Optimized adaptive neuro-fuzzy inference system based on hybrid grey wolf-bat algorithm for schizophrenia recognition from EEG signals

Abstract

Schizophrenia is a chronic mental disorder that impairs a person’s thinking capacity, feelings and emotions, behavioural traits, etc., Emotional distortions, delusions, hallucinations, and incoherent speech are all some of the symptoms of schizophrenia, and cause disruption of routine activities. Computer-assisted diagnosis of schizophrenia is significantly needed to give its patients a higher quality of life. Hence, an improved adaptive neuro-fuzzy inference system based on the Hybrid Grey Wolf-Bat Algorithm for accurate prediction of schizophrenia from multi-channel EEG signals is presented in this study. The EEG signals are pre-processed using a Butterworth band pass filter and wICA initially, from which statistical, time-domain, frequency-domain, and spectral features are extracted. Discriminating features are selected using the ReliefF algorithm and are then forwarded to ANFIS for classification into either schizophrenic or normal. ANFIS is optimized by the Hybrid Grey Wolf-Bat Algorithm (HWBO) for better efficiency. The method is experimented on two separate EEG datasets-1 and 2, demonstrating an accuracy of 99.54% and 99.35%, respectively, with appreciable F1-score and MCC. Further experiments reveal the efficiency of the Hybrid Wolf-Bat algorithm in optimizing the ANFIS parameters when compared with traditional ANFIS model and other proven algorithms like genetic algorithm-ANFIS, particle optimization-ANFIS, crow search optimization algorithm-ANFIS and ant colony optimization algorithm-ANFIS, showing high R² value and low RSME value. To provide a bias free classification, tenfold cross validation is performed which produced an accuracy of 97.8% and 98.5% on the two datasets respectively. Experimental outcomes demonstrate the superiority of the Hybrid Grey Wolf-Bat Algorithm over the similar techniques in predicting schizophrenia.

Introduction

Mental diseases have been demonstrated to have a negative impact on one's physical health. These diseases are diagnosed by the psychiatrists based on their subjective experience rather than learning more about the disorders' pathogenesis. To understand the etiology of the disease, Artificial intelligence (AI) approaches have been applied to aid mental health clinicians in making decisions based on patient data (Kalmady et al. 2019; Liu et al. 2020). One of the most vital global medical illnesses nowadays is the so-called psychiatric disorder that has an impact on all aspects of our lives, including relationships, employment, self-esteem, and the ability to communicate and contribute to the community.

Out of 200 classifications of psychiatric disorders reported by Mental Health America (MHA) (https://apibhs.com//2018/05/17/what-are-psychiatric-disorders), schizophrenia (SZ), bipolar disorder (BD), autism etc. are predominant. Mental illness or disorder can be difficult to recognise because it manifests itself in different ways in different people. Some symptoms include depression, suicidal tendency, asociality etc. Among the mental disorders, SZ is a common chronic mental illness that affects over 21 million worldwide (GBD 2017; https://www.who.int/news-room/fact-sheets/detail/schizophrenia). Schizophrenia causes problems with the level of thinking, emotions, poverty of speech, self-awareness, cognitive impairment, and behaviour. Common characterizations are hallucinations and delusions (Bell et al. 1994). Early death is possible in the case of schizophrenia-affected individuals owing to other complications associated with their illness, and nearly three-fourths of them don’t get proper treatment and care. There is no identified reason for the onset of the disease, but it is influenced by genetic, environmental, and psychosocial factors. Facilitating assisted living conditions through primary health care centres and rehabilitation centres, psychotherapy is a helpful management technique for schizophrenia patients (https://www.mayoclinic.org/diseases-conditions/schizophrenia/symptoms-causes/syc-20354443). Proper treatment and medical care can a offer better quality of life to the affected patients. There is no conclusive test for schizophrenia. The diagnosis is made after a thorough examination of the patient’s medical history, symptoms, and signs. Collateral sources of information, such as family members, acquaintances, teachers, and co-workers, are frequently useful in diagnosis. Neuropsychological tests, brain imaging, EEG, and MRI, CT scans of brain function can be used to rule out physical disorder causes of schizophrenia (Clementz et al. 2016). Lifelong medication is required to treat the disease. After proper identification among healthy people, schizophrenic patients might be effectively diagnosed with various treatments. As a result, computer-assisted diagnosis (CAD) of schizophrenia has become critical for the accurate detection of its sufferers. Diagnosis of SZ is normally carried out using positron emission tomography (PET), structural MRI (sMRI), functional MRI (fMRI), etc., However, these methods are controlled by a number of factors, for instance: high cost of imaging, skills of the expert, and poor image quality due to noise/artifacts induced by patient mobility (Pichler et al. 2008). These demerits can be overcome by the use of electrocardiogram signals (EEG) that can monitor the brain activity through non-invasive scalp electrodes (Lee et al. 2001). Key arguments for choosing EEG for monitoring the brain activities of SZ are high spatial and temporal resolution, the capacity to instantly assess brain functionalities, low technical skill requirements for deployment, and partial or full mobility (Vecchiato et al. 2011; Zhou et al. 2018). EEG signals are widely preferred to diagnose other diseases like epileptic seizures (Ullah et al. 2018; Hejazi and Motie Nasrabadi 2019), Alzheimer’s (AD) (Cicalese et al. 2020), Parkinson’s (PD) etc., (Oh et al. 2020; Xu et al. 2020). Hence, CAD systems employing EEG signals for schizophrenic detection could help neurologists or professionals by serving as a second expert opinion for prompt schizophrenia detection from EEG. Support Vector Machine (SVM), Logistic Regression (LR), Adaptive Boosting (AdaBoost), etc., and other well-known ML algorithms are used to classify EEG signals in order to detect SZ patients (Shim et al. 2016). These ML algorithms are complemented by appropriate feature extraction methodologies because the EEG signals obtained change dynamically and are non-stationary in nature (Kannathal et al. 2005; Veronese et al. 2013). Feature extortion in the time-domain (TD) or frequency domain (FD) is a laborious task and often struggles to handle large volumes of data. As a result, hybrid ML and deep learning techniques have piqued the interest of researchers in overcoming ML shortcomings and for ready deployment in real-time scenarios. Technologies like IoT also aid in tele-monitoring of patients undergoing treatment at healthcare centres through cloud, FOG, and edge computing facilities.

The present work concentrates on the deployment of EEG signals to detect SZ using an adaptive neuro-fuzzy inference system (ANFIS) based on the Hybrid Grey Wolf-Bat Algorithm for accurate recognition. The multichannel EEG is first subjected to pre-processing and filtering, and is then divided into segments of short periods and segregated into delta, theta, alpha, beta, and gamma spectral bands. Due to SZ, the spectral sub-bands show sudden fluctuations in EEG signal activity. The Theta band is linked to memory retention where SZ patients have extreme brain activity compared to healthy people. This band has been meticulously studied in this work. Following the feature extortion and selection, the discriminant features are forwarded to optimized ANFIS for SZ prediction.

