# Detection and Classification of ADHD from EEG Signals Using Tunable Q-Factor Wavelet Transform

Authors: R. Catherine Joy; S. Thomas George; A. Albert Rajan; M. S. P. Subathra; N. J. Sairamya; J. Prasanna; Mazin Abed Mohammed; Alaa S. Al-Waisy; Mustafa Musa Jaber; Mohammed Nasser Al-Andoli
Journal: Journal of Sensors
 (2022)

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## Abstract

The automatic identification of Attention Deficit Hyperactivity Disorder (ADHD) is essential for developing ADHD diagnosis tools that assist healthcare professionals. Recently, there has been a lot of interest in ADHD detection from EEG signals because it seemed to be a rapid method for identifying and treating this disorder. This paper proposes a technique for detecting ADHD from EEG signals with the nonlinear features extracted using tunable Q-wavelet transform (TQWT). The 16 channels of EEG signal data are decomposed into the optimal amount of time-frequency sub-bands using the TQWT filter banks. The unique feature vectors are evaluated using Katz and Higuchi nonlinear fractal dimension methods at each decomposed levels. An Artificial Neural Network classifier with a 10-fold cross-validation method is found to be an effective classifier for discriminating ADHD and normal subjects. Different performance metrics reveal that the proposed technique could effectively classify the ADHD and normal subjects with the highest accuracy. The statistical analysis showed that the Katz and Higuchi nonlinear feature estimation methods provide potential features that can be classified with high accuracy, sensitivity, and specificity and is suitable for automatic detection of ADHD. The proposed system is capable of accurately distinguishing between ADHD and non-ADHD subjects with a maximum accuracy of 100%.


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## Body

## 1. Introduction

Attention Deficit Hyperactivity Disorder (ADHD) is one of the prevailing neuropsychiatric disorders among children, and it frequently persists into adulthood [1, 2]. The word-wide study shows that, about 5-12% of prevalence of ADHD is observed among school-going children, and more manifestation is experienced among male children [3–5]. This disorder has the subtypes such as predominantly inattentive, predominantly hyperactive-impulsive, and the combined type with the primary symptoms of inattention, impulsivity, and hyperactivity [6–8]. Early detection and identification of this disorder and treating in an early stage will be extremely beneficial to children, parents, and especially community health. Currently, clinical interviews, observations, and ratings from multiple sources such as parents and teachers are used to examine and diagnose ADHD [9–11]. The traditional clinical evaluation procedures are time consuming and are subject to ambiguity. Therefore, there is a great need for objective clinical diagnostic methods from the biological signals that reflect the behaviors of ADHD and its subtypes.Electroencephalography (EEG) is the record of the electrical activities of a human brain, which can reveal a great deal about physiology and pathology. EEG signals have been employed in the diagnosis of several neurological illnesses by extracting unique features and classifying them with different classifiers in automated detection systems. Neurophysiological disorders such as alcoholism [12], dementia [13, 14], epileptic seizure [15], schizophrenia [16, 17], Parkinson’s disease [18, 19], and depressive disorder [20, 21] are some of the areas where EEG signals are employed in automatic detection. The EEG signals of ADHD children are different from that normal child in terms of complex randomness, amplitude, and frequency. Researchers have employed several feature extraction techniques and classifiers to analyse EEG signals in the identification of ADHD [22–25]. Researchers have experimented several machine learning algorithms and nonlinear feature extraction approaches such as entropy estimators and classifiers such as support vector machine (SVM), multilayer perceptron, and k-nearest neighbor (KNN) [26–29] to detect ADHD using EEG data. These techniques suffer from higher computational complexity and lower classification accuracy.A quantifiable brain reaction that happens as a direct result of a sensory, cognitive, or motor event is known as an event-related potential (ERP). Mueller et al. used ERP features to analyse 75 ADHD and 75 normal children and have classified ADHD and normal subjects with a classification accuracy of 91% [30]. Different authors worked on the ERP and extracted probable features that can help detect ADHD, and classification is done with a multilayer neural network and categorized with an accuracy close to 96.7%. [27, 31–33]. While some authors investigated the application of complex deep learning algorithms to diagnose ADHD from EEG signals, others explored more efficient machine learning methodologies. For most of the ADHD detection, the authors extracted nonlinear features and classified with standard classifiers such as support vector machine (SVM), multilayer perceptron, and KNN [26, 28, 29, 34]. A deep convolutional neural networks and deep learning networks were experimented to diagnose ADHD in adults and children [35–37].Literature reveals that wavelet transform techniques have higher computational efficiency, and they have the added benefit of being able to distinguish tiny details in a signal. Ahmadlou and Adeli [38] employed a wavelet-synchronization pattern recognition methodology with RBF neural network classifier, to detect ADHD with a maximum accuracy of 95.6%. Sadatnezhad et al. [31] used fractal dimension, AR model, and EEG band power to diagnose ADHD children and achieved a maximum classification of 86.4%. Allahverdy et al. [39] analysed EEG data with the nonlinear features extracted using fractal dimension methods and distinguished ADHD subjects with a classification accuracy of 86%. Ahmadlou and Adeli et al. employed the synchronization likelihood (SL) and fuzzy synchronization likelihood (FSL) frameworks to assess functional connectivity and achieving classification accuracies of 87.5% and 95.6%, respectively, for a synchronization pattern in the theta and delta frequency bands [38, 40]. These wavelets transform methods could not achieve the maximum classification accuracy as they could not dynamically adjust the Q value and had lower reconstruction capabilities. To classify ADHD versus normal subjects, these studies largely used artificial intelligence approaches. Based on the literature, different authors expressed that classification accuracy has to be further improved and the computational complexity has to be reduced. Moreover, challenges prevail in identifying the better feature extraction technique and applying the best classifier algorithm for achieving maximum classification accuracy in ADHD diagnostic methods.To address these difficulties, the authors have experimented an efficient algorithm using tunable Q-wavelet transform (TQWT) with Katz and Higuchi fractional dimension method, that is lighter in computational complexity and with an ANN classifier that provides a maximum classification accuracy. Children with ADHD are identified by the experts and their EEG signals recorded under eyes-open and eyes-closed states are used for this analysis. Potential features are derived from Katz and Higuchi fractal dimensions, which are estimated from the segmented EEG signal subbands. The features extracted through the fractional dimension techniques are classified using the ANN classifier which is a proven effective classifier. The results show that the suggested method is effective in classifying ADHD and normal subjects EEG signals. The main contributions list can be summarized as follows:(i)
The combination of TQWT with Katz and Higuchi fractional dimension method is proven to be an efficient feature extraction method for ADHD detection(ii)
The potential features extracted with the Katz and Higuchi fractional dimension techniques with an ANN classifier brought out with a maximum classification accuracy of 100%(iii)
As the proposed system is lighter in computation with maximum classification accuracy, it can be a resourceful technique for clinical detection of ADHD from the EEG signalsThis work is composed of four major sections. Section2 presents the Materials and Methods, which include data acquisition and feature extraction methods. Section 3 proposes the Results and Discussion, which includes the analysis of various classifier algorithms, performance metrics, and discussion on comparing similar works. Finally, the Conclusion and future works are presented in Section 4.


