Enhancing Alzheimer’s detection from EEG using MVMD and feature optimization algorithm

1.1 Related works

The state-of-the-art studies primarily focus on either binary classification (e.g., NC vs. AD, NC vs. MCI, and AD vs. MCI) or ternary classifications (NC, AD, and MCI) (Puri et al., 2023). Researchers utilized various statistical and spectral features for AD detection, as summarized in Table 1. Various entropy-based methods, including approximate entropy, permutation entropy, detrended fluctuation analysis (Abásolo et al., 2009), and Kolmogorov complexity (Puri et al., 2022), have been introduced in the literature. (Sharma et al., 2019) used a spectral crest factor with Power Spectral Density (PSD) features, achieving 95% accuracy. However, these features are extracted by using full EEG signals without considering their duration. (Nour et al., 2024) employed a combination of 2-Dimensional Convolutional Neural Network (2D-CNN) and deep ensemble learning to identify the AD patient. The method obtained an excellent classification accuracy (CA) of 97.70%. (Aljalal et al., 2024) applied the vibrational mode decomposition (VMD) to detect the MCI using entropy-based features from 11 channels. These features provided the 99.81% CA. However, the 2D-CNN model was overfit due to a small data set. (Oltu et al., 2021) introduced a combination of discrete wavelet transform (DWT) and coherence feature vectors with a Support Vector Machine (SVM) classifier, achieving an accuracy of 96.50%. Similarly, (Stefanou et al., 2025) investigated the fast fourier transform (FFT)-based spectrogram features and classified them using a CNN for two datasets. They obtained a detection accuracy of 79.45% for AD. (Sharma et al., 2019) proposed graph wavelet transforms (GWT), and graph Fourier transform (GFT)-based statistical features with RF and CNN classification models. This method has been validated using the two datasets and is able to obtain a detection rate of 98%. However, this approach is complex, and the CNN model for the given datasets is overfitted.

2.1 MVMD

The multivariate time series, i.e., EEG signals, contains a total of C data channels named y(t) = [y₁(t), y₂(t), ..., y_c(t)]. The MVMD is essentially used to extract the multivariate modulated oscillations v_i(t) = [v₁(t), v₂(t), ..., v_C(t)]. The bandwidth of decomposed modes must be low, and the total modes must be able to restore the original signal. The following procedure was adopted to find the modes (Alsattar et al., 2020).

(a) The v_m(t) can be written in analytic form as Eq. (1),

The bandwidth vi(t) is computed by L2 the norm gradient function of harmonically shifted vi+(t).

(b) The cost function f in MVMD is measured using the following Eq. (2):

Here, the one frequency element vi+(t) was obtained in the mixing of the total vector vi+(t) harmonically.

(c) The multivariate oscillatory BW (modulated) was computed using the spectral range of all channels and formulated the Frobenius norm of the matrix. It is provided as Eq. (3), $\underset{\left(v_{k,c}\right),\left(w_k\right)}{\text{minimize}}=\left(\sum _c\sum _k{\left({\partial }_t\left(v_{+}^{k,c}\left(t\right)e^{-j{w}_{k}t}\right)\right)}_2^2\right)$

Subjected to,

The above-constrained problem can be converted to a non-constrained optimization problem using Lagrange.

L and a quadratic multiplier as follow Eq. (4):

The complex optimization problem can be solved using the different methods of multipliers.

2.2 Reptile search algorithm

(Abualigah et al., 2022) introduced a metaheuristic (MH) approach based on crocodile hunting patterns, termed RSA. This algorithm begins by randomly establishing the i^th candidate optimal feature OFS $x_{i,j}$ randomly as Eq. (5):

Where, $L{B}_j$ and $U{B}_j$ are the min and max values of the jth feature, $ran{d}_{\in U\left(0,1\right)}$ provides a random value of uniform distribution, N is the maximum number of candidates, and M is input features.

