Detection of Alzheimer and mild cognitive impairment patients by Poincare and Entropy methods based on electroencephalography signals

Abstract

Alzheimer’s disease (AD) is characterized by deficits in cognition, behavior, and intellectual functioning, and Mild Cognitive Impairment (MCI) refers to individuals whose cognitive impairment deviates from what is expected for their age but does not significantly interfere with daily activities. Because there is no treatment for AD, early prediction of AD can be helpful to reducing the progression of this disease. This study examines the Electroencephalography (EEG) signal of 3 distinct groups, including AD, MCI, and healthy individuals. Recognizing the non-stationary nature of EEG signals, two nonlinear approaches, Poincare and Entropy, are employed for meaningful feature extraction. Data should be segmented into epochs to extract features from EEG signals, and feature extraction approaches should be implemented for each one. The obtained features are given to machine learning algorithms to classify the subjects. Extensive experiments were conducted to analyze the features comprehensively. The results demonstrate that our proposed method surpasses previous studies in terms of accuracy, sensitivity, and specificity, indicating its effectiveness in classifying individuals with AD, MCI, and those without cognitive impairment.

Introduction

Alzheimer’s disease (AD) is probably the most widespread neurodegenerative disorder affecting millions of individuals worldwide, and approximately 50 million patients are predicted to suffer from this disease [1]. AD can also lead to dementia. Although earlier diagnosis and detection can help to prevent the progression of dementia and thus improve the quality of life of patients, there is no definite cure for AD. In terms of dementia, mild cognitive impairment (MCI) refers to patients who are not severe enough to meet AD diagnostic criteria but have cognitive deficits that are greater than expected for their age. There is the possibility that the MCI patients may progress to AD over time. Therefore, the diagnosis of MCI patients in earlier stages could be crucial in case of preventing the progression of disease.

There are several ways to detect people who suffer from neurodegenerative diseases. Clinically, the main method for identifying AD and MCI patients is a subjective neuropsychological test. In addition, in the case of AD and MCI disorders, analyzing changes in the structure of the brain has been highlighted by researchers. Several studies have been proposed to detect and analyze AD patients based on MR images [2,3,4].

Although imaging systems could yield better results in terms of localization and detection of any abnormalities in the brain, owing to the high cost and time consumption of these procedures, electroencephalography (EEG) is generally used to detect changes and abnormalities in brain activity, since it is noninvasive, fast and inexpensive with high accuracy results. EEG has been proven to be an effective tool for characterizing several disorders, such as sleep disorders [5], epilepsy detection [6, 7], stress disorder, and detecting alcoholism [8]. Therefore, with the aim of developing biomarkers for early detection, diagnosis, and monitoring of disease progression in AD and MCI patients, EEG signal processing methods have been utilized for several decades.

In the literature, numerous studies have been proposed to analyze the EEG signals of AD and MCI patients. To evaluate the EEG signals, the pre-processing step can be implemented to eliminate noise and unwanted data. Since EEG signals have low-frequency bands, an appropriate low-pass filter and wavelets-based filters can be designed [9, 10]. Although combinations of methods have been proposed to examine EEG signals, approaches can generally be categorized into four groups:

• Time domain: Evaluations of EEG signals using time-domain features such as waveform length, zero-crossing and mean absolute value, skewness, and kurtosis were presented in the literature [11,12,13]

• Frequency domain: To analyze characteristics of EEG signals from individuals with MCI, AD, and healthy individuals in the frequency domain, Fourier transform (FT) and short-time FT are used to extract meaningful features [14,15,16,17].

• Time–frequency domain: Since brain activity occurs in low-frequency bands, analyzing the changes in frequency bands is essential in EEG signal processing, in which wavelets are the most used approach for accessing these frequency bands [18,19,20].

• Non-linear methods: For non-linear biomedical signal processing, several methods, including Entropy, Poincare, and Lyapunov exponent analysis, are used to evaluate the complexity of signals and the stability of any steady-state behavior [21,22,23,24].