## 2. Materials and Methods

### 2.1. Data Acquisition

The EEG data set for the proposed approach is created with 5 subjects of ADHD and 5 subjects of normal, in each category under eyes-closed and eyes-open resting state. The EEG signals were recorded from the children age group 7 to 12, after getting parental consent and the children’s consent [25]. Using the unipolar setup, the EEG signals of the individuals are measured using the 10–20 electrode placement system. Individual scalps are carefully prepared with a contact impedance of less than 5K Ω for EEG signal measurement. With a sample rate of 256 Hz, each EEG signal consisting of 6400 sampling points was recorded using a 16-electrode unipolar montage. Each signal was captured for 300 seconds with a 24-bit resolution. Signals which acquired are divided into 25 seconds in the eyes-closed resting state and eyes-open resting state in both ADHD and normal subjects. The EEG signals of ADHD and normal subjects are presented in Figure 1.Figure 1
Single-channel EEG signals for ADHD and normal subjects in eyes-closed and eyes-open condition.The acquired signals are preprocessed using MATLAB (MatLabR2018a) to determine the needed range of signals from each channel. Visual inspection and computerized review are carried out with the aid of specialists and a range of signals that are not acceptable for analysis and further processing are removed. A bandpass filter with cutoff frequencies of 1 Hz and 60 Hz is used to reduce signal noise and to eliminate other artefacts and noise during eye blinking. The power frequency noise is suppressed using a 50 Hz notch filter. Experiments are conducted on a laptop with 4 GB of RAM, a 3.2 GHz CPU, and intel core processor. MATLAB 2018a is used to execute the simulations, and the statistical data are recorded for analysing various performance measures. The functional blocks of the proposed methodology for classifying ADHD and normal subjects using the TQWT algorithm is presented in Figure2.Figure 2
Functional blocks of the proposed methodology.In this proposed methodology, the EEG signals of both ADHD and normal categories are decomposed into 15 levels of subbands by using TQWT technique. The unique fractal dimension features such as katz and higuchi features are extracted from the decomposed subbands reflecting the ADHD and normal behavior. These features are fed as input to the different classifiers such as linear discriminant, logistic regression, support vector machine, artificial neural networks, and ensemble techniques are experimented to compare the performance of each classifier. The best classifier algorithm with higher classification accuracy is evaluated for choosing the better combination to perform the feature extraction and classification. The performance of the proposed methodology is verified with different performance metrics for ensuring its best performances.


### 2.2. Tunable Q-Factor Wavelet Transform (TQWT)

The ratio of the centre frequency to the bandwidth of the filters employed in the transform is known as the Q-factor of a wavelet transform. TQWT has the property of fast decomposition and perfect reconstruction which makes it suitable for application in many biomedical signal processing problems. TQWT’s efficient decomposition and perfect reconstruction properties make it well-suited to a wide range of biological signal processing applications [41]. The TQWT is a wavelet transform that is analogous to the rational-dilation wavelet transform and has been used to investigate EEG signals [12, 42, 43]. The TQWT provides perfect reconstruction of the signal and the energy of the signal is divided into subbands by the TQWT coefficients. It is done with a discrete wavelet transform that performs a double-channel multirate filter bank with low and high-pass filters. With an adjustable Q-factor and a powerful transform for oscillatory signal analysis, this approach is suited for the discrete-time signal analysis [42]. TQWT’s fundamental parameters are its Q-factor (Q), redundancy (r), and the number of levels of decomposition (j) which allow it to analyse signals with a diversity of oscillatory characteristics [44]. TQWT filters are straightforward to reconstruct and implement since they are built up of nonrational transfer functions utilising a Fast Fourier Transform (FFT) with an adjustable Q-factor. In our proposed work, the Q-value factors are modified between 1 and 10, and the classification results are analysed to find the best Q-factor value. The TQWT approach applied to this work is depicted in Figure 3.Figure 3
Flow diagram of TQWT analysis and synthesis filter banks.Figure3 shows the different stages of decomposition applied with the TQWT analysis and synthesis filter banks [45]. An EEG signal is divided into j levels by iteratively applying two-channel filter banks on the signal. At each level of decomposition, the input signal xn with sampling frequency fs is decomposed into a high-pass subband signal x1n and a low-pass subband signal x0n, with sampling frequencies of αfs and βfs, respectively. Here α and β refer scaling factors for the filter banks. Selesnick [42] elaborated a comprehensive description of scaling parameters and proposed that the scaling parameters must fulfil the following criteria to limit redundancy while ensuring perfect reconstruction.
(1)0<β≤1,0<α<1,α+β=1.The characteristic equation of TQWT can be represented as follows:(2)H0ω=1,ω≤1−βπθω+β−1πα+β−1,1−βπ≤ω<∝π0,απ≤ω≤π,(3)H1ω=0,ω≤1−βπθαπ−ωα+β−1,1−βπ≤ω<απ1,απ≤ω≤π,(4)θω=121+cosω2−cosωforω≤π.The bands ofH0ω and H1ω are constructed using transition function θω, which is derived from the Daubechies filter with two vanishing moments. To accomplish the perfect reconstruction criteria, the low-pass filter H0ω and high-pass filter H1ω can be assessed using the relation given in equation (2).
(5)H0ω2+H1ω2=1.The decomposed EEG signals can be reconstructed with the use of a synthesis filter. The relationship between TQWT input parameters and scaling parametersαandβ is related by;
(6)r=β1−α,(7)Q=2−ββ.The criterion of dominant frequency is used to select the appropriate value of decomposition levels (j). According to the dominant frequency criterion, the number of decomposition levels is kept in such a way that the decomposed subbands have the greatest correlation with substantial EEG frequency ranges.In this paper, the following feature vectors are evaluated and analysed:(a)
Q-factor. The value of Q in TQWT determines the oscillatory behaviour of the signals. EEG signals, in particular, are highly oscillatory in nature and have a high Q-value. The theoretical definition of the Q-factor is expressed as Q=2−β/βandα=1−β/r. Based on the values of Q and r, the values of α and β are computed. The value of the Q-factor can be chosen based on the input signal behaviour because it reflects the oscillatory behaviour of the wavelet. If the proposed Q-value is compatible with the input signal’s features, it can accurately extract useful information from the EEG signal.(b)
The maximum number of levelsjmax. The scaling parameters α and β, the number of samples (N) in the input signal are used to calculate jmax, The maximum levels of decomposition,
(8)jmax=logβN/8log1/α(c)
Oversampling rate/redundancy parameter (r). The resonance is controlled by the redundancy factor r, which allows the wavelet to be focused in time without affecting its shape. The oversampling rate is defined as r in this case r=β/1−α. When analysing biological signals, the specific number r=3 has been previously recommended [46]. As a result, throughout this research, the redundancy parameter r is chosen as 3The wavelet transforms technique shall be applied to signals with little or no oscillatory characteristic with a low Q-factor. Most wavelet transforms, except for the continuous wavelet transform, are unable to adjust their Q-factor. This difficulty is solved by TQWT, which allows the Q-factor to be regulated. Moreover, TQWT has been widely employed to investigate a variety of physiological signals [47–49]. Due to the rational transfer functions, the filters are computationally efficient and hence provide direct representation in the frequency domain. As TQWT is a powerful tool for analysing oscillatory physiological signals with lesser computational complexity, the authors felt to apply this technique for the proposed work.


