The database was designed by researchers at Florida State University and recorded from 19 scalp loci (Fp1, Fp2, Fz, F3, F4, F7, F8, Cz, C3, C4, T3, T4, Pz, P3, P4, T5, T6, O1 and O2) of the international 10 - 20 system using a Biologic Systems Brain Atlas III Plus workstation. The letters F, C, P, O and T represent the brain lobes (F: frontal, C: central, P: parietal, O: occipital and T: temporal). The recordings, which comprised four groups (A, B, C and D), were made in two resting states: eyes open (groups A and C) by visual fixation, and eyes closed (groups B and D) using a mandible-bound frontal reference ground. Groups A and B represent healthy controls and consisted of 24 healthy elderly people, with no neurological or psychiatric disorders. The age of healthy people ranged from 61 to 83 years, with an average age of 72 years and the age of AD patients ranged from 53 to 85 years, with an average age of 69 years. Groups C and D consisted of 24 patients with AD diagnosed according to the criteria of the National Institute of Neurological and Communicative Disorders and Stroke (NINCDS), AD and Related Disorders Association (ADRDA) and Diagnostic and Statistical Manual of Mental Disorders (DSM)-III-R, as described above. EEG segments had a recording time of 8 s, which has limited to a bandwidth of 1 - 30 Hz. EEG segments were recorded at a sampling rate of 128 Hz (without eye movements, blinks or myogenic artifacts) and extracted from EEG recordings. An EEG technician was present with each patient during the recordings to monitor the patients’ state of alertness [3]. The database was created on January 21, 2020, and was provided by Dr. Dennis Duke of Florida State University. It is available at https://doi.org/10.17605/OSF.IO/S74QF.

In this study, a model was proposed for the automatic diagnosis of AD based on EEG signals. The steps of the proposed learning model are illustrated in Figure 1. These steps are described in detail.

Figure 1.Architecture of the proposed learning model.

Generally, in preprocessing, the recorded data are cleaned and denoised, the artifacts are eliminated, the redundancies are eliminated, and the missing data and the bottlenecks are adjusted [4].

For spectral analysis, the signal is represented as a mathematical function of one or more variables. The 1^st species of the Chebyshev polynomial, noted T k ( x ) , is a special case of Jacobi polynomials with interesting properties that make them attractive for filter design and optimal polynomial interpolation. Chebyshev polynomials are orthogonal in the interval [−1; 1] with respect to the weight function

The explicit relationship describing Chebyshev polynomials T k ( x ) is the following trigonometric form:

The expansion of a signal s(x) in the “L” order in the orthogonal Chebyshev basis is given by:

The decomposition coefficients α k are then evaluated using the Gauss-Lobatto quadrature method with a quadrature of order L + 1. The Gauss-Lobatto method states that for a quadrature of order L, and a family of orthogonal Chebyshev polynomials T k ( x ) in the interval [−1; 1], with respect to the weight function w ( x ) , the following approximation was made by [5]:

where f ( x ) ∈ L 2 [ a , b ] , x j , are the L nodes of the Gauss quadrature formed by the L roots or zeros of T L ( x ) , and { G j } j = 1 L called Christoffel numbers, is given by

Applying the Gauss-Lobatto quadrature method gives:

The EEG signal is decomposed into a set of Chebyshev spectral coefficients using the DChT Equation (7) [6]:

The main aim of feature extraction is to obtain additional information from the raw signal by transforming voluminous data into a smaller feature vector. After analyzing the data using DChT, the feature extraction methodology analyzes the signals to extract the most important features that are representative of the different signal classes [4]. To identify and quantify the most relevant properties of a signal and facilitate its analysis or classification, 85 parameters were extracted. 31 parameters were extracted using the spectral decomposition coefficients, 22 parameters were extracted using the absolute values of these decomposition coefficients, 30 parameters were extracted using the original signal and 2 parameters were extracted using the reconstructed signal. These two parameters are the Percent Root Square Difference (PRD) and Energy of the approximated signal. 85 parameters were extracted by applying the formulas described below. However, scaling, hyperparameter tuning, and Boruta selection were performed only on each training fold prior to classification. Some of these informative, descriptive, statistical, energetic and entropic parameters are presented below:

MaximumMinimumMean absolute deviation:

PRD (Percent Root Square Difference): for a signal Δ n and the approximate signal δ n n = 1 , 2 , ⋯

Coefficient of asymmetry or skewness coefficient ( α 1 ): μ and σ respectively represent the mean and standard deviation of the set X.