Since brain activity is not linear, non-linear methods could be used to evaluate EEG signals. It has been presented by [25,26,27] that to characterize EEG signals in different circumstances, non-linear methods are beneficial, especially if the amount of data is relatively high. In the literature, few studies focus on classifying three groups: AD, MCI, and healthy individuals. The main objective of this study is to apply machine learning techniques to non-linear features extracted using widely adopted Poincaré and Entropy methods for the classification of these three groups. The proposed method not only addresses the research gap in classifying these three groups but also achieves the highest classification accuracy reported in studies using EEG signals. In addition, the classification between AD-MCI, AD-healthy, and healthy-MCI has been examined.

Related works

Among the broad spectrum of research dedicated to diagnosing Alzheimer’s Disease (AD) and mild cognitive impairment (MCI) using electroencephalography (EEG) signals, this study has conducted a literature review with a specific emphasis on nonlinear methods of analysis.

Several studies have employed entropy-based methods to analyze EEG signals for diagnosing AD and MCI. In [28], the authors used Permutation Entropy (PE) to analyze EEG signals in 2-s epochs, revealing that the complexity of MCI and AD patients is lower than that of healthy individuals, with better classification in the eye-open state. Similarly, [29] applied Dispersion Entropy on sub-frequency bands, followed by an ANOVA-based dimension reduction technique. Spectral Entropy (SpecEn) was introduced in [30] for analyzing EEG signals of AD, MCI, and healthy individuals, contributing to a better understanding of spectral characteristics in these groups.

Wavelet and Approximate Entropy approaches have also been explored in the literature. In [31], the authors investigated the relationship between Wavelet Entropy and power distribution across EEG channels, with the Haar wavelet showing the best performance in distinguishing AD patients from healthy individuals. Similarly, [32] applied Approximate Entropy and Average Mutual Information to classify AD and healthy individuals, achieving an AUC of 0.91. In addition, Chai et al. [33] analyzed sub-frequency bands and multi-scale entropy across 25-s EEG epochs, achieving an AUC of 0.89 in AD detection.

Several nonlinear-based analyses have also been applied to EEG signals for AD diagnosis. Staudinger and Polikar [34] conducted a non-linear analysis of EEG signals from AD and healthy patients. Houmani et al. [35] introduced an epoch-based approach using Shannon Entropy combined with the Hidden Markov Model (HMM) for early diagnosis of AD. Furthermore, Tsallis Entropy was employed in [36] to detect Alzheimer’s disease, and Siuly et al. [37] proposed a combination of Permutation Entropy and autoregression models to identify MCI patients. A comprehensive analysis of sub-frequency bands of all groups was performed by Tzimourta et al. [27], in which statistical time analysis and non-linear methods were employed for each band. In addition, the authors indicated each band’s effectiveness in different brain regions.

Research into the use of entropy-based and optimization algorithms has expanded the potential for EEG-based classification. Simons et al. [38] applied quadratic sample entropy across EEG channels, achieving 78% accuracy in detecting AD. Nonlinear methods, including Singular Value Decomposition, Detrended Fluctuation Analysis, and Higuchi Dimension, were employed to analyze Alzheimer’s disease based on EEG signals, as presented in [39]. The obtained results highlight the effectiveness of the SVD method in achieving high-quality features with almost 93% accuracy in detecting AD and healthy adults. In [40], Multi-scale Fuzzy Entropy was applied to sub-frequency bands to identify AD and Control groups. Although relatively low accuracy was achieved in comparison with other studies, implementing just one algorithm is the strength of the approach. Optimal selection of EEG channels by Intelligent Optimization algorithm with focusing on entropy and the Second Order Difference Plot (SODP) features proposed by [41]. Researchers identified FP1, F3, F4, and P4 channels as most effective for distinguishing between Alzheimer’s disease and healthy controls, achieving high classification accuracy and sensitivity. Combination of several entropy-based feature extraction methods have been considered in [42]. Analysis of different epoch lengths was presented, which showed that the entropy values of the MCI group for lower epoch periods(1 ≤ s ≤ 4) were lower than the control group, and for longer epoch lengths (10 ≤ s ≤ 15), the entropy values of the MCI group were higher than the control group. In addition, [43] used a combination of multi-domain features and feature selection methods to classify motor imagery EEG signals, proposing a novel approach to enhance classification accuracy.