### 2.3. Feature Extraction

The EEG signals are complex and highly nonlinear in nature. Because of the nonlinear and intricate behaviour, nonlinear methods are appropriate tools for analysing brain dynamics and behaviours from the EEG signals. The Higuchi and Katz fractional dimension based feature extraction methods are more predominantly used for EEG signal analysis [50, 51]. In our work, the Higuchi and Katz nonlinear feature extraction techniques are used to identify the potential features that can help discriminate ADHD and normal subjects.


#### 2.3.1. Higuchi Fractal Dimension

A fractal dimension is a tool for determining nonperiodic and irregular time series. The Higuchi fractional dimension has its high accuracy and efficiency in determining fractal dimensions based on curve length measurements. The time series of the EEG signal is segmented intok number of samples, and the mean length of the series/curve is measured using the segment of k samples [52, 53]. The FD Higuchi estimation can be obtained by following four steps for a finite set of time series, i.e., Sn~;n~=1,2,⋯N;N is the number of points on the curve:Stage 1. Generate k number of new time series, for values of k ranging from 1 to kmax, calculate Smk from given time series data.
(9)Smk=Sm,Sm+k,Sm+2k,⋯,Sm+intN−mk.k.In this, the discrete time interval between sample points is represented byk, and the initial time value is represented by mm=1,2,3,⋯..,k.Stage 2. The length Lmk is calculated for each of the constructed time series Smk.
(10)Lmk=∑i=1intN−m/kSm+i.k−Sm+i−1.k.N−1intN−m/k.k.k−1.Here the curve length is given byLmk and N−1∗intN−m/k.k−1 is the normalization factor.Stage 3. The average length Lavgk of the curve is calculated by the following equation for each interval of k:
(11)Lavgk=1k∑m=1kLmkFor all values ofk ranging from 1 to kmax, average length calculation is repeated.Stage 4. The length of the total average curve, Lavgk is proportional to k−D, where D is the Higuchi fractal dimension (HFD). The slope of the least-squares linear best fit is the estimation of the fractal dimension in the curve of lnLavgk versus ln1/k in the curve [52]. The parameter time interval k determined the HFD value. In this analysis, we employed k in a certain range of values, which resulted in a specific HFD value.


#### 2.3.2. Katz’s Fractal Dimension

In the Katz fractional dimension method [54], the ratio of the curve’s total length to the line for the maximum Euclidean distance from the starting point line. In general, the planar curve’s fractal dimension, FDkatz, is determined by the given equation,
(12)FDkatz=logLlogd,where L denotes the overall length of the curve, or the sum of distances between successive points, and d denotes the diameter, which is calculated as the distance between the first and farthest point on the sequence and given as,
(13)L=∑i=1Nwi+1−wi,(14)d=maxwi−w1.Here, the Euclidean distance is denoted by “.". The fractal dimension (FD) compares the number of units that make up a curve to the smallest number of units required to generate a structure with the same spatial area. The measurement units used to compute FDs have an impact on the results. The average step or average distance between successive points, “a” is created as a general unit or yardstick in Katz’s approach [50, 55]. According to Katz’s approach, the fractal dimension FDkatz, is expressed as:
(15)FDkatz=logL/alogd/a=logNlogd/L+logNwhere, Katz proposed normalize L is the length of the middle stage and d is the average distance between successive points a=L/N, where N is the number of steps in the curve.


## 2.1. Data Acquisition

The EEG data set for the proposed approach is created with 5 subjects of ADHD and 5 subjects of normal, in each category under eyes-closed and eyes-open resting state. The EEG signals were recorded from the children age group 7 to 12, after getting parental consent and the children’s consent [25]. Using the unipolar setup, the EEG signals of the individuals are measured using the 10–20 electrode placement system. Individual scalps are carefully prepared with a contact impedance of less than 5K Ω for EEG signal measurement. With a sample rate of 256 Hz, each EEG signal consisting of 6400 sampling points was recorded using a 16-electrode unipolar montage. Each signal was captured for 300 seconds with a 24-bit resolution. Signals which acquired are divided into 25 seconds in the eyes-closed resting state and eyes-open resting state in both ADHD and normal subjects. The EEG signals of ADHD and normal subjects are presented in Figure 1.Figure 1
Single-channel EEG signals for ADHD and normal subjects in eyes-closed and eyes-open condition.The acquired signals are preprocessed using MATLAB (MatLabR2018a) to determine the needed range of signals from each channel. Visual inspection and computerized review are carried out with the aid of specialists and a range of signals that are not acceptable for analysis and further processing are removed. A bandpass filter with cutoff frequencies of 1 Hz and 60 Hz is used to reduce signal noise and to eliminate other artefacts and noise during eye blinking. The power frequency noise is suppressed using a 50 Hz notch filter. Experiments are conducted on a laptop with 4 GB of RAM, a 3.2 GHz CPU, and intel core processor. MATLAB 2018a is used to execute the simulations, and the statistical data are recorded for analysing various performance measures. The functional blocks of the proposed methodology for classifying ADHD and normal subjects using the TQWT algorithm is presented in Figure2.Figure 2
Functional blocks of the proposed methodology.In this proposed methodology, the EEG signals of both ADHD and normal categories are decomposed into 15 levels of subbands by using TQWT technique. The unique fractal dimension features such as katz and higuchi features are extracted from the decomposed subbands reflecting the ADHD and normal behavior. These features are fed as input to the different classifiers such as linear discriminant, logistic regression, support vector machine, artificial neural networks, and ensemble techniques are experimented to compare the performance of each classifier. The best classifier algorithm with higher classification accuracy is evaluated for choosing the better combination to perform the feature extraction and classification. The performance of the proposed methodology is verified with different performance metrics for ensuring its best performances.


