1 Introduction

Electroencephalography (EEG) is a method used to measure brain electrical activity [1]. A series of electrodes are usually placed on the scalp to measure electrical activity in different areas of the brain. EEG data represent brain waves. These waves have different frequencies and are associated with different brain activities. For example, beta waves are usually associated with alertness and attention, while alpha waves usually occur at rest and with eyes closed. Delta and theta waves have slower frequencies and are associated with states such as deeper sleep or meditation [2, 3].

EEG is a technique used in many fields, such as neurology, neurophysiology, psychiatry, and sleep medicine. Some common clinical applications of EEG include diagnosing epilepsy [4], detecting sleep disorders [5], evaluating brain function [6], evaluating developmental disabilities in children [7], and identifying psychiatric disorders [8]. One of these psychiatric disorders is schizophrenia. Schizophrenia is associated with abnormalities in brain function, and EEG is used to detect these abnormalities. When EEG recordings of schizophrenia patients are analyzed, it has been observed that beta activity decreases, gamma activity changes, and P300 responses change [9,10,11].

Recently, artificial intelligence techniques have been used in analyzing EEG data in most fields, as shown in Table 1. Especially by analyzing EEG data using machine learning (ML) algorithms, schizophrenia can be detected in the early stages of the disease. In one of the previous studies, Oh et al. (2019) detected schizophrenia from EEG signals using an eleven-layered convolutional neural network (CNN), a deep learning method. The classification accuracy of the model they developed ranges between 81 and 98% [12]. In another study, Shalbaf et al. (2020) performed schizophrenia detection by converting EEG data into images. Here, they applied images of EEG signals to pretrained AlexNet, ResNet-18, VGG-19, and Inception-v3 algorithms. They evaluated the schizophrenia status of 28 participants using a support vector machine (SVM) classifier. As a result, they achieved 98% classification success with the ResNet-18-SVM algorithm [13]. Supakar et al. (2022) proposed a deep learning-based recurrent neural network (RNN)-long short-term memory (LSTM) model for schizophrenia detection. They classified EEG data obtained from 84 people, including schizophrenia patients and healthy people, with 93–98% accuracy [14]. Sun et al. (2021) developed a hybrid deep learning model by converting time-series EEG data into red–green–blue (RGB) images. As a result, fuzzy entropy features were found to be more successful than fast Fourier transform features in schizophrenia classification [15].

Table 1 Summary of related work on EEG signals
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One of the challenges in analyzing EEG data is working with high-dimensional datasets. Processing data recorded from a large number of electrodes at high sampling frequencies requires high computational power. In this context, it is necessary to extract important features from EEG signals and reduce the sample size [16].

Feature selection is a preprocessing phase that reduces the amount of data and computational complexity by removing unnecessary and redundant features, thereby improving the performance of ML algorithms. Nonetheless, identifying the ideal subset of features in high-dimensional datasets is considered an NP-hard problem. The search space will grow exponentially with an increase in features because a dataset with N features comprises 2N−1 feature subsets. Because the exact methods cannot yield the necessary result in a fair amount of time, metaheuristic algorithms are employed to select the subset of features. Different metaheuristic algorithms are used for feature extraction in ML algorithms [17, 18]. Thus, the data size can be reduced, and a simple structure can be obtained. In addition, owing to metaheuristic algorithms, overfitting can be prevented, and models that generalize better can be created. The most meaningful features in classifying schizophrenia can be determined and useful in developing practical clinical applications. For example, in a study on classifying schizophrenia, Prabhakar et al. (2020) optimized features in EEG data via the Flower Pollination and Eagle strategies using different evolution algorithms, a backtracking search optimization algorithm (BSA) and a group search optimization algorithm (GSO) [19]. The schizophrenia classification accuracy of the optimization algorithms they proposed varied between 82 and 90%. Khare and Bajaj (2022) used a whale optimization algorithm (WOA) for feature extraction from EEG data. They achieved 92% accuracy in classifying schizophrenia with the six features they identified [20].