The contributions include:

1. Optimized ANFIS is developed to detect SZ promptly.

2. For finding the optimal parameters and structure of ANFIS, a hybrid technique called the Hybrid Grey Wolf-Bat Algorithm that combines the benefits of Grey-Wolf optimization (GSO) and Bat optimization (BA) has been proposed (HWBO).

3. The applicability of the HWBO algorithm with the modified two-pass ANFIS learning algorithm in order to maintain a trade-off balance between minimization of the rule-base and accuracy maximization is being investigated.

4. Pre-processing of EEG signals is performed using the Butterworth band pass filter and wICA for artefact removal, from which statistical, time-domain, frequency domain, and spectral features are extracted.

5. Discriminate features are selected using the ReliefF algorithm that contributes to the disease diagnosis.

6. Comparison of the proposed model with similar feature engineering models is performed.

The rest of the paper is organized as: “Related works” Section elucidates some of the literature reviews that relate to SZ detection and ANFIS optimization. The proposed methodology is described in “proposed methodology”. Experimental outcomes are paraphrased in “Results and discussion”. A conclusion is provided in “conclusion”.

Related works

Literure works on SZ diagnosis

This section outlines some of the studies involved in diagnosing SZ through EEG signal analysis. An effective technique based on EEG for SZ detection was proposed by (Boostani et al. 2009) in which autoregressive (AR) model parameters, band power, and fractal dimension features were fed to several classifiers. With an accuracy of 87.51%, the outcomes confirmed the applicability of the BDLDA for the categorization of SZ and healthy controls. (Zhao et al. 2012) developed a technique for schizophrenia diagnosis based on non-linear EEG signal analysis. From EEG, entropy-based features, Lempel–Ziv complexity, and Higuchi fractal dimension features were extorted, and generic programming (GP) was used for selecting the features as reported by (Sabeti et al. 2009). The features were fed to an AdaBoost classifier that attained 91% classification accuracy. Authors in Santos-Mayo et al. (2017) proposed a model for SZ detection from EEG based on p3b waves examined during the task of an auditory odd-ball. (Li et al. 2019) developed a method to differentiate SZ from normal controls using a combination of rest and task p300spatial EEG patterns.

The power spectra have been the most popular aspect, and used to diagnose other psychotic diseases (Johannesen et al. 2016). Statistics such as mean, skewness, and kurtosis have also been used to classify SZ (Alimardani et al. 2018; Tikka et al. 2020). Despite the fact that numerous studies have put forth several features for classifying SZ, these features do not address contradictions in interpreting EEG. Further, they have failed to take advantage of EEG’s most powerful feature: millisecond temporal resolution. To address these issues, brain microstate analysis was performed by (Kim et al. 2021), providing an accuracy of 76.62% in SZ detection. (Chu et al. 2017) used deep learning algorithms, as well as random forest and voting classifiers, to recognize individuals with schizophrenia using resting-state EEG data. Based on fractal information, (Namazi et al. 2019) developed a model to distinguish SZ from normal subjects. Apart from conventional ML approaches, DL methods were also employed in screening for SZ (Oh et al. 2019; Yan et al. 2017; Qureshi et al. 2019; Srinivasagopalan et al. 2019; Zeng et al. 2018; Phang et al. 2020). Convolutional Neural Networks (CNN), Recurrent Neural Networks (R-CNN), and Long Short-Term Memory (LSTM) networks were preferred in categorizing SZ controls and attained reasonable accuracy. Table 1 provides a quick review of the ML and DL techniques employed for identifying SZ patients.

Table 1.

Summary of related works in SZ detection based on feature engineering

Reference	Feature engineering	Classifier	Dataset	Acc. (%)
Shim et al. (2016)	Source and sensor level features - Fisher’s Score feature selection	SVM	SZ:34 HC:34	88.24
Boostani et al. (2009)	Band power Autoregressive (AR) and FD parameters	Boosted Direct LDA	SZ:20 HC:20	87.5
Zhao et al. (2012)	Entropy related non-linear features of alpha band of EEG	BPNN	SZ:31 HC:31	86.1
Sabeti et al. (2009)	AR, band power and FD features; Genetic programming-based features election	AdaBoost	SZ:20 HC:20	91.94
Santos-Mayo etal (2017)	TD and FD features of ERP related wave for different electrode groups selected using J5 feature selection algorithm	MLP	SZ:16 HC:31	93.42
Li et al. (2019)	Inherent spatial pattern of network (SPN) features	LDA/SVM	SZ:23 HC:25	90.48
Johannesen et al. (2016)	Squared amplitude features	SVM	SZ:40 HC:12	87
Oh et al. (2019)	25 s duration EEG segments normalized with Z-score	CNN	SZ:14 HC:14	98.07
Phang et al. (2020)	TD and FD connectivity features	MDC- CNN	SZ:14 HC:14	91.69
Jahmunah et al. (2019)	Non-linear features of filtered, segmented EEG signals; feature selection using Student’s-test	SVM	SZ:14 HC:14	92.91
Deiva et al. (2019)	ERP features of selected regions of the brain	LDA	SZ:11 HC:9	71
Taylor J et al. (2017)	Spatiotemporal images using statistical parametric mapping of scalp EEG’s ERP features	Gaussian process	SZ:21 HC:22	80.48
Buettner et al. (2020)	Multi fractal and Entropy-Based features	RF	SZ:14 HC:14	96.77
Baradits et al. (2020)	Microstate features	SVM	SZ:75 HC:75	82.7

ANFIS optimization

The Adaptive Neuro-Fuzzy Inference System (ANFIS) incorporates the benefits of both Artificial Neural Networks (ANNs) and Fuzzy Logic (FL). However, when used in real-world applications, training of ANFIS parameters is one of the most difficult issues. Many prior studies used techniques such as the genetic algorithm (GA), particle swarm optimization (PSO), and grey wolf optimization to solve the issue of ANFIS training (GWO). The ANFIS model has been shown to be a valuable statistical tool for a variety of applications. The ANFIS model is a resilient and intelligent simulation model because of its capacity to correct for data ambiguity. It encapsulates a process's nonlinear structure, adaptability, and ability to learn quickly. The issue with ANFIS is its parameter optimization. Although ANFIS’ traditional optimization techniques outperform mathematical and computational approaches in terms of estimation accuracy, they are only looking for a local optimum solution.

