# Optimizing Brain-Computer Interface Performance: Advancing EEG Signals
Channel Selection through Regularized CSP and SPEA II Multi-Objective
Optimization

M. Moein Esfahani
Center for Translational Research in Neuroimaging and Data Science (TReNDS)
Georgia State University
Atlanta, Georgia, USA
<EMAIL_ADDRESS>
&Hossein Sadati
Department of Mechanical Engineering
K.N Toosi University of Technology
Tehran, Iran
<EMAIL_ADDRESS>
&Vince D Calhoun
Tri-Institutional Center for Translational Research in Neuroimaging and Data
Science (TReNDS)
Georgia State University, Georgia Institute of Technology, Emory University
Atlanta, Georgia, USA
<EMAIL_ADDRESS>

###### Abstract

Brain-computer interface (BCIs) systems and the recording of brain activity
has garnered significant attention across a diverse spectrum of applications.
Electroencephalography (EEG) signals have emerged as a predominant modality
for recording neural electrical activity. Among the methodologies designed for
feature extraction from EEG data, the method of regularized common spatial
pattern(RCSP) has proven to be an instrumental approach, particularly in the
context of Motor Imagery (MI) tasks. RCSP exhibits remarkable efficacy in the
discrimination and classification of EEG signals. In the pursuit of optimizing
the performance of this method, our research extends to a comparative analysis
with conventional CSP techniques, as well as meticulously optimized
methodologies designed for similar applications. Notably, we employ the meta-
heuristic multi-objective Strength Pareto Evolutionary Algorithm II (SPEA-II)
as a pivotal component of our research paradigm. This is a state-of-the-art
approach in the selection of an subset of channels from a multi-channel EEG
signal with motor imagery tasks. Our main objective is to formulate an optimum
channel selection strategy aimed at identifying the most pertinent subset of
channels from the multi-dimensional electroencephalogram (EEG) signals. One of
the primary ob-jectives inherent to channel selection in the EEG signal
analysis pertains to the reduction of the channel count, an approach that
enhances user comfort when utilizing gel-based EEG electrode systems.
Additionally, within this research, we took benefit of ensemble learning
models as a component of our decision-making process. This technique serves to
mitigate the challenges asso-ciated with overfitting, especially when
confronted with an extensive array of potentially redun-dant EEG channels and
data noise. Our findings not only affirm the performance of RCSP in MI-based
BCI systems, but also underscore the significance of channel selection
strategies and en-semble learning techniques in optimizing the performance of
EEG signal classification.

_Keywords_ BCI; EEG; Motor-Imagery; SPEA-II; RCSP; Ensemble-learning;
MultiObjective-Optimization; SVM; KNN; LDA