In a population-based metaheuristic, the search process consists of two main phases: exploration and exploitation. However, while some metaheuristic algorithms require improvement during the exploitation stage, others must be enhanced during the discovery stage. It is also necessary to enhance both steps in a restricted set of algorithms. During the exploration phase, it is beneficial to behave randomly to cover as much ground as possible in the search space. In contrast, the primary goal of the latter phase is to quickly utilize the locations that show promise. Finding the right balance between these two phases is extremely difficult since population-based metaheuristic algorithms are stochastic. Discrete-time dynamical systems are also referred to as chaotic maps. To effectively find an optimal solution, chaos is incorporated into metaheuristic algorithms to create a balance between exploration and exploitation [21]. Consequently, optimization approaches obtain ergodic and nonrepeating properties of chaos. As a result, it can search more quickly than random search and avoid entering local optima. The performance of optimization algorithms can be greatly improved by all of these advantages [22].

In this study, a new hybrid approach is developed by updating the parameters of the MPA to increase the performance of the algorithm in finding the optimum global solution with a random number sequence obtained from five chaotic maps. Chaotic maps are logistic, tent, henon, sine, and tinkerbell maps. These approaches are known as Chaotic-based Marine Predators Algorithms (Henon Chaotic-based MPA [HCMPA], Tinkerbell Chaotic-based MPA [TICMPA], Logistic Chaotic-based MPA [LCMPA], Tent Chaotic-based MPA [TECMPA] and Sine Chaotic-based MPA [SCMPA]).

The proposed hybrid approach tries to maximize the accuracy rate while minimizing the number of selected features. The MPA is used to determine significant features by determining the best foraging strategy for predators and prey in marine environments. The major goal of using a chaotic method is to overcome the drawbacks of an MPA, such as local optimal traps and premature convergence, and ultimately increase the capacity of the search for exploration and exploitation. To enhance the FS performance of the MPA, the proposed technique employs one-dimensional chaotic maps as random number generators. In addition, the decision tree algorithm was chosen to determine the effect of the selected feature on classification. Decision tree construction can handle high-dimensional data and does not require subject expertise, making it ideal for exploratory knowledge mining [23]. For this reason, decision trees (DTs) and an ensemble of DTs are used in the study.

The contributions of the proposed methods can be listed as follows:

  • We propose hybrid metaheuristic algorithms by combining MPA and five chaotic maps for feature selection in schizophrenia decision tree-based classification using EEG signals.

  • To demonstrate the effectiveness of the SCMPA, the SCMPA is statistically compared with chaotic-based MPA variants on the well-known UCI (Breast, Hepatitis, Liver, Raisin and Heart) (https://archive.ics.uci.edu/ml) datasets.

  • The ability of the SCMPA to perform feature selection in SCZ classification was verified using EEG signals.

The paper is organized as follows. In Sect. 2, the basic and proposed algorithms are defined and mathematicalized. Section 3 presents the experimental setup, evaluation metrics, details about the EEG signal data and preprocessing and the experimental study. Finally, in Sect. 4, the conclusions are given.

2 Methods

2.1 Marine predator algorithm (MPA)

The marine predator algorithm (MPA) was developed by Faramarzi et al., inspired by the prey-predator social relationship between marine predators and their prey [34]. Based on the MPA, the transition between phases in the structure of the algorithm is achieved according to the speed ratio between the prey and the predator [35]. These phases include (1) a high-velocity ratio or when prey is moving faster than a predator, (2) a unit-velocity ratio or when both predator and prey are moving at almost the same pace, and (3) a low-velocity ratio when the predator is moving faster than prey.