The RSA algorithm models crocodile foraging behavior through two distinct phases: exploration and exploitation. The total iteration count is divided into four sequential stages to implement these phases systematically. During the initial two stages (first half), the algorithm simulates crocodile encircling behavior through high and belly walking movements to thoroughly explore the search space. This exploration phase follows the mathematical representation Eq. (6):

where g^th iteration, i^th candidate OFS, and j^th feature $Bes{t}_j\left(g\right)$ represents the optimal solution, while $n_{i,j}$ denotes the hunting operator Eq. (3). The Evolutionary Sense ES(g) Eq. (7) decreases from 2 to −2 throughout the complete iteration cycle, and γ maintains a value of 0.1 to regulate exploration precision. The parameter$R_{i,j}$, calculated according to Eq. (6), narrows the search space and $ran{d}_{\in \left(1,N\right)}$ performs random selection of one candidate OFS from the available options.

where $P_{i,j}$, calculated is the normal difference between the ith candidate and the jth feature value. The average value of the can be computed as Eq. (8):

In this formula, θ regulates exploration sensitivity, and ϵ serves as a minimum threshold value. The mean is calculated as Eq. (9):

The coefficient 2 functions as a scaling factor to generate correlation values within the [0, 2] range, while rand_ (∈ {-1,1}) produces a random integer from the set {−1, 1}.

The exploitation phase models crocodile hunting coordination and collaborative behavior to intensively search the solution space. This stage is mathematically expressed as Eqs. (9 and 10):

The algorithm concludes after completing T iterations, with each candidate OFS set assessed through a predetermined Fitness Function (FF). The optimal feature subset corresponds to the candidate feature set yielding the lowest FF value.

4.1 Environments and implementations

We performed computational testing using a ThinkPad T14s Gen 6 system equipped with Windows 11 Pro 64 ARM operating system, a 3.40 GHz processor, 64 GB of memory, and a Python 3.11 programming environment. For the metaheuristic algorithms (MHA) algorithms, we chose standard configuration values through empirical analysis and established them as: population count of 20 individuals, 100 trial iterations, with each trial repeated ten times incorrectly to reduce the influence of local optimization traps. These algorithm configurations were determined according to their respective research publications to ensure equitable evaluation, and the complete specifications have been presented in Table 3.

4.2 EEG datasets

Here, two datasets are used, and a brief overview of them is provided.

4.2.2 Dataset-B

The dataset contains EEG recordings from three subject groups, including NC, AD, and MCI subjects, which were collected. The detailed specifications of the subjects in this dataset are provided in Table 5. When recording each EEG signal, the eye was closed using a resting position. Further details of the dataset-II are given in (Cejnek et al., 2021). Ethics and consent: this database was approved by the Ethics Committee at Hospital Hradec Kralove (HHK) in Prague, Czech Republic (CUPCR).

Table 5. Details dataset B

Parameters	AD patient	NC subject	MCI patient
No. of subjects	59	102	70
Age (years)	70.5 ± 4.9	72 ± 5.3	67 ± 7.6
Male/Female	29/30	43/59	30/40
Fs	256 Hz	256 Hz	256 Hz
Samples per signal	1000	1000	1000
No. of channels	19	19	19

Two different datasets (Dataset-A: AD and NC, Dataset-B: AD, MCI, and NC) were utilized to validate the proposed method. All the experiments are conducted using Python 3.11 on a machine with a 3.10 GHz Intel i5 processor with 32GB of RAM, HDD: 1 TB SSD M.2 2280 PCIe Gen4 TLC Opal, and running on Windows 11 Home 64 ARM OS. Initially, the artifacts present in the EEG signals, such as muscle artifacts, eye blinks, power line supply frequency, and higher frequencies above 100 Hz, were eliminated using EEGLAB. The notch filter was used to eliminate the 50Hz power frequency. ICA is used to remove the eye blink present in the EEG. Afterward, the recently reported MVMD decomposition method is used due to its superiority over the VMD and empirical mode decomposition (EMD) methods. The MVMD decomposes the EEG signals into nine different IMFs. These IMFs were provided to extract 21 different features, including time, frequency, and complexity-based features.

