From d2727f37f91be46c6d3ab31dfcf4c9e8ff9c54c7 Mon Sep 17 00:00:00 2001 From: paul-loedige Date: Fri, 29 Jan 2021 18:39:33 +0100 Subject: [PATCH] 2. Vorlesung semi-supervised Learning abgeschlossen --- .../Deep Learning.tex | 61 +++++++++++++++++- images/cnn_building_blocks.png | Bin 0 -> 189637 bytes images/cnn_complete.png | Bin 0 -> 182196 bytes images/cnn_example1.png | Bin 0 -> 26613 bytes images/cnn_example_stride1.png | Bin 0 -> 43889 bytes images/cnn_example_stride2.png | Bin 0 -> 41600 bytes images/cnn_feature_map1.png | Bin 0 -> 84592 bytes images/cnn_feature_map2.png | Bin 0 -> 86624 bytes images/cnn_inter_layer_connection.png | Bin 0 -> 26926 bytes images/convolutional filter.png | Bin 0 -> 58155 bytes images/convolutional_operation.png | Bin 0 -> 122510 bytes images/convolutional_vs_fully-connected.png | Bin 0 -> 119803 bytes images/max_pooling.png | Bin 0 -> 82360 bytes images/non-linear_functions.png | Bin 0 -> 64436 bytes images/subsampling.png | Bin 0 -> 158181 bytes 15 files changed, 60 insertions(+), 1 deletion(-) create mode 100644 images/cnn_building_blocks.png create mode 100644 images/cnn_complete.png create mode 100644 images/cnn_example1.png create mode 100644 images/cnn_example_stride1.png create mode 100644 images/cnn_example_stride2.png create mode 100644 images/cnn_feature_map1.png create mode 100644 images/cnn_feature_map2.png create mode 100644 images/cnn_inter_layer_connection.png create mode 100644 images/convolutional filter.png create mode 100644 images/convolutional_operation.png create mode 100644 images/convolutional_vs_fully-connected.png create mode 100644 images/max_pooling.png create mode 100644 images/non-linear_functions.png create mode 100644 images/subsampling.png diff --git a/chapters/Semi-supervised Learning/Deep Learning.tex b/chapters/Semi-supervised Learning/Deep Learning.tex index 1d2f809..7b576b0 100644 --- a/chapters/Semi-supervised Learning/Deep Learning.tex +++ b/chapters/Semi-supervised Learning/Deep Learning.tex @@ -57,5 +57,64 @@ Ein Beispiel für die einzelnen Features könnte wie folgt aussehen:\\ \includegraphics[width = \textwidth]{car features.png} - \section{\ac{CNN}} + \section{\acp{CNN}} \label{cnn} + \acp{CNN} enthalten 3 wichtige Bestandteilen:\\ + \includegraphics[width=.8\textwidth]{cnn_building_blocks.png}\\ + Diese Bestandteile können beliebig oft hintereinander geschaltet sein. + Zudem ist an ein komplettes \ac{CNN} zumeist noch ein weiteres Netzwerk für die Ausgabe der Vorhersage angeschlossen:\\ + \includegraphics[width = \textwidth]{cnn_complete.png} + + \subsection{convolutional stage} + \label{cnn: convolutional stage} + In der \say{convolutional stage} werden \say{convolutional layer} (Faltunsschicht) verwendet. + Diese wenden einen beweglichen Filter (detector) auf die Daten der vorhergegangenen Schicht an. + Hierbei stellt der detector ein Rezeptives Feld dar (vergleichbar mit dem Auge).\\ + \includegraphics[width = \textwidth]{convolutional_operation.png}\\ + \begin{wrapfigure}{h}{.4\textwidth} + \includegraphics[width = .4\textwidth]{cnn_inter_layer_connection.png} + \end{wrapfigure} + Aufgrund der geringen Größe des rezeptiven Feldes ist jedes Neuron in der nachfolgenden Schicht jeweils nur mit wenigen Neuronen in der unterliegenden Schicht verbunden:\\ + \includegraphics[width=\textwidth]{convolutional filter.png}\\ + + \subsubsection{Beispiel} + \label{cnn: example} + Im folgenden wird das Verfahren des convolutional layers anhand von $3\times 3$ Filtern demononstriert. + Diese werden auf einem $6\times 6$ Bild verschoben. + Die Filter sollen jeweils unterschiedliche geometrische Formen erkennen (Filter1: Diagonalen)\\ + \includegraphics[width=.8\textwidth]{cnn_example1.png}\\ + Über den Parameter \say{stride} kann eingestellt werden, um wieviele Elemente der Filter jeweils verschoben wird:\\ + \includegraphics[width = .8\textwidth]{cnn_example_stride1.png}\\ + \includegraphics[width = .8\textwidth]{cnn_example_stride2.png}\\ + Für jeden Filter entsteht durch diese Anwendung ein kleineres Bild, welches aus dem Ausgangsbild errechnet wurde:\\ + \includegraphics[width=.8\textwidth]{cnn_feature_map1.png}\\ + Durch die Anwendung der verschiedenen Filter entsteht hierbei eine mehrdimensionale \say{Feature Map}. + Diese wird allgemein als \say{Tensor} bezeichnet:\\ + \includegraphics[width=.8\textwidth]{cnn_feature_map2.png}\\ + + \subsubsection{Convolutional vs. Fully Connected} + \label{cnn: convolutional vs. fully connected} + Der Vorteil, den der Ansatz der Faltungsschichten gegenüber dem einsatz von \say{fully connected layers} hat ist, + dass deutlich weniger Parameter benötigt werden.\\ + \includegraphics[width = .8\textwidth]{convolutional_vs_fully-connected.png} + + \subsection{non-linear stage} + \label{cnn: non-linear stage} + Es ist mathematisch beweisbar, dass für die Abbildung von gleichen Äquivalenzklassen auf eine Referenzklasse eine nicht-linear Funktion benötigt wird. + Hierbei gibt es mehrere mögliche Funktionen. + Die bekannteste ist hierbei die \say{Sigmoid}-Funktion. + Bei \acp{CNN} wird allerdings meistens die \say{ReLU}-Funktion verwendet.\\ + \includegraphics[width = \textwidth]{non-linear_functions.png} + + \subsection{Pooling} + \label{cnn:pooling} + Beim \say{Pooling} wird die Menge der Elemente in einer Schicht reduziert. + Hierbei wird darauf geachtet, dass nur unwichtige Daten \say{verloren gehen}. + Man spricht auch von \say{Subsampling}.\\ + \includegraphics[width = .8\textwidth]{subsampling.png} + + \subsubsection{Max Pooling} + \label{cnn: max pooling} + Das \say{Max Pooling} ist eine Form des Poolings, bei dem mehrere Elemente einer schicht dadurch zusammengefasst werden, + dass nur die Element mit dem höchsten Wert erhalten bleiben.\\ + \includegraphics[width = .8\textwidth]{max_pooling.png} \ No newline at end of file diff --git a/images/cnn_building_blocks.png b/images/cnn_building_blocks.png new file mode 100644 index 0000000000000000000000000000000000000000..65cbf0740e008ad4078a4d71e8d96b21e13a4d50 GIT binary patch literal 189637 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