## 2.2. Tunable Q-Factor Wavelet Transform (TQWT)

The ratio of the centre frequency to the bandwidth of the filters employed in the transform is known as the Q-factor of a wavelet transform. TQWT has the property of fast decomposition and perfect reconstruction which makes it suitable for application in many biomedical signal processing problems. TQWT’s efficient decomposition and perfect reconstruction properties make it well-suited to a wide range of biological signal processing applications [41]. The TQWT is a wavelet transform that is analogous to the rational-dilation wavelet transform and has been used to investigate EEG signals [12, 42, 43]. The TQWT provides perfect reconstruction of the signal and the energy of the signal is divided into subbands by the TQWT coefficients. It is done with a discrete wavelet transform that performs a double-channel multirate filter bank with low and high-pass filters. With an adjustable Q-factor and a powerful transform for oscillatory signal analysis, this approach is suited for the discrete-time signal analysis [42]. TQWT’s fundamental parameters are its Q-factor (Q), redundancy (r), and the number of levels of decomposition (j) which allow it to analyse signals with a diversity of oscillatory characteristics [44]. TQWT filters are straightforward to reconstruct and implement since they are built up of nonrational transfer functions utilising a Fast Fourier Transform (FFT) with an adjustable Q-factor. In our proposed work, the Q-value factors are modified between 1 and 10, and the classification results are analysed to find the best Q-factor value. The TQWT approach applied to this work is depicted in Figure 3.Figure 3
Flow diagram of TQWT analysis and synthesis filter banks.Figure3 shows the different stages of decomposition applied with the TQWT analysis and synthesis filter banks [45]. An EEG signal is divided into j levels by iteratively applying two-channel filter banks on the signal. At each level of decomposition, the input signal xn with sampling frequency fs is decomposed into a high-pass subband signal x1n and a low-pass subband signal x0n, with sampling frequencies of αfs and βfs, respectively. Here α and β refer scaling factors for the filter banks. Selesnick [42] elaborated a comprehensive description of scaling parameters and proposed that the scaling parameters must fulfil the following criteria to limit redundancy while ensuring perfect reconstruction.
(1)0<β≤1,0<α<1,α+β=1.The characteristic equation of TQWT can be represented as follows:(2)H0ω=1,ω≤1−βπθω+β−1πα+β−1,1−βπ≤ω<∝π0,απ≤ω≤π,(3)H1ω=0,ω≤1−βπθαπ−ωα+β−1,1−βπ≤ω<απ1,απ≤ω≤π,(4)θω=121+cosω2−cosωforω≤π.The bands ofH0ω and H1ω are constructed using transition function θω, which is derived from the Daubechies filter with two vanishing moments. To accomplish the perfect reconstruction criteria, the low-pass filter H0ω and high-pass filter H1ω can be assessed using the relation given in equation (2).
(5)H0ω2+H1ω2=1.The decomposed EEG signals can be reconstructed with the use of a synthesis filter. The relationship between TQWT input parameters and scaling parametersαandβ is related by;
(6)r=β1−α,(7)Q=2−ββ.The criterion of dominant frequency is used to select the appropriate value of decomposition levels (j). According to the dominant frequency criterion, the number of decomposition levels is kept in such a way that the decomposed subbands have the greatest correlation with substantial EEG frequency ranges.In this paper, the following feature vectors are evaluated and analysed:(a)
Q-factor. The value of Q in TQWT determines the oscillatory behaviour of the signals. EEG signals, in particular, are highly oscillatory in nature and have a high Q-value. The theoretical definition of the Q-factor is expressed as Q=2−β/βandα=1−β/r. Based on the values of Q and r, the values of α and β are computed. The value of the Q-factor can be chosen based on the input signal behaviour because it reflects the oscillatory behaviour of the wavelet. If the proposed Q-value is compatible with the input signal’s features, it can accurately extract useful information from the EEG signal.(b)
The maximum number of levelsjmax. The scaling parameters α and β, the number of samples (N) in the input signal are used to calculate jmax, The maximum levels of decomposition,
(8)jmax=logβN/8log1/α(c)
Oversampling rate/redundancy parameter (r). The resonance is controlled by the redundancy factor r, which allows the wavelet to be focused in time without affecting its shape. The oversampling rate is defined as r in this case r=β/1−α. When analysing biological signals, the specific number r=3 has been previously recommended [46]. As a result, throughout this research, the redundancy parameter r is chosen as 3The wavelet transforms technique shall be applied to signals with little or no oscillatory characteristic with a low Q-factor. Most wavelet transforms, except for the continuous wavelet transform, are unable to adjust their Q-factor. This difficulty is solved by TQWT, which allows the Q-factor to be regulated. Moreover, TQWT has been widely employed to investigate a variety of physiological signals [47–49]. Due to the rational transfer functions, the filters are computationally efficient and hence provide direct representation in the frequency domain. As TQWT is a powerful tool for analysing oscillatory physiological signals with lesser computational complexity, the authors felt to apply this technique for the proposed work.


## 2.3. Feature Extraction

The EEG signals are complex and highly nonlinear in nature. Because of the nonlinear and intricate behaviour, nonlinear methods are appropriate tools for analysing brain dynamics and behaviours from the EEG signals. The Higuchi and Katz fractional dimension based feature extraction methods are more predominantly used for EEG signal analysis [50, 51]. In our work, the Higuchi and Katz nonlinear feature extraction techniques are used to identify the potential features that can help discriminate ADHD and normal subjects.


### 2.3.1. Higuchi Fractal Dimension

A fractal dimension is a tool for determining nonperiodic and irregular time series. The Higuchi fractional dimension has its high accuracy and efficiency in determining fractal dimensions based on curve length measurements. The time series of the EEG signal is segmented intok number of samples, and the mean length of the series/curve is measured using the segment of k samples [52, 53]. The FD Higuchi estimation can be obtained by following four steps for a finite set of time series, i.e., Sn~;n~=1,2,⋯N;N is the number of points on the curve:Stage 1. Generate k number of new time series, for values of k ranging from 1 to kmax, calculate Smk from given time series data.
(9)Smk=Sm,Sm+k,Sm+2k,⋯,Sm+intN−mk.k.In this, the discrete time interval between sample points is represented byk, and the initial time value is represented by mm=1,2,3,⋯..,k.Stage 2. The length Lmk is calculated for each of the constructed time series Smk.
(10)Lmk=∑i=1intN−m/kSm+i.k−Sm+i−1.k.N−1intN−m/k.k.k−1.Here the curve length is given byLmk and N−1∗intN−m/k.k−1 is the normalization factor.Stage 3. The average length Lavgk of the curve is calculated by the following equation for each interval of k:
(11)Lavgk=1k∑m=1kLmkFor all values ofk ranging from 1 to kmax, average length calculation is repeated.Stage 4. The length of the total average curve, Lavgk is proportional to k−D, where D is the Higuchi fractal dimension (HFD). The slope of the least-squares linear best fit is the estimation of the fractal dimension in the curve of lnLavgk versus ln1/k in the curve [52]. The parameter time interval k determined the HFD value. In this analysis, we employed k in a certain range of values, which resulted in a specific HFD value.