ANFIS parameters were optimized using quantum behaved PSO as reported by Lin et al. 2012. Aghelpour et al. 2020) developed an ANFIS model combining bio-inspired optimization algorithms for agricultural drought monitoring and compared with similar algorithms. Ant colony optimization (ACO) and GA attained appreciable performance in optimizing ANFIS. Balasubramanian and Ananthamoorthy 2021 reported an improved ANFIS model combining glowworm swarm and differential evolution optimization algorithm for medical diagnosis. Several works (Elbaz et al. 2019; Maroufpoor et al. 2019; have reported the impact of algorithms like GA, GWO and hybrid algorithms for ANFIS parameter adaptation.

From the literature study, it is learnt that, though the DL models have attained better performance, most of them relied on MRI and some on raw EEG. The high dimensionality of raw EEG has increased the computational time of DL methods, which consequently face challenges in real-time deployment. Also, the CNN architectures discussed faced complexity in design with reduced latency. Hence, it’s proposed to design a CAD system using optimized ANFIS for applicability with real time utility.

Materials and method

Adaptive neuro-fuzzy inference system (ANFIS):

Jang 1993) developed ANFIS, a practical AI system that mimics human thinking to handle inexact issues. It’s a basic data-learning method which converts inputs from highly interconnected NN processing components and information links into the desired output using fuzzy logic. It can handle non-linear and complex issues since it includes ANN and fuzzy inference approaches into a single structure. It normally incorporates the following layers: fuzzification, product, normalization, defuzzification, and summation. The network comprises of nodes whose efficiency is mostly determined by the node’s adaptable parameters. The network learning guidelines alter specific parameter values to reduce the difference between the actual and expected output. The general ANFIS structure is shown in Fig. 1.

Fig. 1.

ANFIS Structure

The ANFIS model followed in (El-Hasnony et al. 2020) is used in the proposed study. The ANFIS learning algorithm employs a two-pass learning procedure, forward–backward pass, to update its modified parameters. ANFIS is trained in its parameters using a hybrid gradient descent (GD) and least square (LSE) estimator to minimise error gap between desired and actual output, as provided in Table 2.

Table 2.

ANFIS learning process

Parameters	Forward	Backward
Consequent parameter	Least square estimator	Fixed
Premises parameters	Fixed	Gradient descent
Signals	Output of each node	Error

The node outputs are passed forward (layer 1–4) in the forward pass of the learning method. The resulting parameters are calculated by least squares. In the backward pass, the error signals transmit from the output to the input layer, and the GD method adjusts the premise parameters. The network learns and trains at this point to discover parameter values that are sufficient for the training data.

Layer 1 Fuzzification layer- a gaussian membership function is used with parameters (centre c, width σ). The output of the layer is described by,

$$y_i^{(1)}=Gaussian(x:c:\sigma )=e^{-\frac{1}{2}{\left(\raisebox{1ex}{$x-c$}\!\left/ \!\raisebox{-1ex}{$\sigma $}\right.\right)}^2}$$ 1

Layer 2 Product layer where the layer’s each node responds to a single fuzzy rule in the Sugeno style. The nodes obtain input from the corresponding Fuzzification neurons and calculate the rule’s firing strength. Consequently, the output of the neuron is represented by,

$$y_i^{(2)}={\mathrm{\Pi }}_{i=1}^k{x}_{\mathit{ji}}^{(2)}$$ 2

where $x_{\mathit{ji}}^{(2)}$ is the layer input from layer 1(j)–2 (i).

Layer 3 Normalization layer. This layer’s nodes accept data from the previous layer and calculate the weighted firing power of a particular rule. Consequently, the output of the neuron is represented by,

$$y_i^{(3)}=\frac{x_{\mathit{ji}}^{(3)}}{{\sum }_{j-1}^n{x}_{\mathit{ji}}^{(3)}}={\overline{\mu }}_i$$ 3

where $x_{\mathit{ji}}^{(3)}$ shows the input received as per the neuron j obtained from the layer 2 to neuron i in this layer.

Layer 4 Defuzzification layer. The neurons calculate a specific rule’s weighted measure as follows:

$$y_i^{(4)}=x_i^{(4)}\left[k_{\mathit{io}}+k_{i1}+k_{i2}\right]={\overline{\mu }}_i\left[k_{\mathit{io}}+k_{i1}+k_{i2}\right]$$ 4

The layer 4 input and output are denoted by $x_i^{(4)}$ and $y_i^{(4)}$ respectively.

Layer 5 Overall output of the model.

$$y=\sum _{i=1}^n{x}_i^{(5)}=\sum _{i=1}^n{\overline{\mu }}_i\left[k_{\mathit{io}}+k_{i1}+k_{i2}\right]$$ 5

Grey wolf optimization (GWO)

Developed in 2014 by Mirjalili et al. (2014), the GWO is classified as a top predator. Grey wolves live in a pack (normally 5–12). The algorithm imitates the same leadership and hunting abilities as grey wolves. The pack is composed of 4 levels referred to as alpha (α), beta (β), delta (δ), and omega (ω).The alphas (either male or female) are in charge of leading the pack and making decisions (for instance, hunting, sleeping, and deciding on a wake-up time). The beta wolves support alpha in taking decisions. The omega wolves are always subordinate to all other dominant wolves. The grey wolf optimization algorithm is based on the design of their hunting method to capture their prey. During hunting, all the grey wolves have a natural tendency to encircle their prey. Mathematically, the encircling process is represented by

$$\overrightarrow{D}=\left|\overrightarrow{C}·{\overrightarrow{X}}_p-{\overrightarrow{X}}_{(t)}\right|$$ 6

$${\overrightarrow{X}}_{(t+1)}={\overrightarrow{X}}_p(t)-\overrightarrow{A}·\overrightarrow{D}$$ 7

where $\overrightarrow{D}$ shows the prey – wolf distance, position vector of the wolf and the prey are denoted by $\overrightarrow{X}$, and ${\overrightarrow{X}}_p$ respectively. $\overrightarrow{A.}$ and $\overrightarrow{C}$ random vectors are computed by using

$$\overrightarrow{A}=\left|2\overrightarrow{a}·\overrightarrow{r_1}-\overrightarrow{a}\right|$$ 8

$$\overrightarrow{C}=2\overrightarrow{r_2}$$ 9

The random vectors $\overrightarrow{r_1}$ and $\overrightarrow{r_2}$ are chosen between [0, 1].The component values of vector $\overrightarrow{a}$ reduces linearly from 2 to 0 during iterations.