The primary contribution of this study lies in developing a new computer-based decision support system for the discrimination of AD, MCI, and healthy subjects. Specifically, the key contributions of this study include the application of nonlinear methods in EEG signal analysis, the evaluation of features obtained from each method, and the determination of each group using machine learning algorithms.

Data set

The EEG signals used in this study were gathered at the Neurology Department of Baskent University Hospital, following the guidelines set by the Baskent University Institutional Review Board and Ethics Committee [14]. A total of 35 participants, aged between 65 and 90, participated in the study. The data sizes of the groups were assessed for conformity using “One ROC Curve Power Analysis”. The hypothesis suggests that with 80% power and a 5% error rate, the true detection rate could reach approximately 90%. Demographic characteristics of the participants is given in Table 1.

Table 1 Overview of participants

Every participant underwent a thorough examination to rule out the existence of additional neurological disorders, such as epilepsy, multiple sclerosis, and Parkinson’s disease, as well as depression or other psychiatric disorders. In addition, degenerative dementia syndromes, including frontotemporal dementia, Lewy body dementia, and vascular dementia, were checked, as well as the presence of systolic or uncontrolled hypertension, substance or alcohol abuse, a history of traumatic brain injury, and structural lesions in the brain were also considered and excluded.

19 EEG electrodes were replaced based on the 10–20 international system (Fig. 1), and during resting eyes-closed condition, 7 min of EEG data were recorded using a Nihon Kohden-Neurofax EEG 1200. The sampling frequency and bit resolution are 200 Hz and 16 bits, respectively.

Fig. 1

10–20 system electrode montage

Although a variety of epoch lengths could be considered (as given in the last section, Table 8), an epoch length of 30 s was considered in this study. Accordingly, 14 epochs were examined for each channel, resulting in 490 epochs.

Methodology

This study aims to employ nonlinear methods to extract features from EEG signals. As given in Fig. 2, the proposed method includes 2 steps; in the first step, several methods are employed to extract meaningful features from the EEG signal. The obtained feature set is given to machine learning algorithms in the second step for examination. The performance of the proposed approach is determined by evaluating the test set. Pseudocode of the proposed method is given in Table 2. Two different methods were implemented to extract features. A brief description of them is given below.

Fig. 2

Proposed method’s architecture

Table 2 Pseudocode of proposed method

Entropy

Although Entropy is used in various fields, in nonlinear dynamical systems, entropy can be implemented to quantify the complexity of a system. Since EEG signals are non-stationary and nonlinear, entropy is widely used to evaluate the complexity of signals [29,30,31,32,33,34,35,36,37,38]. In this regard, several entropy-based methods were utilized in this study to extract features from each epoch, as discussed below.

Permutation entropy (PerEn)

To examine the complexity or randomness of the time series, the PerEn determines a certain permutation pattern in the signal [44]. A given time series is first transformed into a series of ordinal patterns in which each pattern specifies the relationship between the current and past sequences. PerEn is defined as follows:

$$\text{PerEn}= - {\sum }_{j=1}^{k!}{p}_{j}{\text{log}}_{2}({p}_{j})$$

(1)

where k is the permutation order, and ${p}_{j}$ is the relative frequency of the permutation pattern. (k is chosen 3 in this study).

Approximate entropy (AppEn)

Given a time series x = {x₁, x₂, x₃, … x_N} in m dimensional phase-space, AppEN states the likelihood of similar patterns of observations [45]. Thus, for high irregularity time series, AppEN would be high.