### 2.3.2. Katz’s Fractal Dimension

In the Katz fractional dimension method [54], the ratio of the curve’s total length to the line for the maximum Euclidean distance from the starting point line. In general, the planar curve’s fractal dimension, FDkatz, is determined by the given equation,
(12)FDkatz=logLlogd,where L denotes the overall length of the curve, or the sum of distances between successive points, and d denotes the diameter, which is calculated as the distance between the first and farthest point on the sequence and given as,
(13)L=∑i=1Nwi+1−wi,(14)d=maxwi−w1.Here, the Euclidean distance is denoted by “.". The fractal dimension (FD) compares the number of units that make up a curve to the smallest number of units required to generate a structure with the same spatial area. The measurement units used to compute FDs have an impact on the results. The average step or average distance between successive points, “a” is created as a general unit or yardstick in Katz’s approach [50, 55]. According to Katz’s approach, the fractal dimension FDkatz, is expressed as:
(15)FDkatz=logL/alogd/a=logNlogd/L+logNwhere, Katz proposed normalize L is the length of the middle stage and d is the average distance between successive points a=L/N, where N is the number of steps in the curve.


## 2.3.1. Higuchi Fractal Dimension

A fractal dimension is a tool for determining nonperiodic and irregular time series. The Higuchi fractional dimension has its high accuracy and efficiency in determining fractal dimensions based on curve length measurements. The time series of the EEG signal is segmented intok number of samples, and the mean length of the series/curve is measured using the segment of k samples [52, 53]. The FD Higuchi estimation can be obtained by following four steps for a finite set of time series, i.e., Sn~;n~=1,2,⋯N;N is the number of points on the curve:Stage 1. Generate k number of new time series, for values of k ranging from 1 to kmax, calculate Smk from given time series data.
(9)Smk=Sm,Sm+k,Sm+2k,⋯,Sm+intN−mk.k.In this, the discrete time interval between sample points is represented byk, and the initial time value is represented by mm=1,2,3,⋯..,k.Stage 2. The length Lmk is calculated for each of the constructed time series Smk.
(10)Lmk=∑i=1intN−m/kSm+i.k−Sm+i−1.k.N−1intN−m/k.k.k−1.Here the curve length is given byLmk and N−1∗intN−m/k.k−1 is the normalization factor.Stage 3. The average length Lavgk of the curve is calculated by the following equation for each interval of k:
(11)Lavgk=1k∑m=1kLmkFor all values ofk ranging from 1 to kmax, average length calculation is repeated.Stage 4. The length of the total average curve, Lavgk is proportional to k−D, where D is the Higuchi fractal dimension (HFD). The slope of the least-squares linear best fit is the estimation of the fractal dimension in the curve of lnLavgk versus ln1/k in the curve [52]. The parameter time interval k determined the HFD value. In this analysis, we employed k in a certain range of values, which resulted in a specific HFD value.


## 2.3.2. Katz’s Fractal Dimension

In the Katz fractional dimension method [54], the ratio of the curve’s total length to the line for the maximum Euclidean distance from the starting point line. In general, the planar curve’s fractal dimension, FDkatz, is determined by the given equation,
(12)FDkatz=logLlogd,where L denotes the overall length of the curve, or the sum of distances between successive points, and d denotes the diameter, which is calculated as the distance between the first and farthest point on the sequence and given as,
(13)L=∑i=1Nwi+1−wi,(14)d=maxwi−w1.Here, the Euclidean distance is denoted by “.". The fractal dimension (FD) compares the number of units that make up a curve to the smallest number of units required to generate a structure with the same spatial area. The measurement units used to compute FDs have an impact on the results. The average step or average distance between successive points, “a” is created as a general unit or yardstick in Katz’s approach [50, 55]. According to Katz’s approach, the fractal dimension FDkatz, is expressed as:
(15)FDkatz=logL/alogd/a=logNlogd/L+logNwhere, Katz proposed normalize L is the length of the middle stage and d is the average distance between successive points a=L/N, where N is the number of steps in the curve.


