# Dimension Reduction Using New Bond Graph Algorithm and Deep Learning Pooling on EEG Signals for BCI
###### Abstract  
One of the main challenges in studying brain signals is the large size of the data due to the use of many electrodes and the time-consuming sampling. Choosing the right dimensional reduction method can lead to a reduction in the data processing time. Evolutionary algorithms are one of the methods used to reduce the dimensions in the field of EEG brain signals, which have shown better performance than other common methods. In this article, (1) a new Bond Graph algorithm (BGA) is introduced that has demonstrated better performance on eight benchmark functions compared to genetic algorithm and particle swarm optimization. Our algorithm has fast convergence and does not get stuck in local optimums. (2) Reductions of features, electrodes, and the frequency range have been evaluated simultaneously for brain signals (left-handed and right-handed). BGA and other algorithms are used to reduce features. (3) Feature extraction and feature selection (with algorithms) for time domain, frequency domain, wavelet coefficients, and autoregression have been studied as well as electrode reduction and frequency interval reduction. (4) First, the features/properties (algorithms) are reduced, the electrodes are reduced, and the frequency range is reduced, which is followed by the construction of new signals based on the proposed formulas. Then, a Common Spatial Pattern is used to remove noise and feature extraction and is classified by a classifier. (5) A separate study with a deep sampling method has been implemented as feature selection in several layers with functions and different window sizes. This part is also associated with reducing the feature and reducing the frequency range. All items expressed in data set IIa from BCI competition IV (the left hand and right hand) have been evaluated between one and three channels, with better results for similar cases (in close proximity). Our method demonstrated an increased accuracy by 5 to 8% and an increased kappa by 5%. b 2021 20  
is not used, the selected features will be sent directly to the classifiers for classification after reducing the dimensions. * In the second method, the following steps are performed respectively: (1) feature extraction, (2) feature selection, and (3) classification. * In the third method, after reducing the dimensions of the features (i.e., feature selection), the following steps are performed, respectively: (1) feature extraction, (2) feature selection, and (3) classification. In some studies, using the first and third methods, a dimensional reduction is used to reduce features, reduce electrodes, or both. In all of the methods mentioned above, the features from a larger set (including channels, etc.) are converted into better and smaller feature sets by removing the less effective features. In most cases, a certain frequency range (8-30 Hz for the brain signal) is processed for specific purposes (such as left and right-hand imaging). In most studies, all the features along with specific channels or whole channels have been considered [15; 16; 17; 18; 19; 20]. In addition, in some studies, one-dimensional or two-dimensional reduction methods are performed for reducing features and the electrodes. However, none of the previous studies examined reducing the frequency range from one to three electrodes. In some articles, certain frequency ranges have been used. In other words, feature reduction is used by reducing the frequency range with a single electrode. Given that human brain signals are generally a combination of different domains, examining them as a single domain is challenging and has been studied in many previous studies [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. In this study, we propose a new optimization algorithm based on the concept of Bond Graph, which is the modeling and simulation language for multi-domain systems. We examined and analyzed the reduction of frequency intervals of brain signals. The main contributions of this paper are as follows:  
1.