In the MPA, the initial solution is determined by using a randomly and uniformly distributed search space. The number of predators is \(n\), the number of iterations is \(m\), the size of the optimization parameter is \(d\), and \(Prey\) represents the initial position of the prey. \({X}_{max}\) and \({X}_{min}\) in Eq. 1 are the maximum and minimum values, respectively, and \(rand\) is a random vector in the range \(\left[\mathrm{0,1}\right]\). In this section, the \(Prey\) matrix, which holds the positions of the initial population, forms the \(Elit\) matrix with the best fitness function.

$${X}_{0}={X}_{min}+rand\left({X}_{max}-{X}_{min}\right)$$
(1)

Phase 1: In this behavior optimization at the first stage, during the first third of the iterations \(\left(iter<\frac{1}{3}maxiter\right)\) at a high speed rate \(\left(v\ge 10\right)\), the best strategy for the predators is not to move at all. \(P=0.5\) in Eq. 2 and 3, \(R\) is defined as a vector containing uniformly distributed random numbers between \(\left[\mathrm{0,1}\right]\), and \({R}_{B}\) is defined as a vector containing random numbers based on the normal distribution of Brownian motion. With Eq. 3, the matrices used by \(Prey\), which move according to Brownian motion, are updated.

$$\overrightarrow{{stepsize}_{i}}=\overrightarrow{{R}_{B}}\otimes \left(\overrightarrow{{Elit}_{i}}-\left(\overrightarrow{{R}_{B}}\overrightarrow{{Prey}_{i}}\right)\right)i=\mathrm{1,2},3\dots ,n$$
(2)
$$\overrightarrow{{Prey}_{i}}=\overrightarrow{{Prey}_{i}}+\left(P.\overrightarrow{R}\otimes \overrightarrow{{stepsize}_{i}}\right)$$
(3)

Phase 2: At this stage, the prey and the predators use different movement methods and move at the same speed during the second third of the iterations of the optimization \(\left(\frac{1}{3}maxiter<iter<\frac{2}{3}maxiter\right)\).

While a predator uses Brownian motion, \(Prey\) uses Lévy motion. According to Eq. 4–5, the movements of the first half of the population are updated. \({R}_{L}\) Levy’s motion is a vector containing random numbers based on a normal distribution.

$$\overrightarrow{{stepsize}_{i}}=\overrightarrow{{R}_{L}} \otimes \left(\overrightarrow{{Elit}_{i}}-\left(\overrightarrow{{R}_{L}}\overrightarrow{{Prey}_{i}}\right)\right)$$
(4)
$$\overrightarrow{{Prey}_{i}}=\overrightarrow{{Prey}_{i}}+\left(P.\overrightarrow{R}\otimes \overrightarrow{{stepsize}_{i}}\right)$$
(5)

According to Eqs. 6–7, the other half of the population is updated. Here, \(CF\) is an adaptive parameter for controlling the step size for predator movement.

$$\overrightarrow{{stepsize}_{i}}=\overrightarrow{{R}_{B}}\otimes \left(\overrightarrow{{R}_{B}}\otimes \overrightarrow{{Elit}_{i}}-\overrightarrow{{Prey}_{i}}\right)$$
(6)
$$\overrightarrow{{Prey}_{i}}=\overrightarrow{{Elit}_{i}}+\left(P.CF\otimes \overrightarrow{{stepsize}_{i}}\right)$$
(7)
$$CF={\left[1-\left(Iter./Max.Iter\right)\right]}^{\left(2.Iter./Max.Iter.\right)}$$

Phase 3: The prey is assumed to move slower than the hunter during the remaining part of the optimization iteration number \(\left(iter>\frac{2}{3}maxiter\right)\). For a low velocity ratio \(\left(v=0.1\right)\), the best strategy for predators is Lévy. The final phase is modeled according to Eqs. 8–9.

$$\overrightarrow{{stepsize}_{i}}=\overrightarrow{{R}_{L}}\otimes \left(\overrightarrow{{R}_{L}} \otimes \overrightarrow{{Elit}_{i}}-\overrightarrow{{Prey}_{i}}\right)$$
(8)
$$\overrightarrow{{Prey}_{i}}=\overrightarrow{{Elite}_{i}}+\left(P.CF\otimes \overrightarrow{{stepsize}_{i}}\right)$$
(9)