## 3. Results and Discussions

The tunable Q-factor wavelet transform approach is used to extract unique features from all 16 channels of EEG signals. EEG data from ADHD and normal subjects are decomposed into multiple levels, and Higuchi and Katz’s fractal dimensional features are obtained. The total extracted features for each fractal measures are 112 since six level wavelet decompositions have been performed using TQWT. Hence, a total of 7 wavelet coefficients with respect to 16 EEG channels (16∗7=112) the size of the features that have been taken. For improved classification accuracy, the optimal selection of quality factor (Q) and decomposition levels (j) is investigated. The redundancy (r) value is fixed to 3 in order to perform better [42, 51]. The TQWT technique is applied on the EEG signals of both ADHD and normal subjects under eyes-closed and eyes-open states for extracting different subbands for different Q and j values. Initially, keeping the Q as 1 and the features are extracted for all the 15 decomposition levels. The unique features extracted with Higuchi and Katz fractional dimension decomposition methods are fed into different classifiers for investigating the efficiency in terms of classification accuracy. Classifiers such as linear discriminant, logistic regression, support vector machine, k-nearest neighbour, ensemble and artificial neural networks are experimented. In all of the experimental conditions, decomposition level 6 achieved maximum classification accuracy. After setting the j value to 6, the Q value is changed from 1 to 10, and the Katz and Higuchi features are computed for each of the 6+1 (7) subbands including one low pass subband are considered. The total number of samples examined in this study is 6400, with 25 second EEG data sets collected. The classification accuracy of each classifier for the EEG signals under the eyes-open state and eyes-closed state are demonstrated in Figure 4.Figure 4
Classification accuracy comparison for different classifiers (a) eyes-closed condition (b) eyes-open condition.
(a)(b)On observing the classification accuracies of different classifiers, the ANN classifier has exhibited the highest classification accuracy among all the classifiers in both eyes-closed and eyes-open states EEG analysis. Because the ANN classifier outperformed all other classifiers in terms of classification accuracy, only the ANN classifier is used for further investigation. The results are analysed under eyes-open state and eyes-closed for both ADHD and normal subjects. The potential features extracted from all the 15 decomposed levels of EEG signal under eyes-closed and eyes-open states. Figure5 demonstrates the classification accuracy of both feature extraction methods under eyes-closed and eyes-open states, respectively, for different decomposition levels. It is evident that the potential features extracted from the Katz have maximum classification accuracy in a greater number of decomposition levels than the Higuchi under eyes-closed state. In the meantime, the Higuchi fractional dimension could provide more features that can reflect ADHD in more decomposition levels under the eyes-open state.Figure 5
Classification accuracy for different decomposition levels for EEG signals under (a) eyes-closed state (b) eyes-open state.
(a)(b)In order to determine the bestQ and j values, a series of experiments are carried out. While keeping the quality factor Q=1 and redundancy factor r=3 as constants and extracting the unique features from Katz and Higuchi fractal dimensions for all the 15 decomposition levels, it exhibits that the classification accuracy reaches its maximum significant in the 6th level in both the feature extraction methods under eyes-closed and eyes-open states. After choosing j=6 as the decomposition level, the quality factor is changed from 1 to 10, and the characteristics extracted from all 7 subbands (j+1) for each value of Q are compared. Unique features extracted using Higuchi fractal dimension and Katz’s fractal dimension techniques are distinct for ADHD and normal subjects EEG signals. An artificial neural network classifier with a 10-fold cross-validation method is used to validate the classified results. The classification accuracy at different Q values while keeping the decomposition levels 6 as constant is shown in Table 1(b).Table 1
(a) Classification accuracy for differentQ values for a fixed decomposition level j=3, (b) Classification accuracy for different Q values for a fixed decomposition level j=6, (c) Classification accuracy for different Q values for a fixed decomposition level j=8
(a)Level=3Eyes-closedEyes-openQKatzHiguchiKatzHiguchi199.1791.6799.0099.00298.7595.9287.4298.75395.9293.1791.6791.67495.9269.3384.0887.42599.1770.0088.1795.92699.1782.5084.0899.17799.1784.0891.6799.17899.1788.8384.0895.92999.1787.4288.1798.751099.1788.1798.7595.92(b)Level=6Eyes-closedEyes-openQKatzHiguchiKatzHiguchi1100.0094.25100.00100.00299.1798.7588.1799.00398.1795.9292.9292.67498.1770.0087.8389.005100.0069.3391.6797.176100.0084.0886.50100.007100.0082.5093.17100.008100.0087.4286.5897.179100.0088.8392.0099.1710100.0078.2593.8397.75(c)Level=8Eyes-closedEyes-openQKatzHiguchiKatzHiguchi199.1791.6799.1799.17298.7595.9284.0898.75398.7591.6790.6790.17498.7569.3386.5088.17599.0068.1790.1795.92699.0082.5086.5099.17799.0084.5091.6799.17899.0086.5086.5098.75999.0084.0889.6798.751099.0069.3391.6795.92The feature extraction techniques used are Katz and Higuchi for both eyes-closed and eyes-open condition. For each technique, 112 features are extracted and given to the ANN classifier. The classification accuracy obtained are shown in the Tables1–3 for different levels 3, 6, and 8 with Q-factor varying from 1 to 10. Among these, level 6 is giving the best accuracy. The features extracted through Katz fractional dimension have a higher potential to discriminate the ADHD and normal subjects under an eyes-closed state. The EEG signals with eyes-closed states are more significant with higher classification accuracy than the eyes-open state in ADHD diagnosis using Katz fractional dimension estimation method. The classification accuracy became maximum at the decomposition level 6 consistently at Q=1 for both feature extraction methods indicating that the filter banks are perfectly tuned to the optimal classification accuracy at the 6th decomposition level.Table 2
Performance metrics for Katz and Higuchi feature extraction methods (a) eyes-closed state (b) eyes-open state.
(a)Level=6AccuracySensitivityNPVMCCF1-scoreG-meanQKatzHiguchiKatzHiguchiKatzHiguchiKatzHiguchiKatzHiguchiKatzHiguchi110094.2510089.1710091.310090.1610093.3310093.95299.298.7598.3397.598.7598.398.5497.899998.3399.0898.54398.295.9295.8391.6797.594.296.692.8297.3394.6797.6295.24498.27095.8366.6797.56596.641.3797.3369.5297.6265.13510069.3310058.3310066.710043.4610065.1710067.23610084.0810076.6710080.410070.521008210083.39710082.510075.8310080.410067.5610080.1710081.7810087.4210080.8310084.610076.410085.6710086.75910088.8310086.6710090.810078.9710087.2410087.161010078.2510073.3310077.110058.7910076.510076.99(b)Level=6AccuracySensitivityNPVMCCF1-scoreG-meanQKatzHiguchiKatzHiguchiKatzHiguchiKatzHiguchiKatzHiguchiKatzHiguchi1100100100100100100100100100100100100288.29976.6797.583.3398.7579.898.068598.3386.6398.54392.992.6787.589.1789.5892.9288.4687.191.839192.7591.39487.88975.8382.58387.1779.128184.1786.7985.9887.44591.797.1784.1795.8388.3397.586.0894.6689.596.6290.7496.15686.510072.510080.8310076.3410082.3310084.24100793.210086.6710090.4210088.3710091.1710092.21100886.697.1773.3310081.331007795.282.597.2984.5197.2599299.1784.1710088.3310086.1198.549099.2991.0299.081093.897.7588.3310090.8310089.5196.2292.679893.497.62Table 3
Summary of comparison for automated detection of ADHD with state-of-the-art techniques.
S.noAuthorsYearParticipantsAge groupFeature extraction methodologyClassifiersClassification accuracy (%)1Ghaderyan et al. [56]202214 ADHD and 19 healthy children6 to 11 yearsDynamic frequency wrappingSparse nonnegative least-square coding99.17%2Tor et al. [34]202145 ADHD, 62 (ADHD+CD) and 16 CD6 to 12 yearsNonlinear featuresKNN classifier97.88%3Ahmadi et al. [35]202113 ADHD-C subtype, 12 ADHD-I subtype, 14 control6 to 11 years oldSpatial and frequency band featuresConvolutional neural network99.46%4R et al. [25]20215 ADHD and 5 normal subjects with eyes-open and eyes-closed state7 to 12 yearsPermutation entropy, Sure entropy, log energy entropy, fuzzy entropyANN classifier99.82%5Ekhlasi et al. [36]202161 ADHD and 60 healthy children9.62 is the mean age of ADHD, 9.85 is the mean age of control groupDirected phase transfer entropyANN classifier89.1%6Moghaddari et al. [37]202031 ADHD and 30 healthy children7 to 12 yearsFrequency band separationDeep CNN98.48%%7Rezaeezadeh et al. [57]202012 ADHD and 12 normal subjects with eyes-closed condition7–12 years oldNonlinear and linear univariate featuresSVM, KNN, PNN99.58%8Dubreuil-Vall et al. [58]202020 healthy and 20 ADHD patientsFeatures extracted from neural networkCNN, RNN, SNN88%9Kaur et al.[59]202047 ADHD and 50 control during the eyes-open, eyes-closed, and continuous performance test (CPT) condition20.3 is the mean age of ADHD, 20.6 is the mean age of normalPhase space reconstruction, statistical featuresSVM, KNN, neural dynamic classifier, enhanced probabilistic neural network, and naive-Bayes classifier93.3%10Altınkaynak et al. [60]202023 ADHD and 23 healthy controls7–12 yearsMorphological, wavelets, and nonlinear based featuresMultilayer perceptron, Naïve Bayes, support vector machines, k-nearest neighbor, adaptive boosting, logistic regression and random forest91.3%11Chang et al. [61]2019100 ADHD, 44 Normal subjects10.9±2.4, 10.6±1.9 mean age of ADHD, 11.3±2.2 mean age of normalTime points, channels input features, saliency mapsDeep EEGNet83%12Boroujeni et al. [29]201950 ADHD and 26 normal cases4 to 15 years oldLyapunov exponent, fractal dimension, correlation dimension and sample, fuzzy and approximate entropiesSVM classifier96.05%13Chang et al. [61]201930 ADHD and 30 control subjectsMean age in the ADHD group was 8 years 5 months ±1 year 11 months, control group was 8 years 5 months ±1 year 8 monthsUnivariate and multivariate featuresSVM classifierAreaunderthecurve=87.78%, sensitivity=80.0%, specificity=80.0%14Bashiri et al. [62]201895 ADHD subjects7 to 18 years oldQEEG features, integrated visual and auditory continuous performance testANN classifierTo determine the existence or absence of attention and response control in ADHD subjects15Khoshnoud et al. [23]201812 ADHD and 12 normal children7–12 years oldFrequency band powers, nonlinear featuresSVM classifier83.33%16Karimu et al. [28]201820 ADHD and 20 normal children7–10 years.Mixture of expert fuzzy modelsContinuous wavelet transform (CWT) and standalone classifier98.01%17Chow et al. [63]201830 ADHD and 30 controls.Mean age for control group 7 years and 10 months ±2 years and 2 months, mean age for ADHD 8 years and 1 month ±2 yearsApEn and TBRLogistic regression81.7%18Mohammadi et al. [27]201630 ADHD and 30 healthy children9.62±1.75 years for ADHD, 9.85±1.77 years for healthy childrenFractal dimension (FD), approximate entropy and Lyapunov exponentMultilayer perceptron93.65%19Khoshnoud et al. [64]201612 ADHD and 10 control groups8-13 years oldLargest Lyapunov exponent and approximate entropyProbabilistic neural network classifier87.5%20Helgadóttir et al. [65]2015310 ADHD and 351 controls5.8 to 14 yearsSpectral features extractionMultivariate diagnostic classifier76%21Tenev et al. [8]201467 ADHD, 50 controls18 to 50 years of ageForward selection for feature extractionSVM classifier82.3%22González et al. [66]201322 ADHD and 21 healthy controls4–15 yearsMultivariate linear and nonlinear interdependence measuresLogistic regression86.7%23Nazhvani et al. [67]201312 healthy ones, 12 with ADHD and 12 with BMD10 to 22 years oldWavelet denoising and synchronous averaging featuresKNN classifier92.85%24Abibullaev et al. [68]20127 ADHD and 3 normal groups7–12 yearsShanon’s entropy, mutual information measuresSVM classifier97%25Ahmadlou and Adeli [40]201112 ADHD and 12 control participants8–13 years oldFuzzy synchronization likelihoodLeave one out cross-validation method87.50%26Ahmadlou and Adeli [38]201047 ADHD and 7 control individuals with eyes-closed7-12 years oldWavelet decomposition and synchronization likelihood method.RBF neural network classifier95.6%27Proposed work20225 ADHD and 5 non-ADHD subjects with eyes-open and eyes-closed state6-12 years oldTunable Q-factor wavelet transformLinear discriminant, logistic regression, support vector machine, artificial neural networks, and ensemble100%