Kurtosis ( β 1 ): μ and σ respectively represent the mean and standard deviation of the set X

Number of Zero Crossings (NZC)Magnitude Peak (PM1):

Latitude factor (LF):

Shape Factor (SF):

Coefficient of Variation (CV):

Dimension reduction techniques such as Principal Component Analysis (PCA) can be applied to reduce the dimensions of the original data and remove irrelevant and redundant information. This reduces the computational costs and reduces noise depending on how many principal components are kept [4].

Machine Learning (ML) and Deep Learning (DL) algorithms were used to perform classification. These include Support Vector Machine (SVM), k-nearest neighbors (kNN), Ensemble Learning (EL) algorithms such as XGBoost, GradientBoosting and AdaBoosting, Random Forest (RF) and Multi Layer Perceptron (MLP).

Some metrics are evaluated after classification:

Confusion matrix

It depicts the structure of the confusion matrix for a binary classifier. The estimates of the possibilities of classification models are derived from the expressions True Positive (TP), True Negative (TN), False Positive (FP) and False Negative (FN), which exist in the confusion matrix [7].

Basic indicators

The performance evaluation criteria in our study consist of measuring the performance of a classification according to the standard criteria described below [7][8]:

1. Accuracy (acc):

2. Sensitivity (Sen) or True Positive Rate (TPR) or Recall:

3. Specificity or True Negative Rate (TNR ou spe):

4. False Positive Rate (FPR):

5. Precision (Pre):

6. F-Measure or F-score:

Receiver Operating Characteristic (ROC) area and Area Under the Curve (AUC):

The ROC curve visualizes the trade-off between TPR and FPR. For each threshold, TPR and FPR were calculated and plotted on one graph. The higher the TPR and the lower the FPR for each threshold, the better. The area below the ROC curve is called the ROC-AUC score, a number that determines how good the ROC curve is [7].

K-fold cross-Validation (KCV):

The KCV technique is one of the most commonly used approaches by practitioners for model selection and error estimation of classifiers. It consists of splitting a dataset into k subsets; then, iteratively, some of them are used to learn the model, whereas the others are exploited to assess its performance [9].

In this database, 19 columns represent each electrode and 1024 rows represent the total duration of the recordings, that is 8 s. This means that one line recorded the amplitude of the electrode for a period of 7.8125 ms. Examples of the data from channel F7 are shown in Figure 2. This figure shows a signal trace for each F7 channel from each group A to D. Group A refers to healthy subjects with open eyes, group B to healthy subjects with closed eyes, group C to AD subjects with open eyes and group D to AD subjects with closed eyes.

Figure 2. EEG signal presentation at electrode F7 for each group (A, B, C and D) [10].

Figure 3 shows the signal obtained at electrode F7 for each group after preprocessing. In this figure, group A is labeled HC_oe, group B is labeled HC_ce, group C is labeled AD_oe, and group D is labeled AD_ce.

Figure 3. EEG signal at electrode F7 after preprocessing.

The dataset consisted of four data groups, each containing the recorded data from 12 patients. Some recordings lasted longer than 8 seconds and, therefore, contained more than 1024 rows for a single patient. Thus, for each data group, there were between 12,288 and 15,360 rows and 19 columns, each representing an electrode. Preprocessing verifies whether patient data is valid (no bottlenecks, missing values, outliers,..) and divides the data by sampling it into rows or data units. The records were fully preserved during preprocessing to prevent subject-level information leaks. The information is categorized based on ocular status, and each patient’s data is added progressively and processed independently during testing.

Spectral analysis involves approximating or interpolating the signals to extract better information. It breaks down a signal into smaller signals to extract characteristics; This is performed using a transfer function. In our case, it is the Jacobi polynomial, in particular the Chebyshev polynomials. Figure 4 shows the interpolation coefficients on the orthogonal Chebyshev basis for each of the HC_oe, HC_ce, AD_oe and AD_ce groups. The graphs in Figure 4 represent the first and second spectral coefficients, respectively.

Using Chebyshev interpolation, the number of columns increases from 19 to 39 as given by Equation (7) to evaluate the spectral coefficients α k .

However, the spectral coefficients gradually decrease until they cancel each other out. This is explained by the Runge phenomenon, which appears to be a consequence of interpolation using the Jacobi polynomial.

After spectral analysis, the dataset has a dimension of 12,288 × 39; and the coefficients obtained after interpolation of the signal in the orthogonal Chebyshev basis will make it possible to extract 85 parameters represented by 102,425 figures in dimensions 1, 2 and 3, as shown respectively in Figures 5-7 for a dataset of size 12,288 × 85.