Additionally, both eddy formation and fish aggregating devices (FADs) have direct impacts on the algorithm. According to the study of Houssein et al. (2021), sharks spend more than 80% of their time near FADs, and for the remaining 20%, they will make a larger jump in various dimensions, likely in search of a setting with a different distribution of prey [36]. The FADs are considered to be local optima; therefore, being aware of the lengthy leaps prevents them from becoming stranded in local optima. and their influence is assumed to be trapped in particular locations in the search space. It is modeled analytically according to Eq. 10.

$${\overrightarrow{Prey}}_{i}=\left\{\begin{array}{cc}{\overrightarrow{Prey}}_{i}+CF\left[{\overrightarrow{X}}_{min}+\overrightarrow{R}\otimes \left({\overrightarrow{X}}_{max}-{\overrightarrow{X}}_{min}\right)\right]\otimes \overrightarrow{U}& if\left(r\le FADs\right)\\ {\overrightarrow{Prey}}_{i}+\left[FADs\left(1-r\right)+r\right]\left({\overrightarrow{Prey}}_{r1}-{\overrightarrow{Prey}}_{r2}\right)& if\left(r>FADs\right)\end{array}\right.$$
(10)

2.2 Proposed chaotic-based MPA

In this study, a hybrid approach was developed by combining different chaos maps with the MPA algorithm. In this proposed algorithm, random number sequences of chaotic maps, which are the main parameters that affect the performance of the MPA, are used. Periodicity, stochastic natural features, remarkable execution, and sensitivity to the initial conditions are what make chaotic maps unique [37, 38].

The eddy or the effects of fish aggregating device (FAD) behavior on marine predators are highly important in the MPA. FADs and long skips, which are among the basic components of the MPA, prevent the algorithm from reaching a local optimum and increase its performance in finding the optimum global solution.

For these reasons, to improve the performance of the MPA, the value of the uniform random coefficient \(r\) given in Eq. 11, which provides the selection of eddies or the effects of FADs, is updated with random number sequences obtained from one- or two-dimensional chaotic maps. The updated mathematical model is given in Eq. 12.

$$r={Chaotic}_{\left(index\right)}$$
(11)
$${\overrightarrow{Prey}}_{i}=\left\{\begin{array}{cc}{\overrightarrow{Prey}}_{i}+CF\left[{\overrightarrow{X}}_{min}+\overrightarrow{R}\otimes \left({\overrightarrow{X}}_{max}-{\overrightarrow{X}}_{min}\right)\right]\otimes \overrightarrow{U}& if\left(r\le FADs\right)\\ {\overrightarrow{Prey}}_{i}+\left[FADs\left(1-r\right)+r\right]\left({\overrightarrow{Prey}}_{r1}-{\overrightarrow{Prey}}_{r2}\right)& if\left(r>FADs\right)\end{array}\right.$$
(12)

Five chaotic maps are employed in our experiments: logistic, tent, henon, sine, and tinkerbell maps. The mathematical equations and visualized maps are provided in Table 2.

Table 2 Behavior of chaotic maps
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2.3 Machine learning

2.3.1 Decision tree (DT)

For problems involving classification and regression (also known as supervised learning), DTs are a very helpful tool. The tree is made up of a root node that branches out into multiple decision nodes based on the characteristics of the dataset, signifying the various “questions” that the tree will try to answer and leaf nodes that signify the decision's result. Since they explicitly match parameters to guide information flow, they train quickly, produce deterministic output (as opposed to the probabilistic output of a neural network), and perform well even with small datasets [39]. To improve performance as a group, they might be coupled in parallel (bagging) or in sequence (boosting). The inner trees of a random forest are fitted to randomly selected subsets of the data using bagging, and the majority decision is used as the output.