### 3.1. Performance Metrics

The classifier’s performance was measured using accuracy, sensitivity, specificity, negative predictive value (NPV) and positive predictive value (PPV), F1-score, G-mean, and Matthew’s correlation coefficient (MCC). The mathematical background of each performance metric is given as follows:The percentage of true positives (TP) and true negatives (TN) over the total number of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) individuals was used to calculate the classification performance for accuracy.(16)Accuracy%=TP+TNTP+TN+FP+FN∗100Sensitivity is calculated by dividing the number of true positive (TP) cases by the number of genuine positive cases, i.e., the total of true positive (TP) and false negative (FN) cases.(17)Sensitivity%=TPTP+FN∗100Specificity refers to the number of true negative (TN) cases found among all actual negative cases, i.e., the total of true negative and false positive (FP) cases.(18)Specificity%=TNTN+FP∗100The ratio of true positives to the number of positive brain maps is known as the positive predictive value (PPV).(19)PositivePredictiveValue%=TPTP+FP∗100The ratio of true negative to the number of negative brain maps defines the negative predictive value (NPV).(20)NegativePredictiveValue%=TNTN+FN∗100The harmonic and geometric measurements of sensitivity and specificity are the F1-score and G-mean, respectively.(21)F1−Score%=2∗Sensiitivity∗PPVSensiitivity+PPV∗100(22)Gmean%=Sensitivity∗Specificity∗100Matthew’s correlation coefficient is a balanced metric that determines both true and false positives and negatives, even if the classes are of different sizes [55]. To determine a result, the MCC takes into account the test’s true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN), and a significant prediction is one. Matthew’s correlation coefficient (MCC) is calculated as:
(23)MCC=TP∗TN−FP∗FNTP+FPTP+FNTN+FN∗100The classification process for ADHD and normal subjects under eyes-closed and eyes-open conditions with different decomposition levelsj varying from 1 to 15 is performed. The above performance metrics are evaluated and plotted against the decomposition levels which is shown in Figures 6 and 7. While comparing the performances in the Katz fractional dimension method, the eyes-closed state shown in Figure 6(a) reflects that the classification accuracy, sensitivity, and all other performance matrices are consistently stable at 100% in the lower decomposition level up to level 6 and the variation observed in higher levels of decomposition. This indicates that significant features are extracted in the eyes-closed state and it has a higher ability of discrimination at lower decomposition levels. In the meantime, the EEG signals with eyes-open states shown in Figure 6(b) indicate that the performance metrices has a lesser value at lower decomposition levels, and improve at higher decomposition levels. It reflects that the potential features to discriminate the ADHD are more significant and the ability of the classifier is increased in higher decomposition levels.Figure 6
Performance analysis of Katz fractional dimension with different decomposition levels (a) eyes-closed state (b) eyes-open states.
(a)(b)Figure 7
Performance analysis of Higuchi fractional dimension with different decomposition levels (a) eyes-closed state (b) eyes-open states.
(a)(b)Table2 presents the statistical details of different performance matrices while keeping the decomposition level 6 as constant and varying the tuning factor Q. The filter banks are tuned for its best performance at decomposition level 6, and observed that the Katz feature extraction method showed higher significance in classifying the ADHD under eyes-closed state with higher classification accuracy and sensitivity. Meanwhile, the Higuchi feature extraction method showed higher performance with higher classification accuracy and sensitivity under eyes-open state.The classification accuracy of the proposed work is compared with the similar works of various authors and observed an improvement in performance. Table3 shows the performance comparison specifically in terms of classification accuracy. The proposed methodology exhibits the maximum performance with 100% classification accuracy.It is clear, classify, and diagnose attention deficit hyperactive disorder from the EEG signals has been used many techniques and applications such as ANN, Fog computing, Internet of Medical Thing, and other methods [69–74].The merit of the proposed methodology is that it has given the highest classification accuracy and this is a robust system as it is validated with 10 fold cross-validation for different classifiers. The limitation of the present work is that it needs preprocessed artifact-free EEG signals, that add an additional signal processing stage to the implementation of the proposed method for real-time diagnostic purposes. Also, the data set shall be extended to fine-tune the system performances in analysing the effectiveness of the proposed system.