$$a=2-t\ast \frac{2}{It{r}_{\mathit{total}}}$$ 10

Itr_total defines the total no. of iterations. Grey wolf’s location (X, Y) alters depending upon where the prey (X*, Y*) is. By altering both $\overrightarrow{A}$ and $\overrightarrow{C}$ vectors, grey wolf’s position could be changed to an optimal solution. According to α, β and δ wolves optimal positions, all the other wolves hunt. and adjust their positions. The position update mechanism is represented as

$${\overrightarrow{X}}_{(t+1)}=\frac{{\overrightarrow{X}}_1+{\overrightarrow{X}}_2+{\overrightarrow{X}}_3}{3}$$ 11

where

$${\overrightarrow{X}}_1={\overrightarrow{X}}_{\alpha }-{\overrightarrow{A}}_1·{\overrightarrow{D}}_{\alpha }$$ 12

$${\overrightarrow{X}}_2={\overrightarrow{X}}_{\beta }-{\overrightarrow{A}}_2·{\overrightarrow{D}}_{\beta }$$ 13

$${\overrightarrow{X}}_3={\overrightarrow{X}}_{\delta }-{\overrightarrow{A}}_3·{\overrightarrow{D}}_{\delta }$$ 14

$${\overrightarrow{D}}_{\alpha }=\left|{\overrightarrow{C}}_1·{\overrightarrow{X}}_{\alpha }-\overrightarrow{X}\right|$$ 15

$${\overrightarrow{D}}_{\beta }=\left|{\overrightarrow{C}}_2·{\overrightarrow{X}}_{\beta }-\overrightarrow{X}\right|$$ 16

$${\overrightarrow{D}}_{\delta }=\left|{\overrightarrow{C}}_3·{\overrightarrow{X}}_{\delta }-\overrightarrow{X}\right|$$ 17

The pseudo code of GWO is presented in Algorithm 1.

Bat algorithm (BA)

Yang 2010) developed and investigated the Bat Algorithm (BA), a well-established, nature- inspired meta-heuristic algorithm. BA works by emulating the echolocation process used by bats to perceive their immediate surroundings and locate prey and/or obstacles. Loudness and rate of pulse emission are the basic intrinsic qualities of the bat that change depending on its proximity to prey. The bat continuously generates SONAR sound pulses that reflect from the prey’s surface, detects and observes the reflected wave. Calculating the time taken for the reflective action, the bat mind maps its prey and tries to approach it. The pulse rate of the emission increases as the bat comes closer to the prey, but the loudness drops. A population of bats follows the common prey at all times. This method is used by the BA to calculate the position of the bats for subsequent iterations around the local optima with regard to the preceding iteration (s). The BA works with initialization of parameters for each bat like velocity vel_i, position x_i, and frequency Q_i, besides loudness loud_i and pulse rates rate_i. Considering the maximum number of iterations as Iter_max, the following equations are considered for updating the properties of each individual iteratively.

$$Q_i=Q_{min}+(Q_{min}-Q_{max})\beta$$ 18

$$ve{l}_j^i=ve{l}_j^i(t-1)+x_{\mathit{Globalbest}}-x_{\mathit{Globalbest}}(t-1)Q_i$$ 19

$$x_j^i=x_j^i(t-1)+ve{l}_j^i$$ 20

where the maximum and minimum frequency are represented by $Q_{min}$ and $Q_{max}$ rrespectively.β is selected randomly between [0 and 1]. For i^th bat with j^th dimension, the position component is represented as $x_j^i$, and the velocity component as $ve{l}_j^i$. The present global best solution is stored as $x_{\mathit{Globalbest}}$. Initially, the loudness and pulse emission rate are chosen at random between [1,2] and [0,1].

$$x_{\mathit{new}}=x_{\mathit{old}}+\in loud(t)$$ 21

$$lou{d}_i(t+1)=\alpha lou{d}_i(t)$$ 22

$$rat{e}_i(t+1)=rat{e}_i(0)[1-e^{-\gamma t}]$$ 23

The fitness of each agent is determined by the Mean Squared Error (MSE); the smaller the MSE, better is the fitness.

$$fitnes{s}_i=MSE=\frac{1}{n}\sum _1^n{[Valu{e}_{\mathit{pred}}-Valu{e}_{\mathit{act}}]}^2$$ 24

The pseudo code for BA is provided in Algorithm 2.

Proposed methodology

In this section, an overall framework for SZ prediction is presented. The methodology starts with the preparation of the EEG dataset acquired from the two public datasets. The collected EEG signals are subjected to pre-processing using a Butterworth band pass filter and wICA for artefact removal, from which statistical, time-domain, frequency- domain, and spectral features are extracted. Discriminate features are selected using the ReliefF algorithm that contributes to the disease diagnosis. The selected are then forwarded to the fully optimized ANFIS model for classification into either SZ or healthy. For finding the optimal parameters and structure of ANFIS, a hybrid technique called the Hybrid Grey Wolf-Bat Algorithm that combines the benefits of Grey-Wolf optimization (GSO) and Bat optimization (BA) is employed (HWBO). The overall framework is picturized in Fig. 2.

Fig. 2.

Overall framework of the proposed SZ detection

In the following subsections, the suggested hybridization of GWO with BA for ANFIS optimization will be discussed.

Hybrid wolf-bat algorithm (HWBO)

The Hybridization of the Grey Wolf and Bat Optimization Algorithm is presented in this section. HWBO combines the finest features of both algorithms: GWO’s high exploration abilities allow for a thorough examination of the search space, whereas the BA, with its high exploitative feature, gives greater local search capability. In our approach, namely, HWBO, GWO is used to explore the problem space and pass the best two solutions to BA to direct its local search. BA explores deeper and finds the optimal solution. MSE is adopted as the fitness function where the objective is to minimize it. In the hybrid method, for each iteration, a single run of GWO is succeeded by a single run of the BA. The position of the GWO algorithm’s three best wolves, α, β and δ, is sent to the BA as an output, which will act as the initial position of the first three bats. The rest of the bats are set up at random. Initialization of the three bats with α, β and δ positions ensures full coverage of the entire search space, which the BA lacked originally, in order to find better optimal solutions. BA then functions in the usual manner, updating the parameters, loudness, and pulse rate as per the equations, and finally, the Global Best solution is updated in case it improves. The location of the α-wolf is initialized to the Global Best result of the previous iteration for the next iteration. The process proceeds. The pseudo code for the Hybrid Wolf-Bat algorithm (HWBO) is illustrated in Algorithm 3.

Adaptation of ANFIS using the proposed HWBO algorithm

The success of ANFIS is determined by how well it learns its structure and tunes its parameters. ANFIS establishes a fuzzy rule base for approximating the desired output. On the other hand, parameter adjustment aids in increasing the model's accuracy. This paper focuses on both the ANFIS optimization goals. The forward pass of the modified two-pass ANFIS learning approach focuses on rule-base minimization, while the backward pass focuses on accuracy maximization. The HWBO is utilised to adjust both the consequent and antecedent parameters of the ANFIS model. According to the proposed algorithm, Table 2 that shows the learning process of the ANFIS is suitably modified and indicated in Table 3. Getting stuck at the local minima is a major constraint of gradient descent, and it may be avoided using meta-heuristic algorithms like the one presented.

Table 3.

