diff --git a/text/thesis/03Results.tex b/text/thesis/03Results.tex index 85ddadb..9b52e06 100644 --- a/text/thesis/03Results.tex +++ b/text/thesis/03Results.tex @@ -2,7 +2,7 @@ \label{chp:results} \section{Classification} \subsection{Comparison of methods of recording} - The different methods of recording (EEG, EMG and Low frequencies) also differ in the results. An ANOVA gives a $p$-Value of $2.09\cdot 10^{-8}$ ($F=108.29$) for all classifications done on 4 different movements and rest. + The different methods of recording (EEG, EMG and Low frequencies) also differ in the results. An ANOVA gives $p<0.001$ for all classifications done on 4 different movements and rest. \begin{figure} \centering \includegraphics[width=0.9\textwidth]{pictures/results/classEEGemgLF.png} @@ -45,7 +45,7 @@ % \caption{EMG-data without and with pause} % \label{fig:pauseEMG} % \end{figure} - When calculating an ANOVA on the data with and without pause we get a $p$-Value of $3.9\cdot 10^{-9}$ ($F=41.68$). + When calculating an ANOVA on the data with and without pause we get $p<0.001$. \subsection{EEG} In figure~\ref{fig:overviewEEG} the different settings for classification based on EEG-data are shown. Default has values as in \ref{mat:default}. The runs with pause leave out the data 1 second before the movement begins (cf. \ref{mat:pause}). Runs with offset have an offset of 1 or 2 (cf. \ref{mat:offset}). \begin{figure} @@ -63,11 +63,11 @@ \label{fig:overviewLF} \end{figure} \subsection{Trade-off parameter} - With a cross validation we compare the results for the soft-margin parameter for $\lambda=0.1,1,10$. The results are shown in figure~\ref{fig:svmCV}. + With a cross validation we compare the results for the soft-margin parameter for $\lambda=0.1,1,10$. The results are shown in figure~\ref{fig:svmCV}.%TODO \section{Regression} \subsection{Comparison of methods of recording} \subsubsection{Velocities} - Predicting velocities from EEG, EMG and Low Frequencies is significantly\footnote{$p\approx1.4\exp{-65}$} pairwise different (cf. figure~\ref{fig:corrEEGemgLF}). The corresponding $p$-Values of the ANOVA are given in table~\ref{tab:pCorr}. + Predicting velocities from EEG, EMG and Low Frequencies is significantly\footnote{$p<0.001$} pairwise different (cf. figure~\ref{fig:corrEEGemgLF}). The corresponding $p$-Values of the ANOVA are given in table~\ref{tab:pCorr}. \begin{figure} \centering \includegraphics[width=0.9\textwidth]{pictures/results/corrEEGemgLF.png} @@ -80,16 +80,16 @@ \begin{array} {r||c|c|c} &EEG&EMG&LF\\\hline - EEG&-&4.7\exp{-17}&3.7\exp{-55}\\ - EMG&4.7\exp{-17}&-&1.2\exp{-7}\\ - LF&3.7\exp{-55}&1.2\exp{-7}&- + EEG&-&<0.001&<0.001\\ + EMG&<0.001&-&<0.001\\ + LF&<0.001&<0.001&- \end{array} \end{math} \caption{$p$-Values for prediction of velocities from EEG, EMG or LF respectively} \label{tab:pCorr} \end{table} \subsubsection{Positions} - Predicting positions from EEG, EMG and Low Frequencies is significantly\footnote{$p\approx2.1\exp{-223}$} different, however not pairwise (cf. figure~\ref{fig:corrEEGemgLFpos}). Positions predicted from EMG and LF are not significantly different. The corresponding $p$-Values of the ANOVA are given in table~\ref{tab:pCorrPos}. + Predicting positions from EEG, EMG and Low Frequencies is significantly\footnote{$p<0.001$} different, however not pairwise (cf. figure~\ref{fig:corrEEGemgLFpos}). Positions