), distorted position data (black)}
-  \end{subfigure}
-  \begin{subfigure}[b]{0.49\textwidth}
-    \centering
-    \begin{adjustbox}{width=\textwidth, height=0.25\textheight}
-      \begin{tikzpicture}
-        \begin{axis}[tick style = {draw = none}, xticklabel = \empty,
-          yticklabel=\empty]
-          \addplot [mark options={scale = 0.7}, mark = o] table [x=x,y=y, col
-          sep = comma] {Plots/Data/sin_conv.csv};
-          \addplot [red, mark=x] table [x=x_i, y=y_i, col sep=comma, color ='black'] {Plots/Data/sin_conv.csv};
-        \end{axis}
-      \end{tikzpicture}
-    \end{adjustbox}
-    \caption{True position (\textcolor{red}{red}), filtered position data (black)}
-  \end{subfigure}
-  \caption[Signal smoothing using convolution]{Example for noise reduction using convolution with simulated
-    positional data. As filter
-    $g(i)=\left(\nicefrac{1}{3},\nicefrac{1}{4},\nicefrac{1}{5},\nicefrac{1}{6},\nicefrac{1}{20}\right)_{(i-1)}$
-      is chosen and applied to the $x$ and $y$ coordinate
-      data seperately. The convolution of both signals with $g$
-      improves the MSE of the positions from 0.196 to 0.170 and
-      visibly smoothes the data.
-  }
-  \label{fig:sin_conv}
-\end{figure}
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/Plots/y.tex

@@ -1,5 +0,0 @@
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "../main"
-%%% End:

TeX/appendixA.tex

@@ -1,6 +1,7 @@
 
 \newpage
 \begin{appendices}
+  \counterwithin{lstfloat}{section}
   \section{Proofs for sone Lemmata in ...}
   In the following there will be proofs for some important Lemmata in
   Section~\ref{sec:theo38}. Further proofs not discussed here can be
@@ -19,6 +20,9 @@
   
     
   \end{Lemma}
+  
+\input{Appendix_code.tex}
+  
 \end{appendices}
 
 

TeX/bibliograpy.bib

@@ -202,3 +202,48 @@ url={https://openreview.net/forum?id=rkgz2aEKDr}
   url = "http://www.sciencedirect.com/science/article/pii/S0925231218310749",
   author = "Maayan Frid-Adar and Idit Diamant and Eyal Klang and Michal Amitai and Jacob Goldberger and Hayit Greenspan"
 }
+
+@online{fashionMNIST,
+  author       = {Han Xiao and Kashif Rasul and Roland Vollgraf},
+  title        = {Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms},
+  date         = {2017-08-28},
+  year         = {2017},
+  eprintclass  = {cs.LG},
+  eprinttype   = {arXiv},
+  eprint       = {cs.LG/1708.07747},
+}
+
+@inproceedings{10.1145/3206098.3206111,
+author = {Kowsari, Kamran and Heidarysafa, Mojtaba and Brown, Donald E. and Meimandi, Kiana Jafari and Barnes, Laura E.},
+title = {RMDL: Random Multimodel Deep Learning for Classification},
+year = {2018},
+isbn = {9781450363549},
+publisher = {Association for Computing Machinery},
+address = {New York, NY, USA},
+url = {https://doi.org/10.1145/3206098.3206111},
+doi = {10.1145/3206098.3206111},
+booktitle = {Proceedings of the 2nd International Conference on Information System and Data Mining},
+pages = {19–28},
+numpages = {10},
+keywords = {Supervised Learning, Deep Learning, Data Mining, Text Classification, Deep Neural Networks, Image Classification},
+location = {Lakeland, FL, USA},
+series = {ICISDM '18}
+}
+
+@article{random_erasing,
+  author    = {Zhun Zhong and
+               Liang Zheng and
+               Guoliang Kang and
+               Shaozi Li and
+               Yi Yang},
+  title     = {Random Erasing Data Augmentation},
+  journal   = {CoRR},
+  volume    = {abs/1708.04896},
+  year      = {2017},
+  url       = {http://arxiv.org/abs/1708.04896},
+  archivePrefix = {arXiv},
+  eprint    = {1708.04896},
+  timestamp = {Mon, 13 Aug 2018 16:47:52 +0200},
+  biburl    = {https://dblp.org/rec/journals/corr/abs-1708-04896.bib},
+  bibsource = {dblp computer science bibliography, https://dblp.org}
+}