ANFIS learning process with HWBO

Parameters	Forward	Backward
Consequent parameters	GWO-BA	Fixed
Antecedent parameters	Fixed	GWO-BA
Rule-base	Reduced number of rules	Fixed
Signals	Rule base minimization	Accuracy maximization

The basic objective behind reducing the rule-base is to focus exclusively on the rules that are highly potential. As a result, the rules which have a major impact on ANFIS' overall decision are considered prospective and kept in the rule-base. Rules that contribute less or are non-contributing are trimmed. As it is computationally less expensive and contains exploration and exploitation capabilities, HWBO accomplished the task of updating ANFIS settings quickly and with greater flexibility than the gradient-based techniques. The total number of ANFIS modifiable parameters is an important aspect of ANFIS because of the processing work required for the adaption process. The difference between each rule's output and the expected output is found out using the error measure given by

$$SE={(O^t-O^r)}^2$$ 25

where target output and rule output are denoted by O^t and O^r respectively. Let the predefined error tolerance be θ, chosen based on trials. The rules with SE > θ are considered weak and are hence pruned. The remaining are thought to be potential and strong, thus they are preserved. After selecting the potentially contributing rules, the overall output is computed by calculating the O_avg.

$$O_{\mathit{avg}}=\frac{1}{n}\sum _{i=1}^n{O}_i^r$$ 26

where n is the no. of selected rules, and $O_i^r$ is the output of i^th rule. The rule-set with the lowest Mean Square Error (MSE), as determined by Eq. (27), is the minimised rule-base, and it is chosen for backward pass.

$$MSE=\frac{1}{m}\sum _{i-1}^m{\left(O_{\mathit{avg}}-O_m^t\right)}^2$$ 27

where O_avg is the average of selected rules outputs, m^th training pair's target output is denoted by $O_m^t$ and m is the no. of training pairs. In the proposed study, the rule error tolerance, θ is set as 0.01 with a 0.005 overall error tolerance. The proposed HWBO-ANFIS is elucidated in Algorithm 4.

Figure 3 illustrates the optimized ANFIS model with HWBO optimization.

Fig. 3.

ANFIS model with HWBO optimization

Results and discussion

Two trials have been performed to assess the efficiency of ANFIS-HWBO. Firstly, an experiment is conducted for efficiency evaluation and robustness of the proposed approach in producing a minimal error, and the second to predict the SZ using datasets 1 and 2, which will be discussed later in this section.

Model evaluation

Various metrics used to compute the efficacy of ANFIS optimization and to check the efficacy of the solutions’ performance was reported in (Ewees and Aziz 2020). The following metrics are adopted to check the ANFIS – HWBO performance is highlighted below:

1. Mean squared error (MSE):

   $$\text{MSE}=\frac{1}{\text{n}}\sum _{\text{i}=1}^{\text{n}}{\left({\text{y}}_{\text{i}}-\overline{{\text{y}}_{\text{i}}}\right)}^2$$ 28

   The data points are denoted by n, the observed values by y_i and predicted values by $\overline{{\text{y}}_{\text{i}}}$.

2. Mean squared error (MSE):

   $$\text{RMSE}=\sqrt{\frac{1}{\text{n}}\sum _{\text{i}=1}^{\text{n}}{\left({\text{y}}_{\text{i}}-\overline{{\text{y}}_{\text{i}}}\right)}^2}$$ 29
3. Co-efficient of correlation (R²):

   $${\text{R}}^2=1-\sum _{\text{i}=1}^{\text{n}}\frac{{\left({\text{y}}_{\text{i}}-\overline{{\text{y}}_{\text{i}}}\right)}^2}{{\left({\text{y}}_{\text{i}}-\overline{\text{y}}\right)}^2}$$ 30
4. Standard deviation (SD):

   $$\text{SD}=\sqrt{\frac{1}{\text{n}-1}\sum _{\text{i}=1}^{\text{n}}{\left({\text{y}}_{\text{i}}-\overline{{\text{y}}_{\text{i}}}\right)}^2}$$ 31
5. Accuracy:

   $$\frac{\text{TP}+\text{TN}}{\text{TP}+\text{FN}+\text{TN}+\text{FP}}$$ 32
6. F1- Score:

   $$2\ast \frac{(\text{Precision})(\text{Recall})}{\text{Precision}+\text{Recall}}$$ 33

   where Precision = $\frac{\text{TP}}{\text{TP}+\text{FP}}$, Recall = $\frac{\text{TP}}{\text{TP}+\text{FN}}$.
7. Mathew’s Correlation Coefficient (MCC):

   $$\frac{(\text{TP}\times \text{TN})-(\text{FP}\times \text{FN})}{\sqrt{(\text{TP}+\text{FP})(\text{TP}+\text{FN})(\text{TN}+\text{FP})(\text{TN}+\text{FN})}}$$ 34

   where TP, FP, FN, and TN calculated using Table 4.
8. AIC: It’s a criterion for determining whether or not a statistical model has been properly adapted.

   $$AIC=nlog\left[\frac{1}{n}\sum _{i=1}^n{\left(C_{d(observed)i}-C_{d(predicted)i}\right)}^2\right]+2k$$ 35

where k - no. of the model’s estimated parameters.

Table 4.

Confusion matrix

		Actual/true class
		P	N
Predicted class	P	True positive (TP)	False positive (FP)
	N	False negative (FN)	True negative (TN)

TP: Number of correct predictions that an instant is positive

FP: Number of incorrect predictions that an instant is positive

FN: Number of correct predictions that an instant is negative

TN: Number of incorrect predictions that an instant is negative

Investigation of different generations and adaptability

Examination of various fuzzy inference system generations is outlined in this section. Grid partitioning (GP), subtractive clustering (SC), and fuzzy c-means clustering (FCM) are three fuzzy inference algorithms in the ANFIS paradigm. Outcomes with the statistical indices for the three generations are presented in Table 5.

Table 5.

Statistical indices for three generations of ANFIS

Generation	RMSE	AIC
GP	0.0378	− 1134.46
SC	0.0314	− 1147.88
FCM	0.0248	− 1176.65

As seen from Table 5, the RMSE for GP, SC, and FCM is 0.0378, 0.0314, and 0.0248, respectively. FCM simulates higher efficiency compared to two other generations. Furthermore, the AIC for FCM is computed as -1176.65. Thus, this generation of ANFIS is used in the study.

Evaluation of ANFIS with HWBO on model optimization

Two datasets (DS-1 and 2) are utilized to find the efficacy of the proposed system (ANFIS-HWBO).