The similarity between pairs is calculated by $\text{d }({x}_{m}\left(\text{i}\right), {x}_{m}\left(\text{j}\right))$ which is the maximum absolute difference between their respective scalar components, i.e., the maximum norm:

$$d\left[X\left(i\right), X\left(j\right)\right]=\underset{k=\mathit{ }\text{1,2},\dots ,m}{\text{max}}\left|x\left(i+k-1\right)-x(j+k-1)\right|$$

(2)

For each i = 1 i N m C 1, the correlation integral C^m_i can be formed as

$${C}_{r}^{m}\left(r\right)=\frac{1}{N-m+1} \sum_{j=1}\uptheta (\text{r}-\text{d }({x}_{m}\left(\text{i}\right), {x}_{m}(\text{j}))$$

(3)

where θ is Heavyside function (θ(x) = 1 for x > 0, θ(x) = 0, otherwise]). Then, φ is defined as

$$\varphi^{m} \left( r \right) = \frac{1}{N - m + 1} \mathop \sum \limits_{i = 1}^{N - m + 1} \ln C_{r}^{m} \left( i \right)$$

(4)

This procedure continues for the m + 1 dimension, and AppEn is defined as follows:

$$\text{AppEn}\left(m,r,\uptau , N\right)= {\uptheta }^{m}\left(r\right)- {\uptheta }^{m+1}(r)$$

(5)

where m is the number of phase space dimensions, r is the tolerance, N is the time series length, and τ is lag.

Sample entropy (SamEn)

Sample entropy is a modified version of AppEn that outperforms in the independence of length of the time series as well as trouble-free implementation and is defined as [46]

$$\text{SamEn}= - \text{log}(\frac{A}{B})$$

(6)

where A and B are the total number of vector pairs having d(x _m+1 (i), x_m+1(j)) < r of length (m + 1) and the total number of vector pairs having d(x_m(i), x_m(j)) < r of length m, respectively.

Spectral entropy (SpecEn)

The measure of unpredictability and randomness of a time series by SpecEn is associated with the power spectrum of the components of a signal [47]. SpecEn is high if the power of signals has a wide range of frequencies:

$${H}_{2}(X)= -\text{log}\sum_{i=1}^{n}{p}_{i}^{2}$$

(7)

where p_f is the power spectral density Fourier transform at frequency f.

Bubble entropy (bEn)

A modification of permutation entropy was given by [48] as Bubble Entropy. This new perspective is free of parameters m and r. For each vector in m-dimensional phase space, the Renyi entropy is calculated by

$${H}_{2}(X)= -\text{log}\sum_{i=1}^{n}{p}_{i}^{2}$$

(8)

and bEn is achieved by the Renyi entropy of successive dimensions divided by normalization factor log (m + 1/m-1):

$${\text{bEn}} = \left( {H_{{{\text{swaps}}}}^{m + 1} - H_{{{\text{swaps}}}}^{m} } \right)/\log \left( {m + 1/m - 1} \right)$$

(9)

Entropy of entropy (EoE)

EoE computes Shannon entropy twice for a signal utilizing a multiscale approach [49]. EoE consists of two steps; in each step, the Shannon entropy is implemented into a time series. First time series x = {x₁, x₂, …., x_N,} is divided into several consecutive nonoverlapping windows w = {x_(j-1)τ+1,…, x_(j-1)τ+τ}, then Shannon Entropy is implemented into each window. The probability of certain patterns is calculated by

$${p}_{jk}= \frac{\text{total number of} {x}_{j}\text{over} {w}_{j}^{\tau }\text{in} \text{state} k}{\tau }$$

(10)

where k is the state index from 1, and Shannon entropy is consequently implemented as follows:

$${y}_{j}^{\tau }= -\text{log}\sum_{k=1}^{{s}_{1}}{p}_{jk}\text{ln}{p}_{jk}$$

(11)

$${y}_{j}^{\tau }= -\text{log}\sum_{k=1}^{{s}_{1}}{p}_{jk}\text{ln}{p}_{jk}$$

In addition, consequently, EoE is computed under different time scales τ:

$$EoE= -\sum_{l=1}^{{s}_{2}}{p}_{l} ln{p}_{l}$$

(12)

Wavelet entropy (WE)

For non-stationary signals, wavelet entropy combines wavelet decomposition with the order within wavelet coefficients [50]. Wavelet Entropy calculates the entropy of the normalized wavelet coefficients by considering them as an empirical probability distribution:

$$WE= \sum_{i}\sum_{j}{\left.\left|{wt}_{ij}\right.\right|}^{2}$$

(13)

where the probability mess function is

$$P\left({wt}_{ij}\right)= {\left.\left|{wt}_{ij}\right.\right|}^{2}IE$$

(14)