TeX/further_applications_of_nn.tex

@@ -2,9 +2,13 @@
 
 As neural networks are applied to problems of higher complexity often
 resulting in higher dimensionality of the input the amount of
-parameters in the network rises drastically. For example a network
-with ...
-A way to combat the
+parameters in the network rises drastically.
+For very large inputs such as high resolution image data due to the
+fully connected nature of the neural network the amount of parameters
+can ... exceed the amount that is feasible for training and storage.
+A way to combat this is by using layers which are only sparsely
+connected and share parameters between nodes. This can be implemented
+using convolution.\todo{Überleitung besser schreiben}
 
 \subsection{Convolution}
 
@@ -18,7 +22,7 @@ functions is integrated after one has been reversed and shifted.
 This operation can be described as a filter-function $g$ being applied
 to $f$,
 as values $f(t)$ are being replaced by an average of values of $f$
-weighted by $g$ in position $t$.
+weighted by a filter-function $g$ in position $t$.
 The convolution operation allows plentiful  manipulation of data, with
 a simple example being smoothing of real-time data. Consider a sensor
 measuring the location of an object (e.g. via GPS). We expect the
@@ -29,7 +33,7 @@ the data to reduce the noise. Using convolution for this task, we
 can control the significance we want to give each data-point. We
 might want to give a larger weight to more recent measurements than
 older ones. If we assume these measurements are taken on a discrete
-timescale, we need to introduce discrete convolution first. Let $f$,
+timescale, we need to introduce discrete convolution first. \\Let $f$,
 $g: \mathbb{Z} \to \mathbb{R}$ then
 
 \[
@@ -39,7 +43,7 @@ Applying this on the data with the filter $g$ chosen accordingly we
 are
 able to improve the accuracy, which can be seen in
 Figure~\ref{fig:sin_conv}.
-\input{Plots/sin_conv.tex}
+\input{Figures/sin_conv.tex}
 This form of discrete convolution can also be applied to functions
 with inputs of higher dimensionality. Let $f$, $g: \mathbb{Z}^d \to
 \mathbb{R}$ then
@@ -51,12 +55,12 @@ with inputs of higher dimensionality. Let $f$, $g: \mathbb{Z}^d \to
 This will prove to be a useful framework for image manipulation but
 in order to apply convolution to images we need to discuss
 representation of image data first. Most often images are represented
-by each pixel being a mixture of base colors these base colors define
+by each pixel being a mixture of base colors. These base colors define
 the color-space in which the image is encoded. Often used are
 color-spaces RGB (red,
 blue, green) or CMYK (cyan, magenta, yellow, black). An example of an
 image split in its red, green and blue channel is given in
-Figure~\ref{fig:rgb} Using this 
+Figure~\ref{fig:rgb}. Using this 
 encoding of the image we can define a corresponding discrete function
 describing the image, by mapping the coordinates $(x,y)$ of an pixel
 and the
@@ -75,13 +79,13 @@ channel (color) $c$ to the respective value $v$
     \begin{tikzpicture}  
       \begin{scope}[x = (0:1cm), y=(90:1cm), z=(15:-0.5cm)]
         \node[canvas is xy plane at z=0, transform shape] at (0,0)
-        {\includegraphics[width=5cm]{Plots/Data/klammern_r.jpg}};
+        {\includegraphics[width=5cm]{Figures/Data/klammern_r.jpg}};
         \node[canvas is xy plane at z=2, transform shape] at (0,-0.2)
-        {\includegraphics[width=5cm]{Plots/Data/klammern_g.jpg}};
+        {\includegraphics[width=5cm]{Figures/Data/klammern_g.jpg}};
         \node[canvas is xy plane at z=4, transform shape] at (0,-0.4)
-        {\includegraphics[width=5cm]{Plots/Data/klammern_b.jpg}};
+        {\includegraphics[width=5cm]{Figures/Data/klammern_b.jpg}};
         \node[canvas is xy plane at z=4, transform shape] at (-8,-0.2)
-        {\includegraphics[width=5.3cm]{Plots/Data/klammern_rgb.jpg}};
+        {\includegraphics[width=5.3cm]{Figures/Data/klammern_rgb.jpg}};
       \end{scope}
     \end{tikzpicture}
   \end{adjustbox}
@@ -104,6 +108,14 @@ convolution
   (I * g)_{x,y,c} = \sum_{i,j,l \in \mathbb{Z}} I_{x-i,y-j,c-l} g_{i,j,l}.
 \]
 