Figure 4. Spectral coefficients after interpolation by the Chebyshev polynomial.

Figure 5. 1D parameter features: PRD.

Figure 5 presents the 1D parameter features. It contains two graphs. Graph (a) represents the “eyes opened” parameter and graph (b) the “eyes closed” parameter. Figure 5 presents the characteristic PRD in relation to the sample in dimension 1. As defined by formula (9), the PRD represents the difference between the original signal and the reconstructed signal for each of the parameters “eyes opened” and “eyes closed” for sick and healthy individuals. This difference is minimal. This means that signal interpolation on the orthogonal Chebyshev basis was carried out with minimal error.

Figure 6. 2D parameter features: PM1 and PRD.

Figure 6 presents 2D parameter features. It contains two graphs. Graph (a) represents the “eyes opened” parameter and graph (b) the “eyes closed” parameter. For each of the “eyes opened” and “eyes closed” parameters, Figure 6 shows the relationship between the PRD and PM1 characteristics for healthy and sick individuals. The PM1 parameter is defined using formula (12). Note that the higher the signal intensity, the lower the signal reconstruction error.

Figure 7. 3D parameter features: Min, Max and NZC.

Figure 7 presents 3D parameter features. The Min, Max and NZC characteristics are observed for the parameters “eyes opened” in graph (a) and “eyes closed” in graph (b) for both sick and healthy individuals. In this figure, the values of the metrics are much more concentrated towards the center, which means that the minimum and maximum values fall within a relatively narrow range and the distribution is random.

After application of the PCA, the result of the dimension reduction is a matrix of size 85 × 85, and the datasets are represented in dimensions 1, 2 and 3 as shown in Figures 8-10.

Figure 8. PRD parameter as a function of 1D sample size after dimension reduction.

Figure 9. 2D parameter after dimension reduction.

Figure 8 shows two PRD plots, in graphs (a) and (b), which represent the signal reconstruction error in the Chebyshev orthogonal basis for the “eyes opened” and “eyes closed” parameters respectively. After dimension reduction using PCA, the error becomes increasingly smaller.

Figure 9 shows the peak signal magnitude as a function of the reconstruction error for parameters “eyes opened” and “eyes closed” in graphs (a) and (b) respectively. The metrics were increasingly concentrated towards the center and of low intensity for both healthy and sick individuals.

Figure 10. Min, Max and NZC parameters after dimension reduction.

Figure 10 shows the minimum, maximum and number of positive values in the signal for parameters “eyes opened” and “eyes closed” in graphs (a) and (b) respectively. After dimension reduction with PCA, the metrics were increasingly concentrated towards the center and of lower intensity for both healthy and sick individuals.

In this subsection, three categories of results are presented. The first category of results was obtained using dimension reduction, the second category was obtained without dimension reduction and the third category of results was obtained without spectral analysis and without dimension reduction.

3.5.1. Classification Results Using Dimension Reduction

After parameter extraction and dimension reduction by signal interpolation in the orthogonal Chebyshev basis, the very low-dimensional parameter vectors were used directly as classifier inputs.

Using the SVM algorithm, on a dataset of which 80% is used for training and 20% for testing, the ROC curve obtained in Figure 11 shows that the classifier is not very discriminative, with an AUC = 0.426.

The associated confusion matrix is given by

and leads to the following metric values: Acc = 42.65%, Sen = 43.59%, Spe = 41.38%, Pre = 50% and F-Score = 46.58%.

Figure 11. ROC curve obtained for SVM classification with dimension reduction.

Using the kNN algorithm on a dataset in which 80% was used for training and 20% for testing, the best result was obtained with k = 1. The corresponding ROC curve is shown in Figure 12.

Figure 12. ROC curve obtained for kNN classification with dimension reduction.

The associated confusion matrix is given by

This leads to the following metrics deduced: Acc = 39.71%, Sen = 41.03%, Spe = 37.93%, Pre = 47.06%, F-Score = 43.84%. In this case, these metric values show that the kNN classifier performed less well than the SVM classifier.

Using the XGBoost algorithm on a dataset in which 80% was used for training and 20% for testing, the following metric values were obtained: Acc = 84.38%; Pre = 76%; Sen = 100%; F-score = 86% and AUC = 0.844. This shows that the XGBoost classifier used here is highly discriminative and delivers a precise result.