Fuzzy entropy (FuzzEn)

Fuzzy entropy (FuzzEn) provides robust estimates of signal uncertainties, even in the presence of noise, and is highly responsive to changes in information content [51]. By analyzing short signals, FuzzEn can achieve reliable and stable estimations. The similarity degree between two vectors x_m(i) and x_m(j) can be defined as

$${D}_{ij}^{m}= \mu \left({d}_{ij}^{m}, n, r\right)= {e}^{\frac{{{- (d}_{ij}^{m})}^{n}}{r}}$$

(15)

where d_ij^m is the distance between two vectors x_m(i) and x_m(j), and μ is the fuzzy membership function. θ is defined as

$${\uptheta }^{m}\left(n,r\right)=\frac{1}{N-m} \sum_{1}^{N-m}(\frac{1}{N-m-1} \sum_{j=1, j\ne 1}^{N-m}{D}_{ij}^{m})$$

(16)

Therefore, FuzzEn for time series is obtained by

$$\text{FuzzEn}\left(m,n,r,N\right)=\text{ln}{\uptheta }^{m}\left(n,r\right)-\text{ln}{\uptheta }^{m+1}(n,r)$$

(17)

where r is similarity tolerance which was chosen 0.25 times the standard deviation of the signal. m, n and N are embedding dimension, number of datapoints and length of the time series, respectively.

Disperse entropy (DispEn)

To quantify the regularity of the time series, DispEn was introduced by [52], which uses the normal cumulative distribution and maps the original signal to the dispersion signal. Therefore, higher complexity results in higher DispEn value.

First, a mapping function is implanted to normalize the time series:

$${y}_{f}= \frac{1}{\sigma \sqrt{2\pi }} {\int }_{-\infty }^{x}{e}^{\frac{{-(s-\mu )}^{n}}{{2\sigma }^{2}}} ds$$

(18)

where Ϭ is the variance, and μ is the expectation of the normal data distribution. Normalized data are defined as follows:

$${y}_{f}^{m}=\left[{y}_{f}+ {y}_{f+\tau }, \dots , {y}_{f+(m-1)\tau }\right]$$

(19)

where j = 1, 2, …, n − (m − 1)τ, m is phase space dimension and τ is time lag. Then, y^m is grouped into c classes:

$${z}_{i}^{c}=\text{round}(c. {y}_{f}+0.5)$$

(20)

$${z}_{f}^{m, c}=[{z}_{f}^{c}, {z}_{f+\tau }^{c},\dots ,{z}_{f+(m-1)\tau }^{c}]$$

(21)

and the relative frequency of each dispersion pattern is achieved by

$$P\left(\pi \right)= \frac{\text{Number} \{\pi \}}{N-(m-1)\tau } (1\le i\le {c}^{m})$$

(22)

where P(π_i) represents the ratio of the number of ith dispersion patterns to the number of embedding vectors, finally, based on Shannon entropy, DispEn is defined as

$$\text{DispEn} \left(m, c,\uptau ,N\right)= - \sum_{\pi =1}^{{c}^{m}}P\left(\pi \right).\text{ln}(P\left(\pi \right))$$

(23)

where m is the number of dimensions of the phase space, and τ is lag. N and C are number of classes and length of time series, respectively.

Attention entropy (AttEn)

To overcome the disadvantage of earlier entropy methods, which based on counting the frequency of all observations, AttEn was presented by analyzing the frequency distribution of the intervals between the critical observations in a time series [53]. In this method, first local minimum and maximum are computed and then create sets of intervals between these minimums and maximums. Then, the probability of each element appearing in the set based on the number of appearances is calculated by applying Shannon entropy:

$$\text{AttEn}(f)= -\sum_{l}f \text{ln}({f}_{l})$$

(24)

Poincare plot

To assess the qualitative characteristics of biological signal patterns, the phase space technique can be used. Several methods have been presented thus far, and one of the most commonly used methods is the Poincare plot. A Poincare plot is a nonlinear method in analyzing time series and represents the geometrical pattern of a chaotic system’s dynamics. In the biomedical signal evaluation and feature extraction, a Poincare plot could help understand the correlation of data points [54,55,56]; for example, in ECG signal analysis, a Poincare plot represents the dynamics of Heart Rate Variability (HRV) [57]. Visualizing one-dimensional biomedical signals and utilizing image processing techniques are crucial in medical diagnosis and treatment planning. Geographical feature analysis, which was implemented in several studies, proposed to extract meaningful features from Poincare and phase-space followed by artificial intelligence and machine learning tools to analyze the intrinsic behavior of diseases, such as depression, recognition of seizure and alcoholism disorders [8, 58, 59].

