\chapter{Discussion}
\label{chp:dis}
\section{EMG}
\label{dis:emg}
    Predictions of velocities and positions are quite bad from EMG.
    The prediction of the $y$-dimension is a bit better than $x$ ($p<0.05$) for velocities. For positions there is no significant difference ($p\approx 0.31$). Predicting $\theta$ is worse significantly ($p<0.001$) for positions and velocities (also see tables \ref{tab:corrKin} and \ref{tab:corrPos}). %Results?

    A correlation about $0.2$ cannot be used for a BCI. There might be some way of improving the predictions and it might be done several times to higher the correlations, finding another approach however is more promising.\\
    In addition when a BCI is needed often the are no EMG signals since the muscles do not work as they are told (e.g. after stroke) and so do not generate the corresponding activity.

    Out of these reasons we only use EMG as benchmark for other approaches: If the muscles would work this correlation could be reached.
\section{EEG}
\label{dis:eeg}
    Predictions from EEG to velocities and position are significantly better than those from EMG (see tables \ref{tab:pCorr},~\ref{tab:corrKin},~\ref{tab:pCorrPos} and \ref{tab:corrPos}).\\
    This might be because EMG has a hard time classifying the different movements due to massive activity while moving. This can be seen in the confusion matrix (\ref{fig:cmEMG}). Many data points belonging to class 2 or 4 are classified as 3 in error. The classification between movement and rest however works fine.\\
    All in all few samples are classified as class 2 even though the training was done on a balanced set. This could mean that features of class 2 are found in other classes too and by that do not have strong predictive power.

    The classification results we found for EEG are similar to them of \cite{Shiman15}. They found a classification accuracy of 39.5\%, we have a mean classification of 40.4\% and for targets only (no rest) even 43.6\%. However our findings for discrimination of movement and rest in EEG are a lot worse ($64.6\%$ vs. $38.5\%$). This is probably due to the training of our SVM since when only discriminating between movement and rest we also score $57.1\%$. Higher frequencies with more muscle artifacts (cf. \ref{res:topo} and \ref{dis:topo}) are more predictive for the difference between movement or rest however less predictive for the different classes. So the SVM when trained to distinguish the classes gives higher predictive power to the lower frequencies.

    When predicting velocities or positions from EEG there is no significant difference between $x$ and $y$. The difference between $x$ and $y$ and the angle $\theta$ is larger for velocities than for absolute positions since the absolute angle prediction a lot better than the prediction of change.\\
    This again is an indication that the actual position is more important for the activity in brain than the change of position as itself.
\section{Low Frequencies}
\label{dis:lf}
    Our findings concerning low frequencies are a lot less promising than e.g. in \cite{Lew14}.\\
    The reason for that might be that the movements were not self induced but extrinsically motivated by a cue. \citeauthor{Lew14} however use low frequencies exactly for the purpose to detect voluntary movement.\\
    We show that the use of low frequencies (at least as we did it here) has no advantage over the use of EMG (see table \ref{tab:pCorr}). This might also be a hint that movement artifacts were have the biggest part in low frequencies while moving. This however makes it impossible to use them for continuous tasks.\\
    Low frequencies are great to early detect voluntary movement but are not applicable in our configuration.

    Which is interesting nevertheless is, that low frequencies also occur in rest. Quite some of the movements are classified as rest (see figure \ref{fig:cmFull}). If a sample is classified correctly as movement it is quite likely that is is also classified correctly - however with an preference on class 3 again. This matches the understanding of low frequencies as pre-movement activation mainly belonging to voluntary movement. The subjects probably plan all the possible movements while in rest to execute then once the stimulus was shown.
\section{Velocities and Positions}
\label{dis:velPos}
    We expected better performance when predicting velocities instead of absolute positions. Our findings however show the opposite. The performance is quite a lot better when predicting positions directly.\\
    This might mean that both EMG and EEG data carry more information about the actual configuration and not only about the change.