2.3.2 Random forest (RF)

RF is a well-liked and adaptable ensemble technique that involves a wide range of ML tasks and data types, and it is known for its effectiveness in many real-world applications [40]. Building an ensemble, or forest, of decision trees derived from a randomized version of the tree induction procedure is the basis of the RF family of techniques. Given that decision trees typically have high variation and low bias, which increases their likelihood of benefiting from the averaging process, they are excellent candidates for ensemble approaches. A bootstrapped sample of the training data was used to train each tree. Therefore, this approach creates diversity among the trees [41].

2.3.3 Extremely randomized trees (extra trees-ET)

ET is an ensemble ML technique that shares many similarities with random forests. Its main applications include classification and regression in data mining, image and text analysis, and various ML tasks, and it has become popular because it is highly effective and efficient for a variety of data types [42]. ET creates a collection of decision trees, similar to random forests. They do, however, go beyond the idea of randomness. In ET, a random subset of features is chosen for each node, and the best split is selected from those random features, as opposed to choosing the best split for each node individually. This additional unpredictability can result in more robust models by preventing overfitting. Bootstrapping, which creates several subsamples of the training data with replacement, is a technique commonly used by ETs [43]. One of these bootstrapped datasets serves as the training set for each decision tree in the ensemble. Because the feature selection and bootstrapping steps are randomized, ETs are capable of handling noisy data with great effectiveness [44].

3 Experimental study

In this study, we conducted two different experiments. In the first experiment, we evaluate which of five different chaotic map-based MPA algorithms performs well in feature selection on benchmark datasets. We then choose sine, the chaotic map that performs rather well. In the second experiment, classifications are made with DT-based algorithms on EEG signal datasets comprising 14 subjects and datasets obtained as a result of the features selected with the SCMPA. The aim is to determine whether the proposed SCMPA can extract the features that best represent the dataset. The experimental setup, evaluation criteria, benchmark datasets, feature selection and classification experiments are described below. The proposed system architecture is shown in Fig. 1.

Fig. 1
figure 1

The proposed system architecture

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The proposed system architecture is shown in Fig. 1.

3.1 Experimental setup

To verify the feasibility and effectiveness of the proposed SCMPA, experiments employing a dataset of 14 subjects and four different classification algorithms, namely, DT, RF, and ET, are carried out. The classification performances obtained without using any feature selection method (only the original feature set) and obtained through the features selected with SCMPA are also compared. MATLAB 2023b was used to conduct all the numerical experimental studies. SCMPA is run 20 times with a population of 30 and 60 iterations.

To realize ML algorithms, the needed parameters are determined. The main parameters of the algorithms are as follows: the Gini index is utilized as a splitting criterion for DTs to determine which splitting characteristic is optimal for each node. Since the maximum depth of the tree for DT is set to “none”, nodes extend until every leaf is cut. At least two samples are needed for the internal node algorithm to be split. In addition to the parameter settings in the DT, the number of estimators in the ET and RF are set to 100.

3.2 Evaluation criteria

The F score with tenfold cross-validation (CV) was used to evaluate the performance of the proposed framework for each subject. The F score is the harmonic mean of the precision and recall. where true positive (TP) is the number of correctly classified healthy signals and false positive (FP) is the number of schizophrenia signals classified as healthy. The number of false negatives (FNs) represents the number of healthy signals classified as schizophrenia, and the number of true negatives (TNs) represents the number of correctly classified schizophrenia signals. In terms of TP, FP, FN, and TN, the formulas for the performance metrics are given below.

$$Precision=\frac{TP}{TP+FP}$$
(13)
$$Recall=\frac{TP}{TP+FN}$$
(14)
$$Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$$
(15)
$$F-score=\frac{2\times Precision\times Recall}{Precision+Recall}$$
(16)

In addition to the F score, the performance of each model was assessed using the area under the receiver operating characteristic (ROC) curve (AUC). The overall AUC was used to evaluate the performance of the models across all possible categorization criteria. The range of the AUC value is 0 to 1. The model has a good ability to classify data if the value is near 1. The true positive rate (TPR) was plotted against the false positive rate (FPR) with the TPR on the y-axis and the FPR on the x-axis representing the ROC curve.