The time lag should be specified beforehand to examine the Poincare plot of the time series. Therefore, serial dependence of time series could be examined via predictions from previous observations. The lag is generally set to 1 in a typical Poincare plot, so the signal is plotted vs. its lag delay. As depicted in Fig. 3, the x-axis is the time series (here it is one epoch), and the y-axis is the lagged time series. Five different features are extracted from the plot as follows: (1) SD1: the standard deviation of the points calculated along the direction perpendicular to the line 1; (2) SD2: the standard deviation of the points along the line 2; (3) the rate of SD1/SD2; (4) the rate of SD2/SD1; and (5) the area of the ellipse.

Fig. 3

Poincare plot’s characteristics of a simple EEG signal

Classification

Machine learning algorithms are generally used to make predictions and analyze the data set [59]. This study used several methods to properly examine data set and obtained features. In the following, a short description of methods is given.

K-nearest neighbor

K-nearest neighbor (KNN) classifier makes prediction based on the distance of test data set with training data. Based on predefined values for k, it measures the new sample instance with training instances around it, and using majority voting, it assigns a label to the test instance.

Support vector machine

SVM (Support Vector Machine) operates by identifying the optimal hyperplane. Objective of SVM classifier is to locate the maximum margin hyperplane which exhibits the most significant distance between the support vectors, which are the closest data points in the space.

Bagged tree

The bagging algorithm gathers the outputs of the base classifiers, which are trained on instances and combines them by voting for the labels to make predictions.

		Actual Labels
		AD	Control	MCI
Predicted Labels	AD	A	B	C
	Control	D	E	F
	MCI	G	H	I
Measures	FN	B + C	D + F	G + H
	TN	E + F + H + I	A + C + G + I	A + B + D + E
	FP	D + G	B + H	C + F

Performance metrics

To evaluate the original data set, the physician’s point of view about the diagnosis was considered standard. To examine the performance of classifiers, several measures were considered. Since there are three classes, the confusion matrix can be defined. The sensitivity, specificity, and accuracy are mainly used metrics that can provide information about the outcomes of machine learning algorithms. These measures are defined as follows:

$$\text{Accuracy}= \frac{\text{True Positive}+\text{True Negative} }{\text{All possibilities}}$$

(25)

$$\text{Sensitivity}= \frac{\text{True Positive} }{\text{True Positive}+\text{False Negative}}$$

(26)

$$\text{Specificity} = \frac{\text{True Negative} }{\text{True Negative}+\text{False Positive}}$$

(27)

Experiments and results

Parameters

To better examine the data set and avoid overfitting, in this study, K-fold cross validation was considered. The number of folds was set to 5. In addition, the test-train ratio was selected as 0.3, and none of the subjects in the train set were not used for testing. after training, the model was tested using an unused test set. For the SVM classifier, the kernel function was chosen as Cubic and Quadric SVM with box constraint level set to 1, and kernel scale mode was selected as “auto”. Number of neighbors was chosen as 1 and 3 for KNN. The parameters of Bagged Trees were adjusted as follows: the maximum number of splits was set to 489, and the number of learners was set to 30. Furthermore, for entropy methods, phase space dimension and tolerance rate were chosen as 2 and 0.25 times the standard deviation of signal, respectively. C in DispEn is set to 6. In addition, the time lag for both the Poincare and Entropy approaches set to 1.