    Our findings do not match them of \cite{Ofner12} who found similar results for position and movement. However the task used by \citeauthor{Ofner12} was different from ours as they used self-motivated movement.
\section{Pause}
\label{dis:pause}
    The use of a 1 second pause before movement onset only shows significant differences for classification of EMG and predicting Synergies from low frequencies.
    \subsection{Classification from EMG}
        When doing classification from EMG data there is an great improvement when leaving the whole second before movement onset out. This results from the way we did the classification. Since we decided on when the movement starts based on the EMG data.\\
        What this finding shows is that the threshold is chosen well to classify the movements.
    \subsection{Synergies from Low Frequencies}
        There is a significant improvement for predicting Synergies from low frequency data. This shows again what \cite{Lew14} proposed; in low frequency features we find mainly pre-movement activation. Activity while moving is probably mostly occluded by motor commands.
\section{Offset}
\label{dis:offset}
    Applying an offset when using EEG-data or not does not make a significant difference. This is probably due to our configuration with EEG windows as large as 1 second. If smaller windows were used an offset could help, here there is no difference.
\section{Synergies}
\label{dis:synergies}
    \subsection{Number of Synergies}
    \label{dis:noSyn}
        As shown in section~\ref{res:noSyn} 2 and 4 Synergies are good values for Autoencoder since the slope of the mean prediction is steeper before than after. Another neuron doesn't improve the result as much as the last.\\
        For PCA and NNMF this value is reached at 3 as figure \ref{fig:noSyn} shows.
    \subsection{Autoencoder, PCA or NMF}
        In many applications the synergies computed with different methods perform similar, however some differences can be found.
        \subsubsection{Prediction from EEG}
            PCA data is predicted from EEG significantly worse than e.g. autoencoder data ($p<0.001$). Between NMF and autoencoder there is no significant difference.\\
            We conclude autoencoder and NMF are to prefer when looking for good predictability from EEG.
        \subsubsection{Number of Synergies}
            With our data we can not show a better performance of an autoencoder with only 2 synergies. Similar to the other methods of synergy calculation there is a significant decrease in predictive performance.
    \subsection{Prediction via Synergies}
        Of course the prediction via Synergies is a bit worse than direct prediction, since the machine learning techniques could do the same dimensionality reduction and also much more.\\
        This decrease however is not large which suggests that synergies are a valid step in between.\\
        In addition the prediction of synergies from EEG are significantly ($p<0.05$) better than the prediction of EMG. So the representation as synergies probably matches the representation in the brain better. This could mean that the controlling of a prostheses should be done via synergies - representing the representation in the brain and being easier to implement than a prosthesis listening to 32 EEG channels.
    \subsection{Comparison with EMG}
        The results show that the dimensionality reduction from 6 dimensional EMG to 3 dimensional Synergies (here via autoencoder) does not cost much information when predicting velocities and positions.\\
        For velocities there is no significant difference and even for positions the mean only differs about $0.03$ (EMG: $0.23$, Autoencoder: $0.20$).\\
        For the use of Synergies this is a great sign: Most of the information being present in the muscle activity can be condensed to few synergies. This strongly supports the idea of synergies.\\
        Figure \ref{fig:predictEMGSyn} shows that Synergies can be predicted better from EEG than EMG. Part of this effect may be explained by lower dimensionality however this is not the only reason since PCA is predicted similarly well as EMG. Another explanation is that Synergies represent an intermediate step between EEG and EMG. They are lacking some of the instability and noise of EMG and at the same time are more focused than the EEG signal.
\section{Topographical information}
\label{dis:topo}
    In the beta channel (see figure \ref{fig:topoBeta}) we see high activity in the right hemisphere. This is probably an artifact of muscle movements since the commands to drive the right arm should be produced in the left hemisphere.\\
    However - as we see in prediction from EMG - the muscle activity is not very predictive for the direction of movement. EEG is even better than EMG meaning there has to be more information the decision is based on than movement artifacts.\\
    This information for example can be found in the alpha band (see figure \ref{fig:topoAlpha}). Here we see clear activation in the left hemisphere and no impact of movement artifacts since the right hemisphere shows no prominent activation.\\
    What is interesting in the alpha band is that main activation is measured in the occipital lobe usually associated with visual processing. Since the cue was presented auditory our findings support the idea of the dorsal pathway. This pathway is often called \qq{Where Path} or sometimes \qq{How Path} of visual processing opposing to the ventral \qq{What Path} (cf. \cite{Ungerleider82}). The dorsal pathway is said to be involved in reaching tasks. This is supported by our findings.

    When comparing reaches to different targets we also find differences in other brain regions. For example when comparing classes 2 and 4 we find differences differences in anterior regions of the parietal lobe (see figure \ref{fig:topoAlpha24}). Positive values stand for higher activation in class 2.
    \begin{figure}
        \centering
        \includegraphics[width=0.9\textwidth]{pictures/results/topoAlpha24.png}
        \caption{Differences in activity comparing class 2 and 4 in alpha band for subject FS in the 3rd session}
        \label{fig:topoAlpha24}
    \end{figure}