Using the AdaBoost algorithm, on a dataset in which 70% was used for training and 30% for testing, the following results were obtained: Acc = 80.77%; Pre = 82%; Sen = 81%; F-score = 81%. The corresponding ROC curve is shown in Figure 13. The AdaBoost classifier performed well on this dataset. This makes it a good tool for distinguishing sick from healthy subjects.

Figure 13. ROC curve obtained for Adaboost classification with dimension reduction.

Using the GradientBoosting algorithm, on a dataset in which 80% was used for training and 20% for testing, the ROC curve in Figure 14 was obtained.

The associated confusion matrix is given by

This led to the following metric values: Acc = 83.82%; F-score = 83.58%; Sen = 82.35% and Pre = 84.84%. According to the results of the experiments, the GradientBoosting classifier is one of the best tool for diagnosing patients.

Using the GradientBoosting algorithm by varying the percentages of the dataset used in the training and testing phases to achieve learning accuracy based on the percentage of the dataset used in the training phase, Figure 15 was obtained. In this figure, the x-axis represents the training set percentage and the y-axis represents the accuracy after classification. The experiment began with a value of 5% for the training set and 95% for the testing set. At this value of x, the accuracy was 58.33%. The abscissas evolved in steps of 10%. Accuracies evolved from 56.82% to 88.64% and were calculated for different values of the abscissas from 5% to 95%. The best accuracy is obtained with a training set percentage of 88% and a testing set percentage of 12%. However, the accuracy curve increases with the training set.

Figure 14. ROC curve obtained for GradientBoosting classification with dimension reduction.

Figure 15. Evolution of accuracy in GradientBoosting classification with dimension reduction.

Using the Random Forest algorithm on a dataset in which 80% was used for training and 20% for testing, results in an accuracy of 73.53%, Pre = 72.22%, Recall = 76.71%, F1-score = 74.29% and AUC= 0.735. The associated confusion matrix is given by

The corresponding ROC curve is shown in Figure 16. RF classifier is one of the best tool for diagnosing patients.

Figure 16. ROC curve obtained for Random Forest classification with dimension reduction.

The data used for classification using artificial neural networks such as the MLP were divided into three blocks; 70% of the data were used for training, 15% for validation and the remaining 15% for data prediction. The data at the input of the classifier correspond to the various features extracted in the previous phase. RandomizedSearchCV is a powerful technique for optimizing the hyperparameters of a machine learning model.

Table 1. Results for MLP classification with RandomisedSearchCV.

The results obtained using the RandomizedSearchCV algorithm to tune the hyperparameters are listed in Table 1. The accuracy was observed by varying the hyperparameters used in the MLP architecture. This makes it possible to search for hyperparameters and architectures that maximize the precision.

Table 2 lists the results obtained without using the RandomizedSearchCV algorithm to tune the hyperparameters. In order to avoid overlearning, the SGD

Table 2. Results for MLP Classification without RandomisedSearchCV.

optimizer was used. The values of the hyperparameters were taken at random and the regularization techniques used for classification were designed to improve the test accuracy by enhancing learning. After this series of experiments with the MLP, the best accuracy obtained was 59.38% with the architecture 85-1000-1 with a dataset divided into three parts: 80% for the training set (20% of the training set was used for the validation), 10% for the testing set and the remaining part for the prediction. The ROC curve obtained after this classification is shown in Figure 17 with AUC= 0.488. This value shows that the classifier is discriminative, and with this average accuracy, it can briefly distinguish sick from healthy individuals.

3.5.2. Classification Results without Dimension Reduction

Using the kNN algorithm on a dataset of which 80% is used for training and 20% for testing, the best result was obtained when k=20. The corresponding ROC curve is shown in Figure 18.

The associated confusion matrix is given by

This leads to deducing the values of the following metrics: Acc = 71.80%, Recall = 69.16%, Pre = 73.01% and F-Score = 71.03%. It can be observed that the kNN classifier in this case performs better without dimension reduction.

Using the XGBoost algorithm on a dataset of which 70% is used for training and 30% for testing, the following metric values were obtained: Acc = 92.72%, Pre

Figure 17. ROC curve obtained for MLP classification with dimension reduction.

Figure 18. ROC curve obtained for kNN classification without dimension reduction.

= 95%, Recall = 90%, F1-score = 93% and Auc = 0.927. The XGBoost classifier is more discriminating and can easily distinguish between sick and healthy patients with precision. A closer look at the accuracies obtained after classification is shown in Figure 19. The best accuracy was 93.24%, obtained with a training set of 90% and a testing set of 10%.