predicted from EMG and LF are not significantly different. The corresponding $p$-Values of the ANOVA are given in table~\ref{tab:pCorrPos}. \begin{figure} \centering \includegraphics[width=0.9\textwidth]{pictures/results/corrEEGemgLFpos.png} @@ -102,9 +102,9 @@ \begin{array} {r||c|c|c} &EEG&EMG&LF\\\hline - EEG&-&3.2\exp{-91}&2.3\exp{-204}\\ - EMG&3.2\exp{-91}&-&0.34\\ - LF&2.3\exp{-204}&0.34&- + EEG&-&<0.001&<0.001\\ + EMG&<0.001&-&0.34\\ + LF&<0.001&0.34&- \end{array} \end{math} \caption{$p$-Values for prediction of positions from EEG, EMG or LF respectively} @@ -112,7 +112,7 @@ \end{table} \subsection{Compare Prediction direct and via Synergies} \subsubsection{Velocities} - There is a significant\footnote{$p\approx1.7\exp{-24}$} difference between the predictions. The different synergies however have no significant difference ($p\approx0.87$). Also see figure~\ref{fig:directVia}. + There is a significant\footnote{$p<0.001$} difference between the predictions. The different synergies however have no significant difference ($p\approx0.87$). Also see figure~\ref{fig:directVia}. \begin{figure} \centering \includegraphics[width=\textwidth]{pictures/results/predictKinfromEEG.png} @@ -120,7 +120,7 @@ \label{fig:directVia} \end{figure} \subsubsection{Positions} - There is a significant\footnote{$p\approx2.7\exp{-146}$} difference between the predictions. The different synergies however have no significant difference ($p\approx0.85$). Also see figure~\ref{fig:directViaPos}. + There is a significant\footnote{$p<0.001$} difference between the predictions. The different synergies however have no significant difference ($p\approx0.85$). Also see figure~\ref{fig:directViaPos}. \begin{figure} \centering \includegraphics[width=\textwidth]{pictures/results/predictPosfromEEG.png} @@ -131,7 +131,7 @@ \subsubsection{Offset} Offset makes no significant difference when predicting Synergies\footnote{Autoencoder: $p\approx0.81$, PCA: $p\approx0.77$, NMF: $p\approx0.60$} or velocities ($p\approx0.99$) or positions ($p\approx0.98$). \subsubsection{Pause} - Whether there is a pause of 1s or only 0.5s doesn't make a significant difference for Autoencoder ($p\approx0.13$), PCA ($p\approx0.29$), NMF ($p\approx0.054$) or Velocities ($p\approx0.95$). + Whether there is a pause of 1s or only 0.5s doesn't make a significant difference for Autoencoder ($p\approx0.13$), PCA ($p\approx0.29$), NMF ($p\approx0.05$) or Velocities ($p\approx0.95$). \subsection{EMG} Using a offset or not does not make any difference since the offset is only applied on EEG-data (cf. \ref{mat:offset}).\\ Predicting synergies from EMG does not make sense since they are computed from EMG (cf. \ref{mat:synergies}).\\ @@ -142,7 +142,7 @@ Offset makes no significant difference for predicting Autoencoder ($p\approx0.50$), PCA ($p\approx0.59$), NMF ($p\approx0.38$), velocities ($p\approx0.97$) or position ($p\approx1.0$). \subsubsection{Pause} There is no effect of pause for velocities from low frequencies ($p\approx0.73$).\\ - However there is an effect for Autoencoder ($p\approx3.2\exp{-6}$), PCA ($p\approx0.0001$) and NMF ($p\approx3.7\exp{-9}$). + However there is an effect for Autoencoder ($p<0.001$), PCA ($p<0.001$) and NMF ($p<0.001$). The plot shows a better performance with a shorter pause and more data taken in (see figure~\ref{fig:lfToAutoencPause}) \begin{figure}