## 4 Pattern Recognition
### Restricted Boltzmann Machines
The step-up value of 0.1 was selected because higher increments made the learning unstable. A cost value of \(2\cdot 10^{-4}\) was selected since it facilitated the learning process of CD by increasing the mixing rate of the Markov chain. All the algorithms were implemented using Matlab(tm) on Windows(tm) 7 professional 64-bit operating system. The computer used to run the algorithms had an Intel(r) CPU E5-2618L v3 @ 2.30 Ghz with 16 cores and 24 GB RAM. ## 6 Results

For the first part of the results, the classification accuracy (or mapping accuracy in the case of SOM) was obtained for each algorithm using a frequency band of (8-30) Hz and no regression filtering over the EOG. Then, the band was reduced for all subjects to (8-12) Hz and (22-30) Hz using an average of the frequencies obtained in [37], and the EOG artifacts were also reduced through the regression procedure. ### Frequency Band of (8-30) Hz and no EOG Filtering

First, for a better comparison, the frequency response of every subject is shown in Figure 13. It is then followed by the results of SOM shown in Figure 14, which shows the final internal representation of the two classes inside the SOM network for each subject. Furthermore, Table 2 shows the winner neuron of the SOM for both classes for each subject. Table 3 shows the resultant training and testing accuracy of the four remaining methods. Figure 13: The average frequency response over three bipolar recordings: C3, Cz and C4. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Class 1 & 45 & 78 & 75 & 12 & 85 & 13 & 72 & 26 & 67 \\ \hline Class 2 & 46 & 67 & 72 & 86 & 73 & 22 & 42 & 26 & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The position of the the winner neuron for Class 1 and Class 2 of SOM with a frequency band of (8–30) Hz and no regression filtering over the EOG. Figure 14: SOM representation of the different classes for the nine different subjects, including the winner neuron. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline  & & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Train & LDA & 65 & 57 & 57 & 78 & 68 & 58 & 67 & 70 & 72 \\  & SVM & 83 & 93 & 98 & 99 & 99 & 94 & 96 & 94 & 98 \\  & BP & 66 & 56 & 56 & 77 & 68 & 58 & 67 & 71 & 72 \\  & RBM & 67 & 57 & 56 & 77 & 68 & 57 & 68 & 70 & 73 \\ \hline Test & LDA & 62 & 53 & 50 & 76 & 65 & 53 & 63 & 69 & 69 \\  & SVM & 51 & 50 & 50 & 50 & 49 & 51 & 49 & 52 & 50 \\  & BP & 63 & 52 & 53 & 76 & 66 & 55 & 63 & 68 & 70 \\  & RBM & 63 & 54 & 52 & 77 & 66 & 55 & 63 & 69 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the training and testing accuracy (in percentage) for nine different subjects using Linear Discriminant Analysis (LDA), Supported Vector Machines (SVM), ANN trained with Back Propagation (BP) and Restricted Boltzmann Machine (RBM) with a frequency band of [8–30] Hz and no regression filtering over the EOG. Table 5 enumerates the results for the training and testing accuracy using LDA, SVM, BP and RBM with the reduced frequency band and with the EOG reduction regression method. Finally, Figure 18 shows the training time (seconds) required by each of the five methods with the selected frequency bands ((8-12) Hz and (22-30) Hz) and EOG correction. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Class 1 & 25 & 47 & 14 & 37 & 77 & 77 & 42 & 16 & 33 \\ \hline Class 2 & 52 & 46 & 39 & 24 & 67 & 39 & 23 & 35 & 71 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of the position of the winner neuron for Class 1 and Class 2 of SOM with a frequency band of [8-12] Hz and [22-30] Hz and with regression filtering over the EOG. Figure 17: SOM representation, including the winner neuron, of the different classes for the nine different subjects with more limited frequency bands.