When evaluating the performance of a model using data that are not utilized during training, the CV is employed. The fundamental idea of CV is to eliminate some data, use the remaining data to create a model, and then estimate the samples that are omitted. For a total of k iterations, the data are divided into k folds, with the excluded samples serving as the test sample in each fold. The ultimate success of the k-fold CV is determined by averaging the k performances that are acquired. In this investigation, a 10 × CV was used.

3.3 Dataset

The publicly available EEG signal dataset from the Institute of Psychiatry and Neurology in Warsaw, Poland, was used for the experimental study [45]. The dataset included 14 patients (7 males: 27.9 ± 3.3 years, 7 females: 28.3 ± 4.1 years) with paranoid schizophrenia (SZ) and 14 healthy controls (HCs) (7 males: 26.8 ± 2.9 years, 7 females: 28.7 ± 3.4 years). The EEG signals were recorded for fifteen minutes while the patients were in an eyes-closed resting state. Using the conventional 10–20 EEG montage (shown in Fig. 2, where A1 and A2 are reference electrodes) with 19 EEG channels, Fp1, Fp2, F7, F3, Fz, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4, T6, O1, and O2, data are collected at a sampling frequency of 250 Hz. However, every channel’s EEG data contain 225,000 samples; the first 100 s of the signals are taken into account. This dataset is available at http://dx.doi.org/https://doi.org/10.18150/repod.0107441. The EEG recordings from HCs and SZ patients are shown in Fig. 3.

Fig. 2
figure 2

The standard 10–20 system of EEG electrode maps

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Fig. 3
figure 3

EEG signal samples of (left column) HCs and (right column) patients with SZ

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We must address significant differences in the raw EEG data since this frequently results in the ML algorithm underperforming when there is a significant difference in the numerical attributes of the dataset. In this study, we normalize the raw EEG data and transform the data into the [0, 1] range by using min–max normalization.

$${x}_{{i}_{scaled}}=\frac{{x}_{i}-{x}_{min}}{{x}_{max}-{x}_{min}}$$
(17)

where \({x}_{i}\) represents the \({i}_{th}\) data point, \({x}_{min}\) represents the minimum-valued data point, \({x}_{max}\) represents the maximum-valued data point, and \({x}_{{i}_{scaled}}\) is the normalized form of \({x}_{i}\).

3.4 The performance of the feature selection algorithms

3.4.1 Case study-I: Comparison of the performance of the original MPA and chaotic map-based MPA algorithms on benchmark datasets

In this study, five datasets (https://archive.ics.uci.edu/ml) are selected to verify the effectiveness and efficiency of the algorithm developed for feature selection. The number of features, number of instances, number of classes, and category of data definitions for the selected datasets are given in Table 3. The main objective of these experiments is to evaluate the performance of the MPA on different chaotic maps and determine the optimal chaotic map. The number of populations and the maximum number of generations for each method are 30 and 60, respectively. The mean (mean), standard deviation (std), and minimum (best) values of the different evaluation indices after 20 runs for each dataset are shown in Table 4. Additionally, Table 4 compares chaotic-based MPAs with different chaotic maps with the original MPA in terms of feature selection.

Table 3 List of datasets employed in the experiments
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Table 4 Statistical results of fitness values evaluated by SCMPA and MPA variants on benchmark datasets
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Table 4 shows that the chaotic MPA outperforms the original MPA when various chaotic maps are used. Additionally, it should be noted that across all the datasets, the SCMPA and tent map achieved the best fitness values with the fewest selected feature results when compared to the others. Compared with the other maps, the breast has the best performance at 0.0033 using LCMPA. Hepatitis showed its best performance at 0.1011 with TECMPA. While Liver demonstrated superior performance at 0.1915 using the TICMPA when compared to other map options, Raisin revealed a top performance value of 0.0964 through the HCMPA. The heart exhibited the highest performance value at 0.0222 according to the TECMPA compared to the other maps. All these results prove that chaotic-based MPA algorithms reduce the number of selected features while increasing the quality compared to the MPA.