Dataset - 1 (DS-1) Two groups of participants are included in the dataset http://brain.bio.msu.ru/eeg_schizophrenia.htm. The participants were psychiatrist-screened adults and were separated into two classes: healthy controls (HC = 39) and those who exhibited schizophrenia symptoms (SZ = 45) during the resting state. The dataset was prepared by Prof. N.N. Gorbachevskaya (Leading Researcher at The Mental Health Research Centre) and Dr. S.V. Borisov (Senior Researcher at the Faculty of Biology at M.V. Lomonosov Moscow State University) in the Laboratory for Neurophysiology and Neuro-Computer Interfaces at M.V. Lomonosov Moscow State University. Each EEG signal consists of 16 channels, viz., F7, F3, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4, T6, O1 and O2. Sampled at 128 Hz, the captured EEG signals are of60sec duration, each of them having 7680 EEG voltages (mV). Multi-channel EEG is utilised in the study owing to its high spatial and temporal resolution (Blumenfeld and Clementz 1999). Figure 4 illustrates the temporal view of 16-channel EEG signals for healthy controls (HC) and SZ.

Fig. 4.

a Scalp EEG of Healthy person b Scalp EEG of SZ person

Dataset - 2 (DS-2) This set contains 19 channel EEG recording obtained from 14 patients (7 M and 7 W) with SZ and 14 HC of similar age group and gender. The signal captured is of 15 min duration with the subjects in a relaxed state with closed eyes.These19-channel signals are captured with the help of electrodes like FP1, FP2,F7, F3, Fz, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4,T6, O1, O2, sampled at 250 Hz (Olejarczyk and Jernajczyk 2017) from the scalp.

In this work, the performance of ANFIS-HWBO is investigated by comparing it with different meta-heuristic algorithms such as differential evolution algorithm (DE), ant colony optimization algorithm (ACO), grey wolf optimization algorithm (GWO), crow search algorithm (CSA), genetic algorithm (GA), particle optimization algorithm (PSO), and standard ANFIS.

The dataset is split into 60% training and 40% testing in all trials. Table 6 displays the parameters set for all algorithms. The parameters have been adopted in this study because they have achieved excellent results in earlier studies (Ewees and Aziz 2020; Penghui et al. 2020). All the tests are carried out on a Windows 10 Pro 64-bit computer with Intel (R) 16 GB of RAM and a Core (TM) i7-8550U CPU running at 1.80 GHz (1.99 GHz). All implementation is done in MATLAB (2018a).

Table 6.

Parameter settings

Algorithm	Parameter	Value
ANFIS	Error goal	0
	Decrease rate	0.9
	Initial step	0.01
	Increase rate	1.1
	Max. epochs	100
ANFIS-GA	Crossover %	0.7
	Mutation %	0.5
	γ, β	0.2, 8
	Mutation rate	0.1
ANFIS-ACO	Selection pressure	0.4
	Zeta	1
ANFIS-PSO	C1, C2	2
	Vmax, Vmin	0.9, 0.2
	W, Wdamp	1, 0.99
ANFIS-CSA	Flight length	1.5
	Awareness probability	0.05
ANFIS-GWO	A	[2:0]
ANFIS-BAT	Loudness, pulse rate	0.99, 0.5
	Qmin, Qmax	1, 1

All optimization algorithms have the following parameters: maximum no. of iterations = 100, population size (n) = 25, upper bound = 10. lower bound = 10.

Another experiment is conducted to assess the adaptation process of ANFIS using the proposed HWBO algorithm. With a rule error tolerance = 0.01, adaptability of the optimized ANFIS model is denoted in Table 7. From Table 7, it can be inferred that the proposed optimization using HWBO optimizes the ANFIS with a reduction in the rule base, offering a better accuracy of 99.45% with the lowest MSE. Also, GA attained a higher rule base early in the 80^th iteration, followed by ACO, PSO, etc. The lowest accuracy is recorded by GA. GWO and BAT attained satisfactory accuracy on 100 iterations, next only to HWBO. This experiment validates the validity of our recommendation and can be used to improve the ANFIS parameter optimization process.

Table 7.

Results of the modified two-pass ANFIS learning algorithm

Algorithm	Optimized rule-base	# of iterations	MSE	Accuracy (%)
GA	110	80	0.232	89.67
ACO	93	90	0.107	90.11
PSO	87	95	0.086	93.89
CSO	74	85	0.065	94.65
GWO	70	100	0.054	95.86
BAT	68	100	0.028	96.90
HWBO	51	100	0.015	99.45

Evaluation of ANFIS with HWBO on SZ categorization

In the following section, the proposed model for SZ disease prediction is discussed. The sequence of the process is illustrated in Fig. 2.

EEG pre-processing

The detected EEG signals are generally influenced by a variety of artefacts caused by the patients’ mobility or body posture, as well as additive noise (Upadhyay et al. 2016). To reduce the artefacts, an II-order Butterworth Band Pass Filer (BPF) is applied, operating between 0.1 Hz and 50 Hz for DS-1 and between 0.1 Hz and 125 Hz for DS-2. The artifact-contaminated components are then detected and removed using the wavelet-enhanced independent component analysis (wICA) approach as reported in (Castellanos and Makarov 2006). With ICA, wICA makes use of the wavelet threshold to improve artefact removal and may thus better recover the neuronal activities that are concealed in the artefacts. To possess uniform statistical features, the EEG signals are segmented into segments of 5 s of short duration (pseudo-stationary) (Subha et al. 2008). For precision, the same duration is allotted for both the datasets. The short-duration signals can easily be processed using IoT and cloud devices to be used in real time. Fast Fourier transform (FFT) is applied to convert the signals from TD to FD and the obtained FD signals are then categorized into mutually disjoint bands, comprising of delta δ: 0:1 Hz–4 Hz, theta θ₁: 4 Hz–6 Hz, theta θ₂: 6 Hz–8 Hz,alpha α: 8 Hz–12 Hz,beta β:12 Hz–30 Hz and gamma γ: ≥ 30 Hz.SZ patients show variations in EEG patterns in the theta band.

Feature extraction

Feature extraction is a crucial step in EEG signal classification. The current study considers features such as statistical, TD, FD and spectral features from EEG segments of 5 s duration for each spectral band. The electrodes are clustered into 5 regions of interest (ROI): left anterior (Fp1, F7, F3), right anterior (Fp2, F4, F8), left posterior (T7, C3, P7, P3, O1), right posterior (C4, T8,P4, P8, O2), and central (Fz, Cz, Pz).The thirty five features are computed for each channel of the EEG. Table 8 provides features that are extracted from the 5 ROIs:

Table 8.