+As images are finite in size for pixels close enough to the border
+that the filter ... the convolution is not well defined. In such cases
+padding can be used. With padding the image is enlarged beyond .. with
+0 entries to
+ensure the convolution is well defined for all pixels. If no padding
+is used the size of the output is reduced to \textit{size of input -
+  size of kernel +1} in each dimension.
+
 Simple examples for image manipulation using
 convolution are smoothing operations or
 rudimentary detection of edges in grayscale images, meaning they only
@@ -143,38 +155,38 @@ wise. Examples of convolution with both kernels are given in Figure~\ref{fig:img
   \centering
   \begin{subfigure}{0.3\textwidth}
     \centering
-    \includegraphics[width=\textwidth]{Plots/Data/klammern.jpg}
+    \includegraphics[width=\textwidth]{Figures/Data/klammern.jpg}
     \caption{Original Picture}
     \label{subf:OrigPicGS}
   \end{subfigure}
   \begin{subfigure}{0.3\textwidth}
     \centering
-    \includegraphics[width=\textwidth]{Plots/Data/image_conv9.png}
+    \includegraphics[width=\textwidth]{Figures/Data/image_conv9.png}
     \caption{\hspace{-2pt}Gaussian Blur $\sigma^2 = 1$}
   \end{subfigure}
   \begin{subfigure}{0.3\textwidth}
     \centering
-    \includegraphics[width=\textwidth]{Plots/Data/image_conv10.png}
+    \includegraphics[width=\textwidth]{Figures/Data/image_conv10.png}
     \caption{Gaussian Blur $\sigma^2 = 4$}
   \end{subfigure}\\
   \begin{subfigure}{0.3\textwidth}
     \centering
-    \includegraphics[width=\textwidth]{Plots/Data/image_conv4.png}
+    \includegraphics[width=\textwidth]{Figures/Data/image_conv4.png}
     \caption{Sobel Operator $x$-direction}
   \end{subfigure}
   \begin{subfigure}{0.3\textwidth}
     \centering
-    \includegraphics[width=\textwidth]{Plots/Data/image_conv5.png}
+    \includegraphics[width=\textwidth]{Figures/Data/image_conv5.png}
     \caption{Sobel Operator $y$-direction}
   \end{subfigure}
   \begin{subfigure}{0.3\textwidth}
     \centering
-    \includegraphics[width=\textwidth]{Plots/Data/image_conv6.png}
+    \includegraphics[width=\textwidth]{Figures/Data/image_conv6.png}
     \caption{Sobel Operator combined}
   \end{subfigure}
 %   \begin{subfigure}{0.24\textwidth}
 %     \centering
-%     \includegraphics[width=\textwidth]{Plots/Data/image_conv6.png}
+%     \includegraphics[width=\textwidth]{Figures/Data/image_conv6.png}
 %     \caption{test}
 %   \end{subfigure}
   \caption[Convolution applied on image]{Convolution of original greyscale Image (a)  with different
@@ -344,7 +356,7 @@ In order to illustrate this behavior we modeled a convolutional neural
 network to ... handwritten digits. The data set used for this is the
 MNIST database of handwritten digits (\textcite{MNIST},
 Figure~\ref{fig:MNIST}).
-\input{Plots/mnist.tex}
+\input{Figures/mnist.tex}
 The network used consists of two convolution and max pooling layers
 followed by one fully connected hidden layer and the output layer.
 Both covolutional layers utilize square filters of size five which are
@@ -359,7 +371,7 @@ The architecture of the convolutional neural network is summarized in
 Figure~\ref{fig:mnist_architecture}.
 