Figure 1: Diagram illustrating the Proposed Channel Selection Method

##  1 Introduction

The evolution of brain-computer interfaces (BCIs) stands as a tailored system
that performs at the intersection of neuroscience, computer science, and
engineering [1][2], [3]. This combination has given rise to a pioneering
technology that enables direct communication between the human brain and
external devices, transcending the traditional boundaries of human-machine
interaction [4]–[6]. BCIs hold immense potential across a spectrum of
applications, ranging from medical rehabilitation to augmenting human
capabilities and understanding the brain’s dynamics [2]. The Brain-Computer
Interface systems mainly performs in neural recording/decoding and stimulation
[3]. Early experimentation involved noninvasive approaches like implementing
direct implantation of electrodes into the brain to decipher neural activity
with mainly EEG/fNIRS signal recording systems[7], [8] which leverage
electroencephalography (EEG) to capture neural signals from the scalp
surface[1], [8]–[10]. The advent of BCIs empowering individuals to control
external devices through neural [commands mainly with EEG
signals…rephrase][1]. This innovation came with profound implications,
offering a lifeline for those with motor disabilities and opening avenues for
communication restoration. Furthermore, BCIs offered new methods into
understanding neural processes, enabling researchers to detect complexities of
cognition and mental states [1], [8], [10]. Motor-imagery tasks represent a
captivating realm where the human mind’s capacity to simulate movement
converges with cutting-edge neuro studies. The inception of motor imagery
research dates back several years, where pioneers began investigating the
neural signatures accompanying imagined actions. This endeavor marked a
paradigm shift, transcending traditional notions of motor control and paving
the way for novel applications that extend beyond the realm of basic
neuroscience [11]–[13]. EEG signals hold the key to unlocking the intricacies
of motor imagery. These electrical signals, captured non-invasively from the
scalp, offer a window into the brain’s activity during cognitive tasks,
including motor imagery. By analyzing the spectral patterns and spatiotemporal
dynamics of EEG signals, researchers have uncovered distinct neural correlates
associated with various motor imagery tasks. These discoveries serve as the
foundation for decoding intentions and translating them into tangible actions
through BCIs [14]. The realm of optimization, a foundation in various
disciplines, continuously seeks solutions to complex problems by navigating a
land-scape of possibilities. As problems become increasingly intricate,
traditional optimization techniques often grapple with the curse of
dimensionality and the need to simultaneously balance conflicting objectives
[15], [16]. This predicament gave rise to a transformative innovation – Multi-
Objective Metaheuristic Optimizations – an interdisciplinary combination of
optimization theory and metaheuristic algorithms [17], [18]. In this study, we
use optimization meta-heuristic algorithms and compare the results with our
proposed techniques and other algorithms to improve performance [1],
[19]–[21]. The journey of Multi-Objective Metaheuristic Optimizations traces
its roots to the mid-20th century [15], [22], [23], when researchers
recognized that many real-world problems entailed multiple, often competing
objectives. Conventional optimization methods struggled to handle the
intricate trade-offs inherent in these scenarios, sparking a quest for
techniques capable of exploring diverse solution spaces [17], [18].
Metaheuristic algorithms emerged as a class of strategies that sidestepped the
rigid constraints of deterministic approaches [16], [24], adopting an
iterative, exploratory approach that mimicked natural evolutionary processes
like evolution, swarm behavior, and simulated annealing. The rise of multi-
objective optimization was a significant change. Instead of looking for just
one best solution, multi-objective optimization aimed to uncover a set of
solutions that represented different trade-offs between objectives [1]. This
set, known as the Pareto front, offered decision-makers a spectrum of choices,
allowing them to make informed decisions that aligned with their preferences
and priorities. In former methodologies, the integration of elitism. was not
explicitly incorporated. However, a few years later, the significance of this
concept in the context of multi-objective optimization was acknowledged,
leading to its incorporation in a new generation of algorithms. This marked
the introduction of elitist multi-objective evolu-tionary algorithms such as
SPEA by Zitzler[25], [26] and NSGA by Deb [1], [8], [10].These evolutionary
strategies underscored the emphasis on preserving elite solutions within the
population, thereby enhancing the convergence towards optimal solutions across
multiple objectives. In this study, we present an approach to EEG signal
processing and also strategies for mitigating noise and redundancies. We also
provided an in-depth exposition of the Regularized CSP technique and its
relevance and application within the context of our research. Subsequently, we
delve into the SPEA-II and its components, elucidating their roles and
significance in our analytical framework. Furthermore, we offer an overview of
the dataset employed in our study and the experimental procedures undertaken
by our methodologies. Finally, the authors intend to provide readers with a
better understanding of the implications, significance, and potential future
directions arising from our research efforts.