List of features extracted

Fea No	Feature	Formula/definition	Domain
1	Mean (μ)	$\frac{1}{N}{\sum }_{N-1}^{N}x[n]$	Statistical
2	Variance (Var)	$\frac{1}{N-1}{\sum }_{N-1}^N{\left[x[n]-\mu \right]}^2$	Statistical
3	Standard deviation (σ)	$\sqrt{\frac{1}{N-1}{\sum }_{N-1}^N{\left[x[n]-\mu \right]}^2}$	Statistical
4	Skewness (Sk)	$\frac{1}{N-1}{\sum }_{N-1}^N{\frac{\left[x[n]-\mu \right]}{\sigma }}^3$	Statistical
5	Kurtosis (Kur)	$\frac{1}{N-1}{\sum }_{N-1}^N{\frac{\left[x[n]-\mu \right]}{\sigma }}^4$	Statistical
6	Coefficient of variation CV)	$\raisebox{1ex}{$\sigma $}\!\left/ \!\raisebox{-1ex}{$\mu $}\right.$	Statistical
7	Zero crossing rate (ZCR)	$\frac{1}{N-1}{\sum }_{N-1}^N{l}_R\left(x[n]x[n+1]\right)$	Statistical
8	Width	$\text{Upp}-\text{Low}=Pr[X\ge x]\ge 0.95$ − $Pr[X\le x]\le 0.05$	Statistical
9	Asymmetry	$\frac{\left(Upp+Low-2\times median\right)}{\mathit{width}}$	Statistical
10	Sample entropy (SE)	$-log\frac{A}{B}$	Time
11	Shannon entropy (Hsh)	$-{\sum }_i{P}_{i}log{P}_i$	Time
12	Approximate entropy (AE)	${\varphi }^m(r)-{\varphi }^{m+1}(r)$	Time
13	Permutation entropy (PE)	$-{\sum }_{i-1}^{D!}{P}_{i}log{P}_i$	Time
14	Renyi entropy (RE)	${\text{R}}_{\text{e}n}=\frac{1}{1-\alpha }ln\sum _{i=1}^{n}p{(x_i)}^{\alpha }$	Time
15	Fuzzy entropy (FE)	$H(A)=\sum _{i=1}^n{w}_{i}h(a_i)$	Time
16	Mean spectral amplitude	$S(k)=\frac{1}{N}\sum _{k=0}^{N-1}\left|X_p(k)\right|$	Spectral
17	Spectral power	$P_{\mathit{spectral}}=\frac{1}{N}\sum _{k=0}^{N-1}\left|X_p(k)X_p^{\ast }(k)\right|$	Spectral
18–20	Hjorth descriptors	$Mobility=\sqrt{\frac{Var\left(\frac{d{X}_p(k)}{\mathit{dk}}\right)}{Var(X_p(k))}}$$Complexity=\frac{Mobility\left(\frac{d{X}_p(k)}{\mathit{dk}}\right)}{Mobility(X_p(k))}$$Activity=Var(X_p(k))=\frac{1}{N}\sum _{k=0}^{N-1}{\left[X_p(k)-\overline{X_p(k)}\right]}^2$	Spectral
21	Higuchi fractal dimension (HFD)	$ln(L(k))/ln(1/k)$	Fractal
22	Katz fractal dimension (KFD)	$\frac{{log}_{10}(m)}{{log}_{10}(\raisebox{1ex}{$d$}\!\left/ \!\raisebox{-1ex}{$l$}\right.)+{log}_{10}(m)}$	Fractal
23	Total power (Ptot)	$\sum _{f}PSD(x)$	Frequency
24–27	Absolute band power (Pband)	$\sum _{f_1}^{f_2}PSD(x)$	Frequency
28–31	Mean band power (Pmean)	$\frac{1}{M}\sum _{f_1}^{f_2}PSD(x)$	Frequency
32–35	Relative band Power (Prel)	$P_{\mathit{band}}/P_{\mathit{total}}$	Frequency

Feature selection using ReliefF algorithm

The ReliefF algorithm ranks features according to their weight participation, with the most active features being placed first. As illustrated in Fig. 5, other features contribute far less to the last. As a result, we can choose 15 most potential features based on their weight and exclude characteristics that add to the model’s computational cost.

Fig. 5.

Weight ranking of features

ReliefF chooses T, some instances at random, but subsequently, k searches for the closest same-class neighbors, which are referred to as the nearest hit values of H. The k-nearest neighbours are the scores of one–one among the multiple classes, known as the nearest misses M (T). In this study, the number of nearest neighbours is set at 3. As shown in Fig. 5, for each attribute A, the algorithm updates the accuracy W [A], additionally in relation to T, H, and M (T). The pseudo code for the ReliefF algorithm is given in Algorithm 5.

Using the procedure described above, 35 features chosen from each channel are reduced to 15 optimal features per channel based on their participation at the top of the weighted list for highest accuracy. The remaining ones are ignored because there isn’t much of a difference in output, and this increases the computing weight of a model. Figure 6 depicts the cumulative accuracy Vs no of features, which is set to 15, and which can contribute more than the total variations. 35 features are extracted from each channel of the EEG corresponding to TD, FD, spectral and statistical domains. 15 discriminant features are selected by the ReliefF algorithm and fed to optimized ANFIS for classification.

Fig. 6.

Cumulative accuracy versus no. of features

Classification using ANFIS-HWBO

The suggested work improves the performance of ANFIS by applying a unique prediction model for SZ diagnosis based on the hybrid GWO-Bat algorithm called HWBO. BA is used to assist GWO in refining its behaviour so that it does not get stuck at local minima. The suggested ANFIS-HWBO model improves the ANFIS model by delivering the optimized ANFIS parameters. The features selected by the ReliefF algorithm are forwarded to the optimized ANFIS for classification into SZ and healthy controls.

The mean square error (MSE), root mean squared error (RMSE), co-efficient of correlation (R²), standard deviation (SD), and accuracy are used to evaluate the suggested ANFIS-HWBO model in optimizing the ANFIS parameters. For the SZ dataset, the same setting is used as in the previous experiment. The test is run 10 times. Tables 9 and 10 report the results.

Table 9.

Performance of ANFIS-HWBO on dataset -1

Algorithm	MSE	RMSE	R2	SD	Accuracy (%)
ANFIS	0.1551	0.301	0.7082	0.312	94.25
ANFIS-GA	0.0987	0.311	0.8488	0.348	94.89
ANFIS-ACO	0.0862	0.293	0.8642	0.322	95.62
ANFIS-PSO	0.1045	0.323	0.8875	0.305	96.48
ANFIS-CSO	0.0786	0.280	0.8953	0.299	97.88
ANFIS-GWO	0.0654	0.256	0.9186	0.284	98.11
ANFIS-BA	0.0598	0.244	0.9214	0.281	98.45
ANFIS-HWBO	0.0488	0.221	0.9436	0.263	99.51

Table 10.