 \begin{figure}
-  \missingfigure{network architecture}
+  \includegraphics[width=\textwidth]{Figures/Data/convnet_fig.pdf}
   \caption{architecture}
   \label{fig:mnist_architecture}
 \end{figure}
@@ -380,7 +392,7 @@ gradient calculated on the subset it performs far better than the
 network using true gradients when training for the same mount of time.
 \todo{vergleich training time}
 
-\input{Plots/SGD_vs_GD.tex}
+\input{Figures/SGD_vs_GD.tex}
 \clearpage
 \subsection{\titlecap{modified stochastic gradient descent}}
 An inherent problem of the stochastic gradient descent algorithm is
@@ -631,7 +643,7 @@ Here it can be seen that the ADAM algorithm performs far better than
 the other algorithms, with AdaGrad and Adelta following... bla bla
 
 
-\input{Plots/sdg_comparison.tex}
+\input{Figures/sdg_comparison.tex}
 
 % \subsubsubsection{Stochastic Gradient Descent}
 \clearpage
@@ -741,23 +753,23 @@ mirroring.
 \begin{figure}[h]
   \centering
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist0.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist0.pdf}
     \caption{original\\image}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist_gen_zoom.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist_gen_zoom.pdf}
     \caption{random\\zoom}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist_gen_shear.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist_gen_shear.pdf}
     \caption{random\\shear}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist_gen_rotation.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist_gen_rotation.pdf}
     \caption{random\\rotation}
   \end{subfigure}
   \begin{subfigure}{0.19\textwidth}
-    \includegraphics[width=\textwidth]{Plots/Data/mnist_gen_shift.pdf}
+    \includegraphics[width=\textwidth]{Figures/Data/mnist_gen_shift.pdf}
     \caption{random\\positional shift}
   \end{subfigure}
   \caption[Image data generation]{Example for the manipuations used in ... As all images are
@@ -781,9 +793,9 @@ reduction in overfitting can be seen in
 accuracy decreases with test accuracy increasing. However utlitizing
 data generation as well as dropout with a probability of 0.4 seems to
 be a too aggressive approach as the training accuracy drops below the
-test accuracy. 
+test accuracy\todo{kleine begründung}. 
 