##  2 Methodology

In this study, we introduce our state-of-the-art methodology, as illustrated
in Figure 1. Our primary objective is to determine the optimal set of channels
using the SPEA-II algorithm. This method operates as a subset of the wrapper
approach, focusing on subject-specific channel selection, ensuring that it
operates independently for each subject. This tailored approach to channel
selection within EEG signal processing for motor imagery tasks offers several
advantages, including the reduction of channels to a manageable number,
enhancing the comfort of subjects, and reducing setup and electrode fixation
times. An essential consideration in our study is the risk of overfitting in
classification out-comes when dealing with an excessive number of redundant
EEG recorded channels and signal noise. To address this, we explore five
primary strategies for channel selection: filtering, wrapping, embedding,
hybrid, and human-based methods[27], [28]. Filtering techniques independently
evaluate candidate channel subsets using metrics including distance,
dependence, and consistency. These techniques offer advantages such as
computational efficiency and independence from specific classification algo-
rithms. However, they may exhibit lower accuracy as they don’t account for
combinations of different channels[1], [7], [8], [10]. Wrapper techniques, on
the other hand, evaluate the performance of specific classifiers by
classifying subsets of features and identifying the subset of channels that
per-forms best with a particular classification method. Embedded techniques
rely on re-cursive channel elimination. Hybrid approaches combine filtering
and wrapper techniques to leverage the strengths of both methodologies[1].
This approach allows us to benefit from independent measures while employing a
wrapper method to identify the optimal feature subset. Human-based methods
involve domain expertise, where well-trained experts determine which channels
are most relevant to specific tasks. For instance, experts in brain physiology
may identify channels in the brain’s cortex as crucial for motor imagery
tasks. In our study, we incorporate this expert knowledge into our algorithm
to identify optimal channels within specific brain regions. Our proposed
method predominantly functions as a wrapper technique, employing a specialized
classifier to determine the optimal channel subset. This approach aims to
strike a balance between accuracy and computational efficiency, contributing
to the effectiveness of our channel selection strategy.

###  2.1 SPEA-II Algorithm

SPEA II multi objective optimization algorithm, It is an advanced multi-
objective optimization algorithm, first time proposed by Zitzler et al[1]. It
introduces a significant advanced method in the domain of Pareto-based
optimization. Operating on the foundational principle of Pareto optimization
as applied to fitness functions or objectives, SPEA2 not only incorporates
selection operations but also like NSGA-II features a state-of-the-art method
coupled with an external archiving elite retention mechanism. In this paper,
we delve into a brief introduction of SPEA2, as related to theoretical
foundations while attaining more efficient outcomes within the realm of multi-
objective algorithms. An enhancement in SPEA2, distinguishing it from its
predecessor past version SPEA, is the adoption of an improved fitness
assignment. This algorithm with details accounts for the domination
relationships of each individual, considering both the number of individuals
it dominates and those by which it is dominated. Furthermore, SPEA2 integrates
a nearest neighbor density estimation technique that intricately guides the
search process [25], [26]. This addition empowers the algorithm to navigate
the solution space with heightened precision, thereby augmenting the
convergence towards Pareto-optimal solutions. Notably, SPEA2 introduces a new
ar-chive truncation method that plays a critical role in preserving boundary
solutions. This enhancement ensures that solutions at the edge of the Pareto
front, pivotal for comprehensive problem understanding, are retained within
the solution set. Figure 2 represents a psudocode of SPEA-II.

Figure 2: PseudoCode of SPEA II

####  2.1.1 Pareto Front Solutions

In multi-objective optimization, the Pareto front represents a fundamental
concept that embodies the trade-offs and compromises between conflicting
objectives[17], [18], [25], [26]. It is a collection of solutions where no
single solution can be improved in one objective without sacrificing
performance in another. With that said, these solutions form the frontier of
the solution space, showcasing the optimal compromises that exist among the
multiple objectives under consideration. The Pareto front is a crucial tool
for decision-makers, as it provides a comprehensive view of the diverse
solutions available[1], [7]. By exploring the Pareto front, decision-makers
can gain valuable in-sights into the complex interplay of objectives, aiding
in the selection of solutions that align most closely with their desired
outcomes and objectives.

