diff --git a/rsc/cnn_architecture.png b/rsc/cnn_architecture.png new file mode 100644 index 0000000..f5588ff Binary files /dev/null and b/rsc/cnn_architecture.png differ diff --git a/src/materialandmethods.tex b/src/materialandmethods.tex index 4585a3a..d0a78b0 100644 --- a/src/materialandmethods.tex +++ b/src/materialandmethods.tex @@ -16,6 +16,24 @@ \subsubsection{ROC and AUC} \subsubsection{RESNet} \subsubsection{CNN} +Convolutional neural networks are especially good model architectures for processing images, speech and audio signals. +A CNN typically consists of Convolutional layers, pooling layers and fully connected layers. +Convolutional layers are a set of learnable kernels (filters). +Each filter performs a convolution operation by sliding a window over every pixel of the image. +On each pixel a dot product creates a feature map. +Convolutional layers capture features like edges, textures or shapes. +Pooling layers sample down the feature maps created by the convolutional layers. +This helps reducing the computational complexity of the overall network and help with overfitting. +Common pooling layers include average- and max pooling. +Finally, after some convolution layers the feature map is flattened and passed to a network of fully connected layers to perform a classification or regression task. + +\begin{figure}[h] + \centering + \includegraphics[width=\linewidth]{../rsc/cnn_architecture} + \caption{Architecture convolutional neural network. Image by \href{https://cointelegraph.com/explained/what-are-convolutional-neural-networks}{SKY ENGINE AI}} + \label{fig:cnn-architecture} +\end{figure} + \subsubsection{Softmax} The Softmax function converts $n$ numbers of a vector into a probability distribution. @@ -24,7 +42,7 @@ Its a generalization of the Sigmoid function and often used as an Activation Lay \sigma(\mathbf{z})_j = \frac{e^{z_j}}{\sum_{k=1}^K e^{z_k}} \; for j\coloneqq\{1,\dots,K\} \end{equation} -The softmax function has high similarities with the Bolzmann distribution. \cite{Boltzmann} +The softmax function has high similarities with the Boltzmann distribution and was first introduced in the 19$^{\textrm{th}}$ century~\cite{Boltzmann}. \subsubsection{Cross Entropy Loss} % todo maybe remove this \subsubsection{Adam}