# Dimension Reduction Using New Bond Graph Algorithm and Deep Learning Pooling on EEG Signals for BCI
## 5 Results and Discussion
### Discussion Sampling (Pooling) on Brain Signals  
In all our study cases, sampling is part of deep learning to reduce the dimension in the layers. It is used during the deep learning phase. We use samplings based on four main functions, i.e., maximum, minimum, maximum-minimum automatic function, and no-maximum average function, on the data along with filter banks to reduce the dimension of the channels. The number of channels is fixed, and the dimensional reduction of each channel depends on the window size. The output window sizes for each channel are as follows: window size 3 with four features, window size 4 with one feature, window size 5 with seven features, window size 6 with five features, and window size 7 with three features.  
Window size 4 holds the lowest number of features (i.e., one feature) with 99.88% dimension reduction. So, in our experiment, a total of 22 features out of a total of 19,250 features have been selected for classification for window size 1. Window size 4 holds the highest number of features (i.e., seven features), with 99.2% dimension reduction. So, in our experiment, a total of 154 features out of a total of 19,250 features have been selected for classification for window size 4.  
In addition to the earlier functions, we also used an average function for the sampling in each channel. In the average function, only the average value of the features within each window size is selected. So, the number of output samples for the average function is 22 features.  
The average accuracy of the functions mentioned above is in the range of 55% to 73%. This can be due to the excessive reduction of features in each channel. Therefore, in future works, more features must be considered to examine the main performance. However, despite the very small selection of features, when using a single filter bank, the accuracy of 61.45% to 64.74% is obtained, which is very good considering the very small selected features.  
Compared to the articles on the basic quantum neural network method [65], where the average accuracy of all individuals based on feature extraction is 66.59%, all channels and total data have been involved in the extraction, which is only 2.2% better than our sampling methods with a single filter bank and significant dimension reduction.  
Compared to [PERSON]'s [33] article, feature selection was selected after feature extraction from two channels, i.e., 8 and 12, using a wavelet package. The average accuracy in the range of 67-68% was obtained using a random forest classifier in the frequency range of 8-30, which is only 3-4% better than our sampling methods with a single filter bank and significant dimension reduction.  
In [PERSON]'s article [36], a Mask model has been used on 118 channels to reduce the electrodes and features. As a result, the feature reduction rate was 99%, which is near to our work (i.e., 99.88%). They obtained accuracy in the range of 63-86% for five subjects. The average accuracy was 74% in their work, which is only1% more than our best average accuracy. However, the dimensional reduction in our work was more than their work.