\chapter{Materials and Methods}
\label{mat}
\section{Tools}
    \subsection{EEG}
        Electroencephalography (EEG) is often used for non-invasive BCIs because it's cheap and easier to use than e.g. fMRI. The electrodes have to be spread over the scalp. To allow for comparability there are standardized methods for this. These methods also bring a naming convention with them.
        \subsubsection{10-20 system}
            In this standard adjacent electrodes are placed either 10\% or 20\% of the total front-back or left-right distance apart. This standardization also makes it possible to name each electrode or rather here place. This is done with capital letters for lobes (Frontal, \qq{Central}, Parietal, Occipital and Temporal) and numbers for the specific place on the lobe. Even numbers are on the right side of the head, odd on the left; larger numbers are closer to the ears, lower numbers closer to the other hemisphere. The exact number now refers to the exact position: $$\left\lceil\frac{x}{2}\right\rceil\cdot \frac{d}{10}$$ where $x$ is the number and $d$ the diameter of the scalp. Electrodes in the centre are named with a lower case $z$ e.g. $Cz$.\\ %TODO: figure
            Electrodes between two lobes (10\% instead of 20\% distance) are named with the both adjacent lobes (anterior first) e.g. $FCz$ (between frontal and central lobe).
            Also see figure~\ref{fig:10-20}.
        \begin{figure}[!p]
            \centering
            \includegraphics[width=1\textwidth]{eeg_electrodes_10-20.png}
            \caption{Full 10-20 system}
            \label{fig:10-20}
        \end{figure}
        \subsubsection{Pburg}

\subsection{PCA}
\label{tool:pca}
\subsection{NMF}
\label{tool:nmf}
\subsection{Autoencoder}
\label{tool:autoenc}