Using the AdaBoost algorithm, on a dataset of which 70% was used for training and 30% for testing, the following results were obtained: Acc = 78.03%; Pre = 78%; Sen = 78%; F1-score = 78%. The corresponding ROC curve is shown in Figure 20. The AdaBoost classifier is a good tool for distinguishing sick from healthy subjects.

Figure 19. Evolution of the accuracy in the XGBoost classification.

Figure 20. ROC curve obtained for Adaboost classification without dimension reduction.

Using the GradientBoosting algorithm on a dataset of which 70% was used for training and 30% for testing, results in an accuracy of 84.01%. Using dimension reduction, the best accuracy is achieved using 88% of the dataset for training. Therefore, using this percentage for the training set, the best accuracy obtained was 84.59%, Pre = 85%, Recall = 85%, F1-score = 85% and AUC= 0.85. The associated confusion matrix is given by

The GradientBoosting classifier emerges as one of the best tool for diagnosing patients.

Using the Random Forest algorithm on a dataset of which 80% was used for training and 20% for testing, results in an accuracy of 80.73%, Pre = 83.47%, Recall = 76.63%, F1-score = 79.90% and AUC= 0.807. The associated confusion matrix is given by

The corresponding ROC curve is shown in Figure 21. The Random Forest classifier emerges as one of the best tool for diagnosing patients.

Figure 21. ROC curve obtained for Random Forest classification without dimension reduction.

The data used for classification with artificial neural networks such as the MLP were divided into three blocks; 80% of the data were used for training (20% of the training set is used for validation ), 10% for the test and the remaining 10% for data prediction. The data taken as the input of the classifier correspond to the various features extracted in the previous phase. Therefore, using the architecture 39-1000-1, the hyperparameters are: epochs = 100, batch-size = 32, learning_rate = 0.001, optimizer = SGD, loss = binarycrossentropy, dropout = 0.3 and the best accuracy obtained was 50% with AUC= 0.500. This shows that the classifier is discriminative and, therefore, able to distinguish between sick and healthy people.

3.5.3. Classification Results without Spectral Analysis and without Reduction of Dimension

In this subsection, classification is performed using the original signal without the proposed methodology.

For the AdaBoost algorithm, on a dataset in which 70% was used for training and 30% for testing, the following results are obtained: Acc = 75.91%; Pre = 76%; Sen = 76%; F1-score = 76%. The corresponding ROC curve is shown in Figure 22. The AdaBoost classifier is a good tool for distinguishing sick from healthy subjects.

In this subsection, tests are done. First, the original signal was divided into 96 segments, each 1s in length. Temporal features were then extracted to construct a matrix. These include:

Figure 22. ROC curve obtained for Adaboost classification without spectral analysis and without dimension reduction.

Mean and Standard deviation to see the overall rangeSkewness is given by formula (10) and kurtosis is given by formula (11) to detect whether the original signal contains artifacts or spikesRoot Mean square to determine the total energy of the signal before filteringPeak-to-Peak to detect sudden changes in the signalNumber of zero crossings

The spectral coefficients were divided into 96 segments. Spectral features were extracted from the spectral coefficients obtained after interpolation using the Chebyshev polynomial. These features are used to construct a matrix, which includes the following:

total spectral power: measures the total energy of the signal after filteringspectral centroid: indicates where the main concentration of energy lies in the spectrumspectral bandwidth: measures the spread of energyspectral entropy: measures the disorder or complexity of the spectrummaximum amplitude and its position to determine the dominant filtered frequency and its strength

These two feature matrices are combined and merged into a single dataset. The Boruta algorithm is used to select the most important features. After applying this algorithm, all temporal and spectral features were selected, demonstrating that spectral analysis using Chebyshev polynomial interpolation had a significant impact.

With these two sets of data—where Set 1 corresponds to the temporal characteristics of the original signal and Set 2 corresponds to the characteristics selected by Boruta; the Shapiro test is performed to verify the normality of the data sets. Since the Shapiro test yielded a negative result, the Mann-Whitney U test was applied.

In this test, the null hypothesis (H0) states that the accuracy scores obtained by applying the XGBoost classification algorithm to each group are equal. The alternative hypothesis (H1), on the other hand, posits that accuracy improves when using the selected features, which include Chebyshev coefficients.

At the end of this test, the p-value = 0. This led us to conclude that spectral analysis using the Chebyshev polynomial is significant and beneficial for classification.