Parameters used in SPEA-II algorithm |
---|---
Iteration | 25
Population size | 80
Probability of crossover | 0.75
Probability of mutation | 0.7
Type of selection | tournament
Table 1: SPEA-II Parameters Figure 3: Visualization of the Pareto Front for
Subject Number5

####  2.1.2 Paragraph

The origin of the CSP algorithm goes back to the process of extracting
discriminative spatial patterns from multichannel EEG signals (mainly with
spatial patterns) [2], [3], [29]. The base and foundation of CSP lies in its
ability to transform the EEG channels into a new spatial domain [4], [30],
[31], where the variance of one class is maximized while that of another class
is minimized. the results of the neural activity patterns to certain cognitive
states while attenuating unrelated activity. The benefits of CSP include the
reduction of redundant or noisy data. This research in-tends to implement
various EEG signal noise reduction techniques other than just CSP, aimed at
enhancing signal quality. The CSP was just used as a feature extraction
method. Furthermore, this methodology endeavors to prioritize one task over
another. However, it is important to note that the algorithm is limited to
datasets featuring two tasks. Yet, with some extensions and additional
features, we can improve its applica-tion to datasets with more than two tasks
[4], [30]–[32]. in Regularized CSP method, the optimization terms need the
three parameters $\alpha,\beta and\gamma$. These vectors of parameters, as
shown below, are defined based on [33][10], [34] studies:

$\alpha=\\{10^{-10},10^{-9},10^{-8},10^{-7},10^{-6},10^{-5},10^{-4},10^{-3},10^{-2},10^{-1}\\}$
$\beta=\\{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9\\}$
$\gamma=\\{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9\\}$

Subsequently, it becomes critical to identify the optimal parameters that can
yield peak performance. To achieve this, we endeavor to pinpoint the most
effective parameter values. Furthermore, in the context of feature selection
from the Regularized Common Spatial Pattern (RCSP) results, the following
approach is employed. The process in-volves the utilization of the Minimum
Redundancy Maximum Relevance (mRmR) al-gorithm to discern the most pertinent
subset of features. It is noteworthy that the RCSP yields N*d trials, where N
signifies the number of features extracted through RCSP, and d signifies the
number of filters applied to the signal. With that said, we embark on the
selection of the optimal feature subset tailored to each specific subject. The
outcomes of this selection process shed light on the precise number of
features that comprise the most optimal subset. This strategic approach aids
in enhancing the overall performance and effectiveness of our methodology. CSP
uses spatial filters that extremize the following cost function:

$J(w)=\frac{{w^{T}C_{1}w}}{{w^{T}C_{2}w}}=\frac{{w^{T}X_{1}X_{1}^{T}w}}{{w^{T}X_{2}X_{2}^{T}w}}$
(1)

The signal trial for class I is transformed into a matrix format, where the
rows correspond to channels, and the columns correspond to discrete time
points. Central to our approach is Eq. (1), which evaluates the cost function,
a critical component of our spa-tial covariance matrix for class i. While the
initial goal is to maximize this cost function, it is pertinent to acknowledge
that conventional Common Spatial Pattern (CSP) methods, despite their
widespread use and proven efficacy, come with certain limitations. Among the
main drawbacks is a high sensitivity to noise, a factor that can lead to
overfitting, particularly when dealing with datasets with a limited number of
trials. To overcome these limitations, we adopt the Regularized CSP (denoted
as RCSP) as a new method. The spatial covariance matrix for each of the two
classes should be computed. However, under some conditions it may overfit,
resulting in low classification accuracy. As a result, the RCSP incorporates
an added penalty term in the denominator of the cost function to normalize the
findings and reduce the effect of overfitting. The term $\alpha P(w)$ in this
cost function represents the penalty term, as follows:

$J_{P_{1,2}}(w)=\frac{{w^{T}\tilde{C}_{1,2}w}}{{w^{T}\tilde{C}_{2,1}w+\alpha
P(w)}}$ (2)