Results

Since two different nonlinear tools (Entropy and Poincare) were used in this study, three different experiments were considered to have a better examination of the features obtained. Achieved features by Entropy and Poincare methods were analyzed separately. For each of these experiments, the related method was employed, and features were given to machine learning classifiers. In the next experiment, all features were examined by implementing both Poincare and Entropy approaches. As there are 14 epochs and 19 channels for each patient, the feature matrix for the Poincare (5 features) and Entropy (10 features) methods are 490 × 95 and 490 × 190, respectively. In addition, for the last experiment, total of 15 feature extraction methods were implemented, which generated a feature matrix with a size of 490 × 285. Moreover, since the results of machine learning algorithms depend on the initial conditions and parameters, each algorithm was run 5 times, and the mean of all experiments was considered as the final result.

An example of the Poincare plot for one epoch of EEG data is given in Fig. 4. In this example, electrodes F3–C3 and P3–O1 are depicted for one sample of each group. The x-axis is the time series, while the y-axis is one lagged of that series. As it is obviously seen, there is a geometrical difference between groups. Therefore, in the case of statistical properties, distinguishing between groups would also be straightforward.

Fig. 4

From left to right: Control, AD and MCI for A F3–C3 and B P3–O1 channels

Table 3 shows the evaluation of different feature sets and classifiers. Results of both training and test sets are given. To analyze the effectiveness of features, three different feature sets were constructed. As indicated by the Poincaré plot, the statistical features derived from this plot play a crucial role, achieving an accuracy of 91.9% in classifying the three groups in the test set. For entropy features, SVM and KNN classifiers performed better than the Poincare method. However, if all features are taken into account, a better performance was obtained, which is 97.8% in accuracy, using the SVM classifier with a cubic kernel function.

Table 3 Classification accuracy of the Control, MCI, and AD groups

In addition, since most studies aimed to distinguish between two groups, classification between AD vs. Control, AD vs. MCI, and Control vs. MCI groups was also performed. It was assumed that distinguishing between AD and Healthy individuals would be straightforward, owing to distinct differences between characteristics of EEG signals. As given in Table 4, machine learning algorithms achieved excellent results in distinguishing between groups in which, by considering all features, 98.7% accuracy was obtained using the KNN classifier.

Table 4 Classification accuracy of the AD and Control groups

On the other hand, classification between Control and MCI was more challenging than in previous experiment. Results of the classification of experiments are given in Tables 5 and 6, wherein the best situation, the accuracy is 97.2% and 98.2% for Control vs. MCI and AD vs. MCI, respectively.

Table 5 Classification accuracy of Control and MCI groups

Table 6 Classification accuracy of the AD and MCI groups

Since the SVM cubic classifier achieved successful results, the sensitivity and specificity metrics for test sets for the SVM cubic classifier are given in Table 7. In the classification of 3 groups, in case all features were considered, sensitivity and specificity were 98.6% and 98.2%, respectively, which are more significant than using each method separately.

Table 7 Sensitivity and Specificity metrics for test set in SVM classifier with Cubic kernel function

Discussion

The proposed computer-based decision support system based on Entropy and Poincare features can discriminate all groups with high accuracy. Based on the results obtained in the previous section, entropy features proved particularly powerful, although the Poincaré method also yielded acceptable results. However, by considering all features, more reliable systems with better performance were designed. Our strategy to detect all groups was successful, and an accuracy of 97.8% was achieved by the SVM classifier. This surpasses the 96.5% accuracy achieved in our previous study, which required more complex strategies, such as preprocessing and discrete wavelet transform (DWT) [14]. In addition, 98.6% and 98.2% accuracy, respectively, were obtained for the test set. According to the classifier evaluation, although the KNN and SVM results are similar, the SVM classifier with the cubic kernel function performed slightly better than the other classifiers. Since many related studies have been published in this field, we aimed to compare the obtained results with those of other studies in which nonlinear methods were used.

As given in Table 8 and discussed in Sect. “Related works”, various nonlinear methods with different parameters have been considered in this study. While many studies classify between two groups (e.g., AD and MCI or AD and Control), our method efficiently handles multiclass classification. For a nonlinear dynamical system, the duration of an event is a significant issue and should not be chosen too long or short. Most of the studies consider shorter epoch lengths, which contributes to more computations. For the classification of all groups in literature, based on permutation entropy, Şeker et al. [28] suggested 100% in F1 score, but for better comparison, additional evaluation metrics are needed, such as sensitivity or accuracy. In addition, a limited length of epochs was considered, which increased calculation costs. Among the remaining methods, our proposed method achieved the highest accuracy rate.