Performance of ANFIS-HWBO on dataset -2

Algorithm	MSE	RMSE	R2	SD	Accuracy (%)
ANFIS	0.1374	0.341	0.6892	0.326	93.52
ANFIS-GA	0.0966	0.384	0.7758	0.356	93.94
ANFIS-ACO	0.0842	0.277	0.8542	0.314	94.68
ANFIS-PSO	0.1058	0.386	0.8965	0.354	96.55
ANFIS-CSO	0.0799	0.244	0.8753	0.285	96.89
ANFIS-GWO	0.0651	0.281	0.9086	0.278	97.42
ANFIS-BA	0.0554	0.245	0.9376	0.284	98.05
ANFIS-HWBO	0.0422	0.218	0.9568	0.252	99.32

From Tables 9 and 10, it is inferred that the ANFIS-HWBO model has outperformed all the other algorithms when tested on both datasets. Hence, the hybridization of BA and GWO has improved the ANFIS performance by a margin of 5% increment in accuracy, lesser MSE, RMSE, SD, and high R² values. Considering the performance of the optimized ANFIS-HWBO, an experiment is conducted to investigate the effectiveness of the model on SZ datasets (1 and 2) separately. Figure 7 indicates the results of ANFIS-HWBO on DS-1 and 2 in terms of accuracy, precision, recall, F1-score, and MCC.

Fig. 7.

Performance of ANFIS-HWBO on SZ datasets 1 and 2

It is inferred that the method proposed acts well on both the datasets classifying the conditions as either SZ or healthy controls. A high accuracy of 99.51% is attained on DS-1, followed by 99.32% on DS-2. High F1-score and MCC values are also obtained for both the datasets. The average computational time for the model on DS-1 is 50.45 ms and that of DS-2 is 55.28 ms. A tenfold cross validation is done to reduce bias during testing. The cross-validation reveals any misclassification rate performed by the classifier. This ensures the robustness of the algorithm and classifier. Table 11 illustrates the cross-validation results of the datasets used. It is seen that the cross-validation accuracy across the datasets is appreciably high, ensuring that the model is free from bias. The model is applicable to a wide range of datasets, compensating for any imbalance. A comparison of the proposed work with other similar works based on feature engineering, dataset used, and classifier is summarized in Table 12.

Table 11.

Tenfold Cross validation results

Dataset	F1-Score (%)	MCC (%)	Accuracy (%)
DS-1	95.41	94.23	97.8
DS-2	94.28	92.16	98.5

Table 12.

Comparison of the proposed work with similar feature engineering works

Reference	Feature engineering	Classifier	Dataset	Acc. (%)
Shim et al. (2016)	Source and sensor level features - fisher’s score feature selection	SVM	SZ:34 HC:34	88.24
Boostani et al. (2009)	Band power autoregressive (AR) and FD parameters	Boosted Direct LDA	SZ:20 HC:20	87.5
Zhao et al. (2012)	Entropy related non-linear features of alpha band of EEG	BPNN	SZ:31 HC:31	86.1
Sabeti et al. (2009)	AR, band power and FD features; Genetic programming-based features election	AdaBoost	SZ:20 HC:20	91.94
Santos-Mayo et al. (2017)	TD and FD features of ERP related wave for different electrode groups selected using J5 feature selection algorithm	MLP	SZ:16 HC:31	93.42
Li et al. (2019)	Inherent spatial pattern of network (SPN) features	LDA/SVM	SZ:23 HC:25	90.48
Johannesen et al. (2016)	Squared amplitude features	SVM	SZ:40 HC:12	87
Oh et al. (2019)	25 s duration EEG segments normalized with Z-score	CNN	SZ:14 HC:14	98.07
Phang et al. (2020)	TD and FD connectivity features	MDC- CNN	SZ:14 HC:14	91.69
Jahmunah et al. (2019)	Non-linear features of filtered, segmented EEG signals; feature selection using Student’s-test	SVM	SZ:14 HC:14	92.91
Deiva et al. (2019)	ERP features of selected regions of the brain	LDA	SZ:11 HC:9	71
Taylor J et al. (2017)	Spatiotemporal images using statistical parametric mapping of scalp EEG’s ERP features	Gaussian Process	SZ:21 HC:22	80.48
Buettner et al. (2020)	Multi-fractal and Entropy-Based features	RF	SZ:14 HC:14	96.77
Baradits et al. (2020)	Microstate features	SVM	SZ:75 HC:75	82.7
Proposed work	Statistical, TD, FD and spectral + feature section by reliefF	ANFIS + HGBO	SZ:45 HC:39 SZ:14 HC:14	99.51% 99.32%

From Table 12, it is seen that our proposed model produced better results in both the datasets. With the same datasets used (Oh et al. 2019; Jahmunah et al. 2019; Devia et al. 2019; Buttner et al. 2020), our method produced better results with reduced feature sets.

Limitations and future scope

The current study has limitations that should be considered in future research. A modest public dataset as well as a dataset from a previous study are employed. A large public dataset, on the other hand, can be utilized to verify the robustness of the suggested method for EEG classification. Furthermore, EEG signals obtained during a cognitive activity are easier to distinguish from baseline EEG signals than EEG signals observed during two independent cognitive activities. Future studies will focus on applying the suggested method to clinical datasets in the future, such as ictal vs. inter-ictal or normal EEG pattern categorization.

Conclusion

Psychological disturbance is one of the most complex health problems on the increase, owing to its convoluted and unpredictable signs and symptoms. It is incredibly difficult to diagnose symptoms that differ from person to person. Although a variety of technologies and methods are available to analyze the complicated data associated with mental health, recent advances in the fields of ANN and ML have been widely used and appear to be promising. In this study, the diagnosis of the psychiatric disorder schizophrenia, is investigated by employing a variety of features from EEG signals and an optimized ANFIS model. Pre-processing of EEG signals is performed using the Butterworth band pass filter and wICA for artefact removal, from which statistical, time domain, frequency domain, and spectral features are extracted. Most discriminate features are selected using the ReliefF algorithm, which are then forwarded to ANFIS for prediction into either schizophrenic or healthy. The ANFIS model is optimized using a combination of grey-wolf and bat algorithms, called HWBO, to generate the best fit model. This work explores the applicability of HWBO in the modified two-pass ANFIS learning algorithm to select the optimum rule-base with the utmost accuracy. The proposed model is tested on two distinct datasets, which demonstrated an accuracy of 99.51% and 99.32% on DS-1 and DS-2, respectively, for schizophrenia detection. High values of F1-score and MCC are obtained for both the datasets. To obtain bias-free classification, a tenfold CV is conducted, which achieved 97.8% and 98.5% on DS-1 and DS-2, respectively. Experiments are carried out to evaluate the optimized ANFIS model and compared it with similar optimization approaches. Hybridization of BA and GWO to improve the ANFIS performance resulted in a 5% increment in accuracy, less MSE, RMSE, SD, and high R² values compared to previous experiments. A comparison of the suggested model to the literature demonstrates that it is an effective strategy to accurately and quickly identify people with schizophrenia. By utilizing raw EEG data and integrating it with IoT, the models could let doctors and neurologists visualize schizophrenic patients in hospitals and rehabilitation centres in real time and from afar. ML and DL networks in the field of predictive learning will be heavily deployed in diagnosis and decision-making in the future, but the importance of experts in the field must also be factored in, to reduce misdiagnosis and achieve better accuracy.