-\input{Plots/gen_dropout.tex}
+\input{Figures/gen_dropout.tex}
 
 \todo{Vergleich verschiedene dropout größen auf MNSIT o.ä., subset als
 training set?}
@@ -796,24 +808,56 @@ the available data can be highly limited.
 In these problems the networks are highly ... for overfitting the
 data. In order to get a understanding of accuracys achievable and the
 impact of the measures to prevent overfitting discussed above we and train
-the network on datasets of varying sizes.
-First we use the mnist handwriting dataset and then a slightly harder
-problem given by the mnist fashion dataset which contains PREEDITED
-pictures of clothes from 10 different categories.
-
-\input{Plots/fashion_mnist.tex}
-
-For training for each class a certain number of random datapoints are
-chosen for training the network. The sizes chosen are:
-full dataset: ... per class\\
-1000 per class
-100 per class
-10 per class
-
-the results for training .. are given in ... Here can be seen... that
-for small training sets data generation has a large impact on the accuracy.
-
-\begin{table}
+the network on datasets of varying sizes with different measures implemented.
+For training we use the mnist handwriting dataset as well as the fashion
+mnist dataset. The fashion mnist dataset is a benchmark set build by
+\textcite{fashionMNIST} in order to provide a harder set, as state of
+the art models are able to achive accuracies of 99.88\%
+(\textcite{10.1145/3206098.3206111}) on the handwriting set.
+The dataset contains 70.000 preprocessed images of clothes from
+zalando, a overview is given in Figure~\ref{fig:fashionMNIST}.
+
+\input{Figures/fashion_mnist.tex}
+
+\afterpage{
+  \noindent
+\begin{minipage}{\textwidth}
+  \small
+  \begin{tabu} to \textwidth {@{}l*4{X[c]}@{}}
+    \Tstrut \Bstrut    & \textsc{Adam} & D. 0.2 & Gen    & Gen.+D. 0.2  \\
+    \hline           
+    & 
+    \multicolumn{4}{c}{\titlecap{test accuracy for 1 sample}}\Bstrut    \\
+    \cline{2-5}
+    max     \Tstrut   & 0.5633        & 0.5312 & 0.6704 & 0.6604       \\
+    min               & 0.3230        & 0.4224 & 0.4878 & 0.5175       \\
+    mean              & 0.4570        & 0.4714 & 0.5862 & 0.6014       \\
+    var               & 0.0040        & 0.0012 & 0.0036 & 0.0023       \\
+    \hline
+    & 
+    \multicolumn{4}{c}{\titlecap{test accuracy for 10 samples}}\Bstrut  \\
+    \cline{2-5}
+    max       \Tstrut & 0.8585        & 0.9423 & 0.9310 & 0.9441       \\
+    min               & 0.8148        & 0.9081 & 0.9018 & 0.9061       \\
+    mean              & 0.8377        & 0.9270 & 0.9185 & 0.9232       \\
+    var               & 2.7e-4        & 1.3e-4 & 6e-05  & 1.5e-4       \\
+    \hline
+    & 
+    \multicolumn{4}{c}{\titlecap{test accuracy for 100 samples}}\Bstrut \\
+    \cline{2-5}
+    max               & 0.9637        & 0.9796 & 0.9810 & 0.9805       \\
+    min               & 0.9506        & 0.9719 & 0.9702 & 0.9727       \\
+    mean              & 0.9582        & 0.9770 & 0.9769 & 0.9783       \\
+    var               & 2e-05         & 1e-05  & 1e-05  & 0            \\
+    \hline
+  \end{tabu}
+  \normalsize
+  \captionof{table}{Values of the test accuracy of the model trained
+    10 times 
+    on random MNIST handwriting training sets containing 1, 10 and 100
+    data points per class after 125 epochs. The mean achieved accuracy
+    for the full set employing both overfitting measures is }
+  \small
   \centering
   \begin{tabu} to \textwidth {@{}l*4{X[c]}@{}}
     \Tstrut \Bstrut    & \textsc{Adam} & D. 0.2 & Gen    & Gen.+D. 0.2  \\
@@ -843,14 +887,51 @@ for small training sets data generation has a large impact on the accuracy.
     var               & 2e-05         & 1e-05  & 1e-05  & 0            \\
     \hline
   \end{tabu}
-  \caption{Values of the test accuracy of the model trained 10 times
-    of random training sets containing 1, 10 and 100 data points per
-    class.}
-\end{table}
+  \normalsize
+  \captionof{table}{Values of the test accuracy of the model trained 10 times
+    on random fashion MNIST training sets containing 1, 10 and 100 data points per
+    class. The mean achieved accuracy for the full dataset is: ....}
+\end{minipage}
+\clearpage  % if needed/desired
+}
+
+The random datasets chosen for training are made up of a certain
+number of datapoints for each class, which are chosen at random. The
+sizes chosen for the comparisons are the full dataset, 100, 10 and 1
+data points
+per class.
+
+For the task of classifying the fashion data a slightly altered model
+is used. The convolutional layers with filters of size 5 are replaced
+by two consecutive convolutional layers with filters of size 3.
+This is done in order to have more ... in order to better ... the data
+in the model. A diagram of the architecture is given in
+Figure~\ref{fig:fashion_MNIST}.
+
+For both scenarios the model are trained 10 times on randomly
+... training sets. Additionally models of the same architecture where
+a dropout layer with a ... 20\% is implemented and/or datageneration
+is used to augment the data during training. The values for the
+datageneration are given in CODE APPENDIX.
+
+The models are trained for 125 epoch to ensure enough random
+augmentations of the input images are considered to ensure
+convergence. The test accuracies of the models after training for 125
+epoch are given in Figure~\ref{...} for the handwriting
+and in Figure~\ref{...} for the fashion scenario. Additionally the
+average test accuracies of the models are given for each epoch in
+Figure ... and Figure...
+
+\begin{figure}
+  \includegraphics[width=\textwidth]{Figures/Data/cnn_fashion_fig.pdf}
+  \caption{Convolutional neural network architecture used to model the
+  fashion MNIST dataset.}
+  \label{fig:mnist_architecture}
+\end{figure}
 