The complex optimization problem can be solved by using the alternating direction method of multipliers, which breaks the optimization problem into multiple simple sub-problems. For the EEG-based AD identification method, we have calculated nine modes. These modes are called intrinsic mode functions (IMFs). The first three modes for NC, AD, and MCI have been depicted in Fig. 2. The RSA employed these features to find the most significant features. The average fitness function and number of iterations for both datasets have been plotted in Figs. 3(a and b) for datasets A and B. Only three significant features were selected by the RSA: Petrosian fractal dimension (PFD), low-rank Sparse support vector (LRSSV), and Karl’s entropy (KE). The box plots for these features have been depicted in Fig. 3. From Fig. 3, it can be seen that AD and MCI features are very distinct from NC features. The 2-class and 3-class box plots are shown in different subfigures. The selected features, fitness value, computational time, and accuracy obtained from RSA have been presented in Table 6. The RSA has selected only 32 features to obtain the maximum accuracy of 94.95% using KNN. There was a total of 189 (9 IMFs × 21 features) features from each EEG signal extracted. Out of 189, RSA used only 32 features to obtain good accuracy. The computational time required to process is much less compared to others, i.e., 190.38 s for dataset A and 210.16 s for dataset B. The fitness values for dataset A are 0.0510 and 0.1462 for dataset B, respectively.

Close

Fig. 2.

First three IMFs obtained from AD, MCI, and NC EEG signals using the MVMD method.:

Export to PPT

Close

Fig. 3.

Convergence curve of RSA as a feature selector for (a) Dataset-A and (b) Dataset-B.

Export to PPT

Table 6. Performance parameters obtained for datasets A and B.

Parameter	Value	Dataset-A	Dataset-B
Fitness value	Min	0.0099	0.1401
	Max	0.0510	0.1462
	Mean	0.0170	0.1438
	STD	0.0123	0.0023
Computational time	Min	190.38	210.16
	Max	238.94	245.85
	Mean	48.53	35.41
	STD	98.97	154.5
Optimal features	Min	32.00	33.00
	Max	36.00	39.00
	Mean	34.00	36.00
	STD	04.00	06.00
Accuracy	Min	94.05	93.90
	Max	94.95	94.90
	Mean	94.46	94.50
	STD	0.5100	1.000

The accuracies mentioned in Table 6 are computed using KNN. The other ML models, such as SVM, KNN, NB, RF, AB, and NN, have been trained and tested using 10-fold CV and Leave-One-Subject-Out Cross-Validation (LOSO-CV). methods. The confusion matrix notations for three-class (dataset-A) and two-class (dataset-B) have been presented in Tables 7 and 8, respectively.

Table 7. Three-class (AD vs. MCI vs. NC) confusion matrix.

Actual class	AD	NC	MCI
AD	True AD (TA)	False AD 2 (FA-2)	False AD 1 (FA-1)
NC	False NC (FC-1)	True NC (TC)	False NC (FC-2)
MCI	False MCI (FM-1)	False MCI (FM-2)	True MCI (TM)

Table 8. Conversion table of three-class to two-class confusion matrix (a) NC vs. (AD+MCI), (b) AD vs. MCI, and (c) AD vs. NC.

Actual class	AD	NC
AD	TA	FA-2
NC	FC-1	TC

The classification accuracies for MVMD and RSA for datasets A and B using 10-fold and LOSO CV have been presented in Table 8. The maximum classification rate of 97.50% is obtained from SVM for dataset A. The SVM also performed better for three-class (dataset B) classification, with a rate of 95.90% with a 10-fold CV. The SVM has improved the accuracy by 1%. However, the RSA has reduced the number of features by 80% (32/189). There is a tradeoff between the accuracy and the number of selected features. As the number of features increases, so does the accuracy. The other classifiers, like KNN, also perform better. However, its accuracy is slightly lower than that of the SVM. The performance of all ML models is reduced by 1-2% using the LOSO CV method. However, support vector machine (SVM) performs better in 10-fold and leave-one-subject-out (LOSO) cross validation (CV). The different ML models’ performance with and without RSA has been presented in Table 9. The performance parameters like accuracy, precision (PREC), specificity (SPE), sensitivity (SEN), and F1-score for the SVM with a 10-fold CV have been presented in Table 10. The accuracy bar plots have been depicted in Fig. 4. It is clear from this table that these parameters are also better for SVM. Hence, the use of the RSA helped the SVM model achieve the best classification performance metrics and reduced the computational time by reducing the number of features.

Table 9. Performance parameters obtained for datasets A and B.