The task has the estimation of spatial covariance matrices for both of the two
distinct classes, which is a base step accomplished through the use of Common
Spatial Pattern (CSP) analysis. Nonetheless, when dealing with EEG trial
datasets that include noise or a limited number of trials, there arises the
potential for overfitting in the computed covariance matrix, which can
subsequently lead to suboptimal discrimination results. To address this
inherent challenge, we have used an advanced method that applies a penalty
term into the cost function, strategically incorporated to normalize the out-
comes and mitigate the overfitting effect. This new cost function features the
term $\alpha P(w)$ , denoting the penalty term, thoughtfully appended to the
denominator of the equation, thus yielding the following formulation:

$P(w)=w^{T}Kw$ (3) $\hat{C}_{c}=(1-\beta)s_{c}C_{c}+\beta G_{c}$ (4)
$\tilde{C}_{c}=(1-\gamma)\hat{C}_{c}+\gamma I$ (5)
$G_{c}=\sum_{i\in\Omega}\frac{{N_{c}^{i}}}{{N_{t,c}}}C_{c}^{i}$ (6)
$s_{c}=\frac{{N_{c}}}{{N_{t,c}}}$ (7)

where $\hat{C}_{c}$ signifies the initial spatial covariance matrix associated
with class c, whereas $\hat{C}_{c}$ is the regularized estimate, I is the
identity matrix, $s_{c}$ is a constant scaling parameter denoting the identity
matrix. Eq. (6) is a generic covariance matrix to estimate the more robust
covariance matrix $\hat{C}_{c}$. The generic matrix obtains its initial values
from a given prior data based on subject-to-subject training. The covariance
matrix depends on the other recorded subjects. This term applies to the
replaced $C1$ and $C2$ used in the CSP transfer function by their regularized
estimates.

$Z=W^{T}\cdot x$ (8)

$f_{p}=\log\left(\frac{{\text{var}(Z)}}{{\sum\text{var}(Z)}}\right)$ (9)

In Eq.(8) we applied the computed weights W on the EEG signals x, giving Z as
the mapped EEG trials.
Finally, the extracted features are log power features in Eq. (9), where
$var(z)$ signifies the variance of $\hat{z}$ over the domain samples.
Consequently, from the matrix $Z=[Z_{1},Z_{2},Z_{3},\dots,Z_{n}]^{T}$, which
is the feature matrix, the columns are chosen as follows. The first and last
columns are taken, followed by the second and one to the last, followed again
by the third and two to the last, and this process is done until all columns
are considered. Subsequently, the classification models append on this matrix
of features.

Table 2: Regularized CSP Parameters for Subjects

###  2.2 Source localization with High Laplacian

In this study, we focused on analyzing EEG signals sourced from a dataset
having 64 channels. To enhance the quality of the EEG data, in the present
study we employed a source localization High Laplacian spatial filtering
method, in contrary to the earlier research by the authors [1], [10]. By
taking this approach, we aimed to improve the signal-to-noise ratio (SNR) in
order to enhance the performance of EEG signal classification [1], [7], [8],
[10]. In other publications, the utilization of common average reference (CAR)
and low or large Laplacian spatial filters has been shown to reduce SNR,
consequently leading to enhanced EEG signal classification performance [20],
[35]. It aimed to facilitate the accentuation of localized neural activity
while concurrently mitigating the influence of diffuse signals. This
enhancement is achieved by computing the weighted sum of the potentials
recorded by neighboring electrodes and then subtracting this sum from the
potential measured at the electrode of interest. This process enables the
derivation of low Laplacian spatial filters, thereby refining the
representation of localized neural activity within the EEG dataset.

###  2.3 Digital EEG Signal Filtering

In our study, we filtered the EEG signals using a 5th order bandpass
Butterworth filter in the range of 7-32 Hz.( Unlike prior publication[1],
[10], our approach involved a reduction in the filter order and employed a
wider filter design) This filtering helped remove unrelated components and
noise from the signal, focusing on the frequencies associated with motor
imagery, specifically the mu (8-12 Hz) and beta (18-26 Hz) rhythms, which can
induce event-related synchronization (ERS) and event-related desynchronization
(ERD) phenomena[22], [23], [36]–[38].