 \begin{figure}[h]
   \centering
-  
+  \small
   \begin{subfigure}[h]{\textwidth}
     \begin{tikzpicture}
       \begin{axis}[legend cell align={left},yticklabel style={/pgf/number format/fixed,
@@ -861,16 +942,16 @@ for small training sets data generation has a large impact on the accuracy.
           =1.25pt}]
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_1.mean};  
+        {Figures/Data/adam_1.mean};  
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_02_1.mean};
+        {Figures/Data/adam_dropout_02_1.mean};
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_1.mean}; 
+        {Figures/Data/adam_datagen_1.mean}; 
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_02_1.mean};
+        {Figures/Data/adam_datagen_dropout_02_1.mean};
 
         
         \addlegendentry{\footnotesize{Default}}
@@ -894,16 +975,16 @@ for small training sets data generation has a large impact on the accuracy.
           =1.25pt}]
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_00_10.mean}; 
+        {Figures/Data/adam_dropout_00_10.mean}; 
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_02_10.mean}; 
+        {Figures/Data/adam_dropout_02_10.mean}; 
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_00_10.mean}; 
+        {Figures/Data/adam_datagen_dropout_00_10.mean}; 
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_02_10.mean};
+        {Figures/Data/adam_datagen_dropout_02_10.mean};
 
         
         \addlegendentry{\footnotesize{Default.}}
@@ -924,16 +1005,16 @@ for small training sets data generation has a large impact on the accuracy.
           =1.25pt}, ymin = {0.92}]
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_00_100.mean};
+        {Figures/Data/adam_dropout_00_100.mean};
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_dropout_02_100.mean}; 
+        {Figures/Data/adam_dropout_02_100.mean}; 
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_00_100.mean}; 
+        {Figures/Data/adam_datagen_dropout_00_100.mean}; 
         \addplot table
         [x=epoch, y=val_accuracy, col sep=comma, mark = none]
-        {Plots/Data/adam_datagen_dropout_02_100.mean}; 
+        {Figures/Data/adam_datagen_dropout_02_100.mean}; 
         
         \addlegendentry{\footnotesize{Default.}}
         \addlegendentry{\footnotesize{D. 0.2}}
@@ -945,27 +1026,29 @@ for small training sets data generation has a large impact on the accuracy.
     \vspace{.25cm}
   \end{subfigure}
   \caption{}
-  \label{mnist fashion}
+  \label{fig:MNISTfashion}
 \end{figure}
 
 \begin{figure}[h]
   \centering
   \missingfigure{datagen fashion}
-  \caption{Sample pictures of the mnist fashioyn dataset, one per
+  \caption{Sample pictures of the mnist fashion dataset, one per
     class.}
   \label{mnist fashion}
 \end{figure}
 
 
 \clearpage
-\section{Bla}
+\section{Schluss}
 \begin{itemize}
-  \item generate more data, GAN etc
+  \item generate more data, GAN etc \textcite{gan}
   \item Transfer learning, use network trained on different task and
-  repurpose it / train it with the training data
+  repurpose it / train it with the training data \textcite{transfer_learning}
+  \item random erasing fashion mnist 96.35\% accuracy \textcite{random_erasing}
 \end{itemize}
-\textcite{transfer_learning}
-\textcite{gan}
+
+
+
 
 %%% Local Variables:
 %%% mode: latex

TeX/main.tex

@@ -34,10 +34,13 @@
 \usepackage{todonotes}
 \usepackage{lipsum}
 \usepackage[ruled,vlined]{algorithm2e}
-\usepackage{showframe}
+%\usepackage{showframe}
 \usepackage[protrusion=true, expansion=true, kerning=true, letterspace
 = 150]{microtype}
 \usepackage{titlecaps}
+\usepackage{afterpage}
+\usepackage{xcolor}
+\usepackage{chngcntr}
 