Cross validation	Classifiers	Dataset A		Dataset B
		MVMD	MVMD-RSA	MVMD	MVMD-RSA
10-fold	SVM	96.60	97.50	95.30	95.90
	KNN	95.70	94.95	95.20	94.90
	RF	92.23	93.45	92.23	90.87
	AB	93.21	90.25	93.21	92.56
	NB	92.45	92.85	91.45	90.66
	NN	92.51	89.23	90.51	90.33
LOSO	SVM	94.30	93.25	93.30	92.30
	KNN	92.60	91.78	92.77	90.38
	RF	91.22	90.45	90.23	90.24
	AB	91.21	90.25	93.21	92.56
	NB	90.45	92.85	91.64	90.66
	NN	89.51	89.89	90.78	90.45

Table 10. Performance parameters obtained for dataset-A and dataset-B.

Dataset	ACC	SEN	SPE	PREC	MCC	F1-score
Dataset-A	97.50	96.05	96.83	98.15	97.24	98.29
Dataset-B	95.90	95.58	95.48	95.49	95.62	95.53

Close

Fig. 4.

Performance of the different ML Models with and without RSA for dataset-A and dataset-B.

Export to PPT

4.3 Statistical analysis

Table 11 presents the mean and standard deviation (STD) values of features extracted from EEG signals for AD and NC using the analysis of variance (ANOVA) method. It compares different statistical and nonlinear features such as band power, entropy measures, fractal dimensions, and energy-based metrics. For each feature, the mean and variability are shown for both AD and control groups, along with the corresponding p-values from statistical tests. Very small p-values indicate that most features exhibit significant differences between AD and Normal subjects, showing their strong discriminative ability for AD. These results confirm the significant capabilities of both the MVMD and RSA for the detection of the AD. A statistical evaluation was conducted to determine the significance of differences between the AD and Normal groups across all extracted EEG features. Initially, a one-way Analysis of Variance (ANOVA) test was performed for each feature to assess inter-group variability. To maintain statistical rigor and reduce the likelihood of Type I errors arising from multiple feature comparisons, the Bonferroni correction was applied following the ANOVA test to control the family-wise error rate.

The results revealed that several features, namely Band Power, Root Mean Square, Average Band Power, Relative Power, Log LRSSV, Approximate Entropy, Higuchi’s Fractal Dimension, and Conditional Entropy, exhibited statistically significant differences between the AD and Normal groups (p < 0.05 after Bonferroni adjustment). These features indicate strong discriminative potential for distinguishing pathological EEG activity associated with AD. Furthermore, paired t-tests were performed to validate the statistical significance of performance improvements between classifiers. The tests confirmed that the proposed model achieved significantly better classification accuracy than baseline methods (p < 0.05), reinforcing the robustness and reproducibility of the approach.

4.4 Comparison with existing methods

The comparative analysis with the respective previous studies that have used the same AD EEG datasets has been listed in Table 12. Moreover, the proposed method has been compared with the state-of-the-art methods that have utilized different datasets and have been presented in Table 13.

(Abasolo et al., 2006) and his research team suggested various time-domain entropies such as spectral entropy (SpecEn), shannon entropy (ShEn), quadratic sample entropy (QSE), multiscale entropy (MSEn), and fuzzy entropy (FuzzyEn). However, these time-domain-based features didn’t capture the frequency domain information that can be captured by the various IMFs generated from the MVMD decomposition methods. The table below compares our model with the state of the art based on performance and the number of classes of different datasets. This also includes the features used, the classifiers considered, and the respective accuracy reported by each one. Most of the existing methods rely on handcrafted features, while a few studies use automated features or both. A wide range of classification techniques exists, from SVM and ANN to more complex architectures such as convolutional neural networks (CNN) and ResNet. There are a variety of methods based on different approaches of extraction and classification, with methods based on handcrafted features reaching up to 95% accuracy in cases such as for (Song et al., 2022) method, which employs three pathways for encoding. Automated approaches, such as those by Fouad and Labib (2023), achieve similarly high performance with accuracies hovering around 98%. It combines handcrafted and automated features during classification, yielding promising accuracy with a high of 97.87% optCascadeNet classifier and proving its efficacy in comparison to previously established ones. These models and variations show the advancements made in feature extraction and classification methods for boosting performance on a range of datasets. Moreover, all the previous methods use all the features; they didn’t employ the channel or feature reduction methods before computing the performance of various ML models. Therefore, the proposed approach uses the MVMD with RSA and ML models that overcome the previous issues. This method improved the performance by 3% in two-class classification and 5% in 3-class classification (dataset B).