###  2.4 Ensemble learning Classification

Ensemble learning models [8], was introduced as a new and powerful approach in
machine learning. The ensemble learning consists of the idea of combining
multiple individual models, often of diverse types or trained on distinct
subsets of data, to make collective predictions that tend to be more accurate
and robust than those of any single model. The voting model, as a pivotal
component of this ensemble, consolidates the predictions from its constituent
models, which could be classifiers like decision trees, support vector
machines, or neural networks [37]–[40]. The key idea here is to leverage the
wisdom of the crowd: while individual models may have their limitations and
biases, their collective decision, reached through a voting mechanism, tends
to be more reliable and less susceptible to errors. It often leads to superior
predictive performance and enhances the generalizability of the resulting
system. In our study, we implemented ensemble learning model. The model for
making the final decision and optimizing the performance of our optimization
algorithm [16], [24], [41]. This ensemble learning model comprises several
submodels as depicted in Figure 1, includes Support Vector Machines (SVM) with
both linear and Polynomial Kernels, Linear Discriminant Analysis (LDA), and
K-Nearest Neighbor (KNN) with a parameter ’k’ set to 6.

##  3 Dataset

###  3.1 BCI Competition IV-Dataset1

This dataset includes EEG signals consists of two distinct classes of motor
imagery, meticulously recorded via the BrainAmp MR amplifier system (Brain
Products GmbH, Munich, Germany)[42]–[45], combined with the utilization of
Ag/AgCl electrode caps provided by EASYCAP GmbH. To discuss further, this
dataset meticulously incorporates a total of 100 trials exclusively dedicated
to motor imagery linked with right-hand movements, supplemented by an
equivalent count of 100 trials directed towards the contemplation of left-hand
motor imagery. The data collection procedure was performed with the active
participation of four healthy human subjects, appended by the involvement of
three computationally generated virtual subjects. The data acquisition process
involved the recording of neural signals from precisely 59 EEG locations,
positioned across the scalp to densely cover sensorimotor regions of interest.
The collected signals underwent a comprehensive bandpass filtering operation,
expertly constraining them within the frequency bandwidth of 0.05 to 200 Hz.
Following this, the neural data was digitized at an impressive sampling rate
of 1000 Hz, with precision level of 16 bits (0.1 uV). In this study, we
Notably take advantage of the sophisticated Chebyshev Type II filter to
judiciously down-sample the dataset to a more operationally efficient sampling
rate of 100 Hz[1], [8], [10], [19].

Figure 4: Visualization of a Single EEG Trial in described Dataset

###  3.2 Signal Segmentation

Each participating subject engaged with three distinct motor imagery tasks.
These tasks intricately associated with motor imagery involving the left hand,
the right hand, or the right foot. To facilitate comprehensive analysis and
interpretation, the mentioned dataset was thoughtfully segregated into two
principal segments, denoted as the ’calibration’ and ’evaluation’ phases.
Better visulalization in Figure.4. Calibration Data: Within the initial phase
of the experiment, specifically during the initial two runs, participants were
exposed to four-second visual cues that assumed the form of directional
arrows, judiciously pointing either left, right, or down, meticulously
presented on a screen. Evaluation Data: Subsequent to the calibration phase,
four additional experimental runs were conscientiously executed, with the data
from four of these runs being thoughtfully incorporated into the dataset under
scrutiny. To cue the subjects into motor imagery tasks, we employed soft
acoustic stimuli, manifesting as spoken words such as ’left,’ ’right,’ and
’foot.’ The duration of each motor imagery task was thoughtfully designed to
span a range of temporal periods, encompassing intervals that varied from a
succinct 1.5 seconds to a more protracted 8 seconds. The demarcation of the
termination of each motor imagery phase was aptly conveyed through the cue
’stop,’ further embellishing the temporal diversity inherent to the dataset.