 \captionsetup[sub]{justification=centering}
 
@@ -52,7 +55,123 @@
 \pgfplotsset{compat = 1.16}
 \usepackage[export]{adjustbox}
 
-
+\definecolor{maroon}{cmyk}{0, 0.87, 0.68, 0.32}
+\definecolor{halfgray}{gray}{0.55}
+\definecolor{ipython_frame}{RGB}{207, 207, 207}
+\definecolor{ipython_bg}{RGB}{247, 247, 247}
+\definecolor{ipython_red}{RGB}{186, 33, 33}
+\definecolor{ipython_green}{RGB}{0, 128, 0}
+\definecolor{ipython_cyan}{RGB}{64, 128, 128}
+\definecolor{ipython_purple}{RGB}{110, 64, 130}
+
+\usepackage{listings}
+\usepackage{float}
+
+\newfloat{lstfloat}{htbp}{lop}
+\floatname{lstfloat}{Listing}
+\def\lstfloatautorefname{Listing}
+
+\lstset{
+    breaklines=true,
+    %
+    extendedchars=true,
+    literate=
+    {á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
+    {Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
+    {à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
+    {À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
+    {ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
+    {Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
+    {â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
+    {Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
+    {œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
+    {ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
+    {€}{{\EUR}}1 {£}{{\pounds}}1
+}
+
+%%
+%% Python definition (c) 1998 Michael Weber
+%% Additional definitions (2013) Alexis Dimitriadis
+%% modified by me (should not have empty lines)
+%%
+\lstdefinelanguage{iPython}{
+  morekeywords={access,and,break,class,continue,def,del,elif,else,except,exec,finally,for,from,global,if,import,
+    in,is,lambda,not,or,pass,print,raise,return,try,while},%
+    %
+    % Built-ins
+    morekeywords=[2]{abs,all,any,basestring,bin,bool,bytearray,callable,chr,classmethod,cmp,compile,complex,delattr,dict,dir,divmod,enumerate,eval,execfile,file,filter,float,format,frozenset,getattr,globals,hasattr,hash,help,hex,id,input,int,isinstance,issubclass,iter,len,list,locals,long,map,max,memoryview,min,next,object,oct,open,ord,pow,property,range,raw_input,reduce,reload,repr,reversed,round,set,setattr,slice,sorted,staticmethod,str,sum,super,tuple,type,unichr,unicode,vars,xrange,zip,apply,buffer,coerce,intern,val},%
+    %
+    sensitive=true,%
+    morecomment=[l]\#,%
+    morestring=[b]',%
+    morestring=[b]",%
+    %
+    morestring=[s]{'''}{'''},% used for documentation text (mulitiline strings)
+    morestring=[s]{"""}{"""},% added by Philipp Matthias Hahn
+    %
+    morestring=[s]{r'}{'},% `raw' strings
+    morestring=[s]{r"}{"},%
+    morestring=[s]{r'''}{'''},%
+    morestring=[s]{r"""}{"""},%
+    morestring=[s]{u'}{'},% unicode strings
+    morestring=[s]{u"}{"},%
+    morestring=[s]{u'''}{'''},%
+    morestring=[s]{u"""}{"""},%
+    %
+    % {replace}{replacement}{lenght of replace}
+    % *{-}{-}{1} will not replace in comments and so on
+    literate=
+    {á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
+    {Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
+    {à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
+    {À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
+    {ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
+    {Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
+    {â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
+    {Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
+    {œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
+    {ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
+    {€}{{\EUR}}1 {£}{{\pounds}}1
+    %
+    {^}{{{\color{ipython_purple}\^{}}}}1
+    {=}{{{\color{ipython_purple}=}}}1
+    %
+    {+}{{{\color{ipython_purple}+}}}1
+    {*}{{{\color{ipython_purple}$^\ast$}}}1
+    {/}{{{\color{ipython_purple}/}}}1
+    %
+    {+=}{{{+=}}}1
+    {-=}{{{-=}}}1
+    {*=}{{{$^\ast$=}}}1
+    {/=}{{{/=}}}1,
+    literate=
+    *{-}{{{\color{ipython_purple}-}}}1
+     {?}{{{\color{ipython_purple}?}}}1,
+    %
+    identifierstyle=\color{black}\ttfamily,
+    commentstyle=\color{ipython_red}\ttfamily,
+    stringstyle=\color{ipython_red}\ttfamily,
+    keepspaces=true,
+    showspaces=false,
+    showstringspaces=false,
+    %
+    rulecolor=\color{ipython_frame},
+    frame=single,
+    frameround={t}{t}{t}{t},
+    framexleftmargin=6mm,
+    numbers=left,
+    numberstyle=\tiny\color{halfgray},
+    %
+    %
+    backgroundcolor=\color{ipython_bg},
+    %   extendedchars=true,
+    basicstyle=\scriptsize,
+    keywordstyle=\color{ipython_green}\ttfamily,
+    morekeywords = [3]{Int, Double},
+    morekeywords = [2]{foldRight, case},
+    keywordstyle = [3]{\color{ipython_purple}\ttfamily},
+    keywordstyle = [2]{\color{ipython_cyan}\ttfamily},
+}
 
