# Dimension Reduction Using New Bond Graph Algorithm and Deep Learning Pooling on EEG Signals for BCI
## 4 Experiment and Results
### Experiments and Scenarios
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Public** & **Parameters** & **PSO** & **GA** & **BGA\_Model1** & **BGA\_Model2** & **BGA\_Model3** & **BGA\_Model4** \\ \hline \multirow{4}{*}{Schwefeel} & Mean & 0.19 & 2.04 & \(3.71\times 10^{11}\) & \(4.21\times 10^{-3}\) & \(\mathbf{3.80\times 10^{-56}}\) & \(7.44\times 10^{-46}\) \\  & Std & 0.35 & 0.28 & \(1.33\times 10^{11}\) & \(2.29\times 10^{4}\) & \(\mathbf{1.40\times 10^{-55}}\) & \(1.59\times 10^{-45}\) \\
2.22 & Min & 0.01 & 1.58 & \(1.33\times 10^{+2}\) & \(34.77\) & \(\mathbf{5.31\times 10^{-61}}\) & \(9.97\times 10^{-52}\) \\  & Max & 1.60 & 2.59 & \(5.91\times 10^{112}\) & \(1.27\times 10^{-55}\) & \(\mathbf{7.65\times 10^{-55}}\) & \(5.47\times 10^{-45}\) \\ \hline \multirow{4}{*}{Rastrigin} & Mean & \(1.06\times 10^{+2}\) & 20.52 & \(8.36\times 10^{+2}\) & \(4.67\times 10^{+2}\) & \(\mathbf{0.00}\) & 0.00 \\  & Std & 18.95 & 2.87 & \(1.02\times 10^{+2}\) & \(1.00\times 10^{+2}\) & \(\mathbf{0.00}\) & 0.00 \\  & Min & 59.34 & 14.04 & \(6.12\times 10^{+2}\) & \(2.90\times 10^{+2}\) & \(\mathbf{0.00}\) & 0.00 \\  & Max & \(1.42\times 10^{+2}\) & 26.09 & \(9.83\times 10^{+2}\) & \(6.59\times 10^{+2}\) & \(\mathbf{0.00}\) & 0.00 \\ \hline \multirow{4}{*}{Schwefeel} & Mean & \(-1.00\times 10^{+50}\) & \(-2.54\times 10^{+3}\) & \(-7.84\times 10^{+3}\) & \(-7.99\times 10^{+3}\) & \(\mathbf{-8.06\times 10^{+3}}\) & \(-7.90\times 10^{+3}\) \\  & Std & \(1.95\times 10^{+50}\) & \(4.84\times 10^{+2}\) & \(2.83\times 10^{+2}\) & \(2.31\times 10^{+2}\) & \(\mathbf{4.85\times 10^{+2}}\) & \(5.41\times 10^{+2}\) \\  & Min & \(-7.40\times 10^{+50}\) & \(-3.82\times 10^{+3}\) & \(-8.65\times 10^{+3}\) & \(-8.44\times 10^{+3}\) & \(\mathbf{-9.30\times 10^{+3}}\) & \(-1.01\times 10^{+4}\) \\  & Max & \(-5.80\times 10^{+50}\) & \(-1.78\times 10^{+3}\) & \(-7.32\times 10^{+3}\) & \(-7.62\times 10^{+3}\) & \(\mathbf{-7.22\times 10^{+3}}\) & \(-7.07\times 10^{+3}\) \\ \hline \multirow{4}{*}{Ackley} & Mean & 1.49 & 2.53 & 19.36 & 13.97 & \(\mathbf{-8.90\times 10^{-16}}\) & \(-8.90\times 10^{-16}\) \\  & Std & 0.75 & 0.33 & 0.54 & 2.81 & \(\mathbf{0.00}\) & 0.00 \\  & Min & 0.05 & 1.81 & 18.25 & 7.93 & \(\mathbf{-8.90\times 10^{-16}}\) & \(-8.90\times 10^{-16}\) \\  & Max & 3.71 & 3.07 & 20.01 & 18.15 & \(\mathbf{-8.90\times 10^{-16}}\) & \(-8.90\times 10^{-16}\) \\ \hline \multirow{4}{*}{Griewank} & Mean & 0.10 & 1.36 & \(3.64\times 10^{+2}\) & \(1.49\times 10^{+2}\) & \(\mathbf{0.00}\) & 0.00 \\  & Std & 0.16 & 0.09 & 52.38 & 70.58 & \(\mathbf{0.00}\) & 0.00 \\ \cline{1-1}  & Min & 0.01 & 1.20 & \(2.91\times 10^{+2}\) & 32.94 & \(\mathbf{0.00}\) & 0.00 \\ \cline{1-1}  & Max & 0.83 & 1.54 & \(4.68\times 10^{+2}\) & \(2.81\times 10^{+2}\) & \(\mathbf{0.00}\) & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(Cont.\) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Function** & **Dimension** & **Initial Range** \\ \hline Volunteers (subjects) & 9 & 9 \\ Electrodes (channels) & 22 & 22 \\ Session–Trials & 1–228 & 1–228 \\ Imagination Time–Sample & 4 s-250 & After 0.5 s,3.5 s-250 \\ Rate & 1000 & 875 \\ Classes & Left–right hand, foot, and tongue & Left–right hand \\ Filtering & - & 9 filter banks \\ Order of filtering & - & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The details of data set IIa from BCI competition IV. solutions to problems by reducing the dimension for different modes and extracting each case individually. In this approach, a set of features in the elements is used to represent the location of features in the channels. In the following, we present the details of the models (seven model scenarios) used in our experiments for dimension reduction before the feature extraction (three-dimensional reduction) and the models that are used for dimension reduction after feature extraction:  
1. The first model scenario: a filter bank with one channel for each participant is examined by four algorithms with ELM [61; 62] classification.