##  4 Results

The PSEA-II algorithm was employed in this study to select the optimal channel
subset. A Pareto front, depicted in Figure 3 for subject 5, showcases the set
of optimal solutions generated by the multi-objective evolutionary algorithm.
The Pareto front serves as a valuable tool for decision-making by balancing
the trade-off between the number of selected channels and accuracy. Although
presented in a two-dimensional format in our study, the Pareto front can
manifest in higher dimensions for more complex opti-mization problems. In
figure 3, multiple layers of results has depicted. Also, to illus-trate as a
convex figure, we employed the data with 1-accuracy. As the result, as the
curve of the same legend goes down, the higher accuracy with achieve.
The PSEA-II algorithm was executed for 25 iterations, varying by subject, with
a population size of 80%, a crossover percentage of 75, a mutation percentage
of 70%, and a total of 1374 function evaluations. These parameters are also
detailed in Table 3. The resulting accuracies, along with the number of
selected channels for each subject, are summarized in Table 2. Figure 5
provides a visual representation of electrode locations on the subjects’
scalps, offering multiple channel selection options.
Notably, in every row, the first circle in Figure 5 represents our secondary
objective: minimizing the number of channels at the expense of accuracy, while
the last circle signifies our optimal choice, aiming for the highest accuracy
with the fewest channels. However, it’s observed that the second and third
layers of the Pareto front exhibit lower accuracies compared to the initial
layer.

Figure 5: Discussion of the Number of Optimal Channels Selected and Accuracy
Across Various Proposed Algorithms

##  5 Discussion

To validate the performance of our proposed Regularized CSP algorithm, a
comparative study against recently published results in the introduction was
conducted. Bold entries in Table 2 denote the optimal and highest results.
Remarkably, our algorithm demonstrated superior accuracy performance across
most subjects, with exceptions for subjects 1 and 5. These results were
validated using 10-fold cross-validation, ensuring robustness and reliability.
Furthermore, Figure 5 presents the optimal channel selections for all seven
subjects, aligning with our primary objective of channel minimization while
striving to maximize accuracy. Table 2 conveniently summarizes the accuracy
levels and corresponding channel counts selected, providing a comprehensive
overview of the algorithm’s performance across different subjects.
Overall, the utilization of the PSEA-II algorithm in conjunction with the
Regularized CSP algorithm showcases promising results in optimizing channel
selection for EEG data classification. The ability to balance accuracy with
channel reduction offers practical implications in real-world applications
where resource constraints or processing efficiency are crucial factors.
Further exploration and validation of these methodologies across diverse
datasets and experimental setups could provide deeper insights and potentially
enhance their applicability in various EEG-based applications.

##  6 Conclusion

This study primarily centers on the utilization of the Strength Pareto
Evolutionary Algorithm (SPEA-II) to derive the most optimal channel subset, a
critical aspect in the development of a high-performance Brain-Computer
Interface (BCI) system. Designing an effective BCI system entails a formidable
challenge, primarily stemming from the necessity to identify the optimal
feature set. This endeavor is optimized by the computational time complexity
of the proposed methods and the pursuit of attaining the highest
classification accuracy. In this study for efficient classification and
feature extraction, we have introduced the Regularized Common Spatial Pattern
(RCSP) method and conducted a comparative analysis against alternative
methodologies. In the context of this study, our aim was to ascertain the
ideal channel configuration for the BCI Competition IV dataset 1. To achieve
this, we used an ensemble learning classification model including multiple
kernels to perform EEG trial classification. Our findings underscore the
efficacy of Regularized CSP, a cutting-edge CSP variant enriched with a
penalty term, which consistently delivered superior accuracy outcomes. In
future studies, the inclusion of diverse classification techniques offers
potential for further exploration, affording opportunities for result
comparison. Additionally, there exists the prospect of assessing the outcomes
of alternative evolutionary applications, such as MOPSO or MOEAD, as a new
method of multi-objective evolutionary approach.

Figure 6: Optimal Selected Channels per specific Subjects

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