 \usepackage[style=authoryear, backend=bibtex]{biblatex}
 \urlstyle{same}
@@ -103,14 +222,31 @@
 %\textbf{Seminar Machine--Learning: Unsupervised %Learning} \newline
 %Institut für Mathematik der Universität %Augsburg\\
 %Lehrstuhl für Rechnerorientierte Statistik und %Datenanalyse\\
-\smallskip\hrule\bigskip
 
 \begin{center}
-	{\huge{Electricity Price Forecasting based on Regression Tree Models}}
+  \huge \textbf{Master Thesis}\\
+  \vspace{1cm}
+  \Large \textbf{University Augsburg\\Department of Mathematics\\Chair of
+  Computational Statistics and Data Analysis}
+  \vspace{1cm}
+\end{center}
+
+\begin{figure}[h]
+  \centering
+  \includegraphics[scale=1.3]{Figures/Uni_Aug_Siegel_32Grad_schwarz.png}
+\end{figure}
+
+\begin{center}
+  \vspace{1cm}
+  \huge \textbf{TITLE Neural Network bla blub langer Titel}\\
+  \vspace{1cm}
+  \huge \textbf{Tim Tobias Arndt}\\
+  \vspace{1cm}
+  \Large \textbf{October 2020}
 \end{center}
-\hrulefill
+
 \pagenumbering{gobble}
-\newpage
+\clearpage
 %\setcounter{tocdepth}{4}
 \tableofcontents
 \clearpage

TeX/theo_3_8.tex

@@ -195,13 +195,13 @@ plot coordinates {
         height = 0.6\textwidth]
         \addplot table
         [x=x, y=y, col sep=comma, only marks,mark options={scale =
-          0.7}] {Plots/Data/overfit.csv};  
+          0.7}] {Figures/Data/overfit.csv};  
         \addplot [red, line width=0.8pt] table [x=x_n, y=s_n, col
-        sep=comma, forget plot] {Plots/Data/overfit.csv}; 
+        sep=comma, forget plot] {Figures/Data/overfit.csv}; 
         \addplot [black, line width=0.8pt] table [x=x_n, y=y_n, col
-        sep=comma] {Plots/Data/overfit.csv}; 
+        sep=comma] {Figures/Data/overfit.csv}; 
         \addplot [black, line width=0.8pt, dashed] table [x=x, y=y, col
-        sep=comma] {Plots/Data/overfit_spline.csv};
+        sep=comma] {Figures/Data/overfit_spline.csv};
 
         \addlegendentry{\footnotesize{data}};
         \addlegendentry{\footnotesize{$\mathcal{NN}_{\vartheta^*}$}};
@@ -950,7 +950,7 @@ results are given in Figure~\ref{fig:rs_vs_rs}, here it can be seen that in
 the intervall of the traing data $[-\pi, \pi]$ the neural network and
 smoothing spline are nearly identical, coinciding with the proposition.
 
-\input{Plots/RN_vs_RS}
+\input{Figures/RN_vs_RS}
 
 
 %%% Local Variables: