Our main goal is to examine the classification capabilities of the proposed BWHPat. To this end, we introduced a new EEG classification model incorporating a hybrid and multileveled feature extraction method. This method integrates TQWT (Selesnick 2011), statistical features, and the newly proposed BWHPat. During the feature selection phase, we employed INCA (Tuncer et al. 2020a), while kNN (Peterson 2009) was responsible for classifying the selected features for each channel. Using the classification outcomes from these channels, we formulated a semantic cortex map based on the achieved classification performance and a novel intersection model.

The visual representation of our proposed model can be seen in Fig. 3.

Schematic diagram of the proposed model. ** w: Wavelet bands (these bands, which are wavelet coefficients, have been generated by the TQWT, and they serve as wavelet filters). f: Individual feature vector

It can be noted from Fig. 3 that, the proposed feature engineering model contains four phases, and these phases are (i) feature extraction, (ii) feature selection, (iii) classification, and (iv) cortex map creation.

We generated features using both a statistical feature generator and BWHPat-based feature extractor, resulting in 11 inputs (comprising the raw EEG signal and 10 wavelet bands). The proposed hybrid feature extractor generates 270 features from each input, which includes 256 features from the proposed BWHPat and an additional 14 features extracted by the statistical feature generator. Consequently, 11 individual feature vectors (\(f\)) are generated and concatenated, resulting in feature vector with a length of 2970 (equal to 270 × 11). Subsequently, the INCA feature selector is used to select the most informative features from the generated 2970 features. Finally, the kNN classifier is employed to generate classifier-specific outcomes, with kNN providing channel-specific results. Information fusion techniques are then applied to obtain the optimal result.

To clarify the proposed model better, we have given more details about its phases below. Moreover, we have explained this model step-by-step.

The initial phase of our proposed model centers on feature extraction. We employed TQWT to derive wavelet bands in this phase, thereby establishing a multileveled feature extraction function (Selesnick 2011). We integrated two feature extraction functions: (i) the introduced BWHPat and (ii) a statistical feature extractor. While the statistical feature extraction function yields statistical features, our BWHPat is designed to produce textural features. Additionally, by harnessing wavelet bands, we extracted features specific to frequency bands and generated space domain features directly from the raw EEG signal. The steps for the feature extraction function we introduced are as follows:

Step 1: Generate the wavelet bands deploying TQWT.

$$W=\psi (signal,\mathrm,9)$$

(35)

Herein, \(W\) defines the wavelet bands, \(\psi ()\) function represents the TQWT transformation, and we have used 1,3 and 9 values as the q-factor, redundancy, and number of levels, respectively. We have generated 10 (= number of levels + 1) wavelet bands using this wavelet transform.

The TQWT is chosen for frequency band extraction in the EEG pain classification model due to its following advantages. Firstly, wavelets perform well in multiresolution analysis as they can effectively capture both high and low-frequency components in EEG signals (Adeli et al. 2003). This capacity is crucial for comprehending the intricate dynamics of neural signals associated with pain perception. Additionally, wavelets offer exceptional time–frequency localization, enabling them to capture transient changes in EEG signals over time. This feature distinguishes them from traditional Fourier transform-based methods and renders them well-suited for analyzing non-stationary signals commonly encountered in pain-related brain activity. The wavelets can dynamically adjust their resolution and bandwidth based on the signal's characteristics. This adaptability is essential when working with EEG data, where neural signals exhibit considerable variability in terms of frequency and amplitude during different pain-related events. Finally, wavelet-based approaches provide an extensive set of features that can be extracted from EEG signals, facilitating the capture of unique patterns and characteristics associated with pain perception. Due to these advantages, we have chosen wavelets for feature extraction in the BWHPat model.

Step 2: Extract the feature from the raw EEG signal and generate wavelet bands by deploying the proposed BWHPat and statistical feature extractor. The proposed BWHPat extract 256 textural features and the used statistical feature generator extracts 14 statistical features since the statistical feature generator uses 14 statistical moments and these moments are (1) Tsallis Entropy, (2) Shannon Entropy, (3) Renyi Entropy, (4) Sure Entropy, (5) Log Entropy, (6) Energy, (7) Higuchi, (8) Standard Deviation, (9) Variance, (10) Range, (11) Mean, (12) Median, (13) Minimum and (14) Maximum (Tuncer et al. 2020b). Using the generated wavelet bands, raw EEG signal and the used feature extraction functions, we have generated 11 feature vectors, and the length of each feature vector is equal to 270 (= 256 + 14).

$$_=\varpi \left(\beta \left(signal\right),\xi \left(signal\right)\right)$$

(36)

$$_=\varpi \left(\beta \left(_\right),\xi \left(_\right)\right), s\in \,\dots ,10\}$$

(37)

where \(f\) defines the feature vector, \(\beta ()\) is the proposed BWHPat feature extractor and \(\xi ()\) means the statistical feature extraction function.

Step 3: Merge the generated feature vectors to generate the ultimate feature vector.

$$X=\varpi \left(_,_,\dots ,_\right)$$

(38)

Herein, the ultimate feature vector is denoted using \(X,\) and the length of this feature vector is equal to 2970 (= 270 × 11).

Step 4: Repeat Steps 1–3 until the number of the EEG segments and create a feature matrix.