## 3.1. Performance Metrics

The classifier’s performance was measured using accuracy, sensitivity, specificity, negative predictive value (NPV) and positive predictive value (PPV), F1-score, G-mean, and Matthew’s correlation coefficient (MCC). The mathematical background of each performance metric is given as follows:The percentage of true positives (TP) and true negatives (TN) over the total number of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) individuals was used to calculate the classification performance for accuracy.(16)Accuracy%=TP+TNTP+TN+FP+FN∗100Sensitivity is calculated by dividing the number of true positive (TP) cases by the number of genuine positive cases, i.e., the total of true positive (TP) and false negative (FN) cases.(17)Sensitivity%=TPTP+FN∗100Specificity refers to the number of true negative (TN) cases found among all actual negative cases, i.e., the total of true negative and false positive (FP) cases.(18)Specificity%=TNTN+FP∗100The ratio of true positives to the number of positive brain maps is known as the positive predictive value (PPV).(19)PositivePredictiveValue%=TPTP+FP∗100The ratio of true negative to the number of negative brain maps defines the negative predictive value (NPV).(20)NegativePredictiveValue%=TNTN+FN∗100The harmonic and geometric measurements of sensitivity and specificity are the F1-score and G-mean, respectively.(21)F1−Score%=2∗Sensiitivity∗PPVSensiitivity+PPV∗100(22)Gmean%=Sensitivity∗Specificity∗100Matthew’s correlation coefficient is a balanced metric that determines both true and false positives and negatives, even if the classes are of different sizes [55]. To determine a result, the MCC takes into account the test’s true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN), and a significant prediction is one. Matthew’s correlation coefficient (MCC) is calculated as:
(23)MCC=TP∗TN−FP∗FNTP+FPTP+FNTN+FN∗100The classification process for ADHD and normal subjects under eyes-closed and eyes-open conditions with different decomposition levelsj varying from 1 to 15 is performed. The above performance metrics are evaluated and plotted against the decomposition levels which is shown in Figures 6 and 7. While comparing the performances in the Katz fractional dimension method, the eyes-closed state shown in Figure 6(a) reflects that the classification accuracy, sensitivity, and all other performance matrices are consistently stable at 100% in the lower decomposition level up to level 6 and the variation observed in higher levels of decomposition. This indicates that significant features are extracted in the eyes-closed state and it has a higher ability of discrimination at lower decomposition levels. In the meantime, the EEG signals with eyes-open states shown in Figure 6(b) indicate that the performance metrices has a lesser value at lower decomposition levels, and improve at higher decomposition levels. It reflects that the potential features to discriminate the ADHD are more significant and the ability of the classifier is increased in higher decomposition levels.Figure 6
Performance analysis of Katz fractional dimension with different decomposition levels (a) eyes-closed state (b) eyes-open states.
(a)(b)Figure 7
Performance analysis of Higuchi fractional dimension with different decomposition levels (a) eyes-closed state (b) eyes-open states.
(a)(b)Table2 presents the statistical details of different performance matrices while keeping the decomposition level 6 as constant and varying the tuning factor Q. The filter banks are tuned for its best performance at decomposition level 6, and observed that the Katz feature extraction method showed higher significance in classifying the ADHD under eyes-closed state with higher classification accuracy and sensitivity. Meanwhile, the Higuchi feature extraction method showed higher performance with higher classification accuracy and sensitivity under eyes-open state.The classification accuracy of the proposed work is compared with the similar works of various authors and observed an improvement in performance. Table3 shows the performance comparison specifically in terms of classification accuracy. The proposed methodology exhibits the maximum performance with 100% classification accuracy.It is clear, classify, and diagnose attention deficit hyperactive disorder from the EEG signals has been used many techniques and applications such as ANN, Fog computing, Internet of Medical Thing, and other methods [69–74].The merit of the proposed methodology is that it has given the highest classification accuracy and this is a robust system as it is validated with 10 fold cross-validation for different classifiers. The limitation of the present work is that it needs preprocessed artifact-free EEG signals, that add an additional signal processing stage to the implementation of the proposed method for real-time diagnostic purposes. Also, the data set shall be extended to fine-tune the system performances in analysing the effectiveness of the proposed system.


## 4. Conclusion

The present work is an effective methodology to classify and diagnose attention deficit hyperactive disorder from the EEG signals. The EEG signals of both ADHD and normal subjects recorded under eyes-closed and eyes-open states are preprocessed and the tunable Q-wavelet transform is applied to decompose into different subbands. The Katz and Higuchi fractional dimension feature extraction techniques are applied to extract the features for the effective classification of ADHD and normal subjects with the possible maximum accuracy. TheQ-value and the decomposition levels are optimally tuned to extract the potential features that can bring out the maximum classification accuracy. Different classifiers have experimented and the artificial neural network classifier with a 10-fold cross-validation method is found to be an effective classifier with a maximum classification accuracy of 100%. According to the findings, the level of decomposition and the Q-factor parameter has a significant impact on feature extraction performance. The classification accuracy varies dramatically with different Q-factor values, with decomposition level j of 6 being the most appropriate. Moreover, the Katz fractional dimension algorithm shows better results in eyes-closed states and the Higuchi FD algorithm demonstrates better results under eyes-open states. Different performance metrics are used to measure the effectiveness of the classifier algorithm that has justified the observed results. The features extracted through Katz and Higuchi from EEG signal under the eyes-closed state in lower decomposition levels have higher significance in discriminating ADHD from the normal subjects. Also, the features extracted from the eyes-open state in higher decomposition levels have higher significance in estimating ADHD with higher classification accuracy. With the eyes-closed EEG signals, the Katz feature extraction method showed greater significance with higher sensitivity in diagnosing ADHD. Meanwhile, the Higuchi feature extraction method showed higher performance with higher sensitivity under eyes-open state signals. As the proposed system has given the highest classification accuracy with higher sensitivity, this shall be used in the clinical diagnosis of ADHD.



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*Source: 3590973-2022-09-15.xml*