Table 8 Comparison of the results of the studies in the literature and the proposed methodology

In the classification between AD and MCI patients, our proposed method achieved 98.2% accuracy when using the SVM classifier in case all features were considered. In addition, features obtained by Poincare and Entropy achieved 95.5 and 96.5, respectively, highlighting the importance of features. Amezquita-Sanchez et al. [29] achieved 91% using the dispersion entropy index, while the length of the records is shorter (4 min).

In the case of AD and Control classification, the proposed method acquires 98.7% accuracy while considering all features with the SVM classifier. The proposed model outperforms others, while [29] and [35] achieved approximately 97% and 90% accuracy, respectively. The researchers in [39] achieved an accuracy of 94.72% in distinguishing between AD and Control groups using the SVD feature and kNN classifier. In addition, the application of Auto Mutual Information and Approximate Entropy for classifying AD and Control groups, as proposed by [32], resulted in an accuracy of 91.74%.

Finally, in the case of MCI and Control groups, the proposed method obtained 97.2% accuracy by Entropy features with SMV classifier. Using an auto-regressive model and permutation entropy (PE), Siuly et al. [37] achieved slightly better results in this case. Despite the simplicity method presented by [40] which is using a single entropy measure, the method’s accuracy was 83% which is notably lower than this study, suggesting that this approach may lack robustness and precision in differentiating between healthy and AD individuals. Authors in [41] achieved high diagnostic performance with an accuracy of 93.53%, sensitivity of 98.74% and specificity of 98.25% indicating its robustness in pattern recognition and potential to reduce misdiagnosis. Nevertheless, the computational complexity and reliance on high-quality EEG data may constrain its real-time applicability and generalizability across diverse populations.

Finally, it is essential to note that most EEG signal processing approaches involve filtering to isolate desired frequencies and remove noise. However, this study applied the proposed methodology to raw data without any preprocessing steps.

Conclusions

Alzheimer disease is the most common neurodegenerative disorder in the world. With no specific cure available, early detection is vital for mitigating disease progression through timely intervention. Since the diagnosis and early detection of these diseases are challenging, the proposed computer-assisted method can aid in analyzing the progression of these disorders. This paper evaluated the effectiveness of nonlinear processes in feature extraction from electroencephalography (EEG) records of individuals with AD, MCI, and healthy controls. Two nonlinear methods (Entropy and Poincare) were implemented on the EEG records of AD, MCI, and healthy individuals. The features extracted were then analyzed using various machine learning algorithms to distinguish between the three groups. For the 3-class classification, an accuracy of 97.6% was achieved, while the sensitivity and specificity rates were 98.6% and 98.2%, respectively.

Based on the results obtained, all three groups achieved an acceptable classification rate. When examining the Poincare plot, it was observed that the pattern of each group was different from that of other groups, and based on the statistical analysis of extracted features from the Poincare method, successful results were achieved. On the other hand, the performance of the entropy-based method was better than the Poincare method. The proposed methodology offers a promising alternative to the more expensive and time-consuming MR imaging techniques currently in use. The high rates of accuracy, sensitivity, and specificity achieved indicate the potential of these combined nonlinear methods in facilitating the early detection and diagnosis of AD and MCI.

Although diagnosing Alzheimer’s using MRI image processing approaches is more effective and has a higher accuracy rate, the proposed method makes diagnosis more effective and cheaper with an acceptable high accuracy rate. However, to generalize the reliability of the proposed approach, it is necessary to apply the method to a larger experimental data set. Hence, further investigation should incorporate the application of the method on a high number of objects to validate its robustness. In addition, upon reviewing previous studies, it becomes apparent that decision support systems have employed a limited array of Entropy methods. Future inquiries endeavor to enhance the efficacy of the proposed method by judiciously selecting appropriate entropy methods through the application of feature selection techniques.