# Dimension Reduction Using New Bond Graph Algorithm and Deep Learning Pooling on EEG Signals for BCI
###### Abstract
Introduction of the Bond Graph algorithm (BGA), which demonstrated a good performance compared to the genetic algorithm (GA) and particle swarm optimization (PSO) in the benchmark functions. The assessment was performed by testing on eight benchmarks and EEG brain signals of right and left-hand perception (two classes). Important features of our proposed algorithm (i.e., BGA) include fast convergence and no trapping in the local optimization. 2. The reduction of features, reduction of electrodes, and frequency range have been evaluated simultaneously. 3. Feature extraction and feature selection for time domain, frequency domain, wavelet coefficients, and autoregression have been investigated as feature reduction, electrode reduction, and frequency range reduction. 4. Initially, the features, electrodes, and frequency are reduced, and then, new signals are made based on them using special formulas for each row. Then, a common spatial pattern (CSP) is performed to remove noise and feature extraction, which is followed by classification. 5. A separate study with a deep learning sampling method has been implemented as feature selection in several layers with different functions and different window sizes. This part also includes feature and frequency reduction. In cases 1 to 4, the proposed BGA, GA, PSO, and Quantum Genetic Algorithm (QGA) are used for evaluation. In case 5, no algorithm was required, but simple computational functions were used. The main objective of this study is dimension reduction in single and multi-domain brain signals. For this purpose, five general models (seven model scenarios) have been implemented for testing:  
1. One filter bank and single channel from a set of two filter banks (i.e., 2 and 5) with two channels (i.e., right and left hemispheres of the brain) have been investigated by four main algorithms, i.e., BGA, GA, PSO, and QGA. The two channels' featuresare selected from the right and left hemispheres. The reduction of features for two channels is considered separately for each channel. 2. A combination of filter banks with a single channel from a set of four filter banks (i.e., 2, 5, 6, and 9) and two channels (i.e., right and left hemispheres of the brain) have been investigated with the same algorithms. The reduction of features for two channels is considered separately for each channel. 3. Four general methods, including time domain, frequency domain, wavelet coefficients, and autoregression have been used for feature extraction from a combination of two filter banks (i.e., 2 and 5) as a new signal with a single channel (i.e., right or left hemispheres of the brain), two channels (i.e., right and left hemispheres of the brain), or three channels (i.e., right and left hemispheres and center of the brain). Then, feature selection is done by BGA, GA, PSO, and QGA separately. 4. Feature selection was done by four main algorithms on a combination of filter banks (from filter banks 2, 5, and 6) and two (i.e., right and left hemispheres of the brain) or three channels (i.e., right and left hemispheres and center of the brain). Then, using special formulas, new signals were formed, which were used as input for CSP. Finally, the ELM classifier classified the extracted features from CSP. 5. Feature selection was performed by deep learning sampling with five general functions on all filter banks together or each filter bank individually with all channels in three sampling models. In the first sampling model, each filter bank with the same functions was used in all layers. In the second sampling model, the functions were the same selected for all layers and all filter banks. In the third sampling model, the functions were randomly selected for each layer. The rest of the article is organized as follows: In the Section 2, a summary of previous work on the dimensionality in all items is provided for brain signals.