3.4.2 Case study II: Comparison of the performance of the original MPA algorithm and the chaotic map-based MPA algorithm on the EEG dataset

Metaheuristic algorithms were run on the EEG dataset, and the results obtained are given in Table 5. According to Table 5, the most successful algorithm is the SCMPA, and feature selection is performed with the SCMPA.

Table 5 Statistical results of fitness values evaluated by SCMPA and MPA variants in the EEG dataset
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The features selected for each subject with SCMPA are given in Table 6. According to Table 6, approximately 21% of the features for subjects 1 and 3 were eliminated. Approximately 95% of the features are eliminated for Subjects S2, S4, S5, S7, S9, S10, S11, S12, S13 and S14. For Subjects S6 and S8, approximately 5% of the features are eliminated. The convergence graph obtained from each subject of the SCMPA algorithm is also given in Fig. 4.

Table 6 Selected features with SCMPA
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Fig. 4
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Convergence of each algorithm for each subject

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Additionally, the total rank of MPA and its variants was calculated using Friedman's mean rank test for the EEG dataset as shown in Table 7. Results show that most of the subjects SCMPA ranked first compared to other algorithms.

Table 7 Friedman’s mean rank statistics
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3.5 Classification experiments

In this section, to verify the effectiveness of the SCMPA in SZ recognition, we conduct two types of classification experiments: original feature set-based and selected feature set-based.

3.5.1 Experiment-I: Original feature set-based EEG classification

Classification was performed with tenfold cross-validation via the DT, RF and ET algorithms on the original dataset for each subject, and the obtained performance values are given in Table 8.

Table 8 Performance of each classification algorithm for each subject (original features)
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An examination of the results reveals that the DT algorithm achieved relatively less successful classification than did the other two algorithms. However, when evaluated in general, it cannot be ignored that all the classification models applied were successful. This study aimed to determine whether the same or higher success rate can be achieved with a smaller feature set. Thus, instead of working with the entire feature set, one can focus on important features and work with a smaller feature set.

3.5.2 Experiment II: Selected feature set-based EEG classification

Determining which subset of features performs best in classification is crucial since reducing the number of dimensions in the data can result in reduced calculation time and information processing costs. In this section, classification is performed for each subject based on the features selected with the SCMPA, and the performance values are given in Table 9.

Table 9 Performance of each classification algorithm for each subject (selected features)
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Based on Table 9 above, the results show that selected feature set-based EEG classification with a tenfold CV gives more accurate results than does the original feature set-based EEG classification.

SZs and HCs were accurately classified according to the results displayed above. The confusion matrix and ROC curves, shown in Fig. 5, suggest that nearly 100% accuracy can be attained in the robust discrimination of HCs and SZ patients by using only one electrode.

Fig. 5
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Confusion matrices and ROC curves for each subject

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The comparison between classification with original features and SCMPA selected features are given in Table 10. Based on the results, it can be clearly seen that the same or even better results can be achieved with fewer features.

Table 10 Comparison of the F1-score of DT, RF and ET with original features and SCMPA selected features for EGG dataset
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4 Conclusions

In this study, a new hybrid algorithm is proposed that involves modifying the parameters of the MPA algorithm to improve the algorithm's performance by using a random number sequence derived from five chaotic maps. The goal of the proposed algorithms is to minimize the number of features chosen during feature selection while maximizing the accuracy rate for the EEG signal classification task. Compared with other chaotic-based MPAs, the HCMPA, TICMPA, LCMPA, and SCMPA can be used to select more representative features from the experimental dataset. The SCMPA selects a different number of features for each subject. These features are fed into a DT based on three different classifiers. The experimental results show that more stable and accurate results are achieved via classification via SCMPA-selected features. The only shortcoming with SCMPA is that SCMPA handles only single-objective continuous optimization problems. Consequently, the following can be regarded as the main topics of future research: devising SCMPA to address binary, multi-objective, and discrete space optimization problems.