In the feature selection phase, we employed the Iterative neighborhood component analysis (INCA) (Tuncer et al. 2020a). We aimed to extract the most informative features from 2970 features. INCA is an enhanced iteration of the NCA feature selector, integrating additional functionalities for a more refined feature selection process (Goldberger et al. 2004).

It operates through an iterative mechanism, introducing a structured process that includes the generation of loss values. This iterative nature, coupled with the incorporation of a check-balance structure helps to distinguish INCA from NCA. The check-balance structure entails evaluating and balancing the contributions of various features, ensuring a comprehensive assessment of the feature space. This is particularly crucial for the INCA, as it employs a loss value generation function to calculate the loss values for all selected feature vectors. This process is crucial in determining the optimal selected feature vector, as it systematically analyzes the impact and significance of each feature within the dataset. Through this meticulous evaluation, the INCA feature selector identifies and prioritizes the most relevant features, contributing to the overall effectiveness of the feature selection process.

One of the key strengths of INCA is its ability to navigate through the feature space dynamically, adapting to the evolving characteristics of the dataset. The iteration process and the check-balance structure work synergistically to determine the optimal feature vector from the pool of selected feature vectors. This optimization is guided by the minimization of loss values, enhancing the selector's capability to identify the most discriminative features relevant to the classification task.

Step 5: Generate the qualified indexes of the features by deploying the NCA feature selector.

$$index=\mathcal\left(X,y\right)$$

(39)

where \(index\) defines the qualified indices of the features, \(\mathcal(.,.)\) represents the NCA function and \(y\) means the actual output.

Step 6: Select feature vectors iteratively and compute the loss values of these feature vectors by deploying the kNN classifier.

$$ \beginl} } \left( \right) = X\left( \right),x \in \left\ \right\},} \hfill \\ },}, \ldots ,x} \right\},dm \in \},}, \ldots ,NoE\} } \hfill \\ \end $$

(40)

$$loss\left(x-stv+1\right)=kNN\left(sf^,y\right)$$

(41)

Herein, \(sft\) defines the selected feature vector, \(stv\) implies the start value of the iteration, \(fnv\) is the final value of the iteration, \(loss\) means of the misclassification value array and \(NoE\) represents the number of EEG signal.

Step 7: Choose the best feature vector according to the computed loss values.

where \(idx\) defines the index of the minimum misclassification value and \(sfeat\) is the ultimately selected feature vector.

During the classification phase, we utilized the kNN (Peterson 2009) classifier to produce results. The kNN classifier is among the most widely used distance-based classifiers in literature. Furthermore, NCA can be viewed as the feature selection counterpart of kNN. Consequently, we combined INCA and kNN to achieve superior classification performance. The classification steps for the introduced BWHPat are detailed below.

Step 8: Classify the selected feature vector by deploying the kNN classifier and generate the outcome.

$$out=kNN\left(sfeat,y\right)$$

(44)

Herein, \(out\) is the outcome of the used channel.

Step 9: Repeat Steps 1–8 until the number of channels and compute the classification results of each channel.

The mathematical model used to produce interpretable results utilizing the cortex is presented in this phase. In this stage, we obtained channel-wise outcomes to pinpoint the active channels for the pain classification phase. The cortex maps are based on the amplitudes or types (alpha, beta, gamma, or theta) of the EEG signals. In this work, we developed the cortex map utilizing classification results. The step-by-step explanation of cortex map creation is given below.

Step 10: Compute the classification accuracy for all channels using the outcomes generated during the classification phase for all three cases used.

$$ca_^=\varphi \left(ou_,y\right), j\in \left\,\dots ,24\right\}, t\in \left\,3\right\}$$

(45)

Here, \(cac\) means of the classification accuracy and \(\varphi ()\) is the classification accuracy calculation function. We have used three cases. Therefore, we have computed the classification accuracies for all cases.

Step 11: Calculate the median values of the classification accuracies for all three cases used.

$$medval(t)=median\left(ca^\right)$$

(46)

where \(medval\) defines the median value and we have computed three median values in this step.

Step 12: Find the channels with classification accuracies that are higher than median values and store these channels as meaningful channels.

$$find\left(ca^,medval\right)=\left\mc^\left(q\right)=j \wedge q=q+1, ca_^>medval(t) \\ skip, ca_^\le medval(t)\end\right.$$

(47)

where \(find(.,.)\) represents the finding function and \(mc^\) is the meaningful channel of the tth case.

Step 13: Apply intersection operation to meaningful channels to get ultimate/general meaningful channels for pain detection.

$$umc=\bigcap_^mc^$$

(48)

Herein \(umc\) is the ultimate/general meaningful channel for the pain classification using EEG signals.

Using the generated channels, we have presented interpretable results in the field of neuroscience and identified the most meaningful channels for addressing this problem.

Regarding the significance of the median and intersection functions in generating the cortex map, these functions play a crucial role in streamlining the identification of meaningful channels. The median values capture the central tendency of classification accuracies across different cases. Channels surpassing these median values provide a refined selection based on consistent performance.

The intersection operation further refines this selection by identifying channels that consistently exhibit meaningful classification across all three cases. The resulting ultimate/general meaningful channel (\(umc\)) represents a consolidated set of channels that collectively contribute to effective pain detection in EEG signals. This approach enhances the interpretability of the cortex map, offering insights into the specific brain regions affected by pain.

The 13 steps above have been defined in the proposed EEG signal classification model.