54 patients with AGA who were treated in the Medical Cosmetic Center of Tongji Hospital from January 2020 to October 2020 were selected as the research objects, and all agreed to receive treatment in this hospital for a long time. Among them, there were 31 males and 23 females. Besides, they were 18–60 years old, and the average age was 39.15 ± 4.07 years. The criteria for inclusion were defined to include patients who were older than or equaled to 18 years old, and conformed to AGA diagnostic criteria. The criteria for exclusion were defined to include patients who suffered from hair loss caused by resting period, physiological and postpartum hair loss, and other cause, had neuropsychiatric diseases, and were accompanied with other serious systemic diseases. In addition, they were grouped into the control group (n = 27) and the intervention group (n = 27) based on the different ways of psychological intervention. The process was approved by the ethics committee of Tongji Hospital, and all the research objects included in this study signed the informed consent forms.

The optimization mathematical model of meta heuristic algorithm can be expressed as follows. min f ( x ) , s . t . g i ( x ) = 0 , i = 1,2 , L , m ; h j ( x ) ≥ 0 , j = 1,2 , L , n . (1)

In the Eq. 1, x stands for the decision variable, representing the p-dimensional vector, and its calculation method is x = { x 1 , x 2 , ⋯ , x p } T ∈ ℝ p . Besides, f ( x ) means the objective function, g i ( x ) indicates the equality constraint function, h j ( x ) represents the inequality constraint function, and s . t . expresses the abbreviation of “subject to,” which means “restricted to.”

The Filter algorithm in feature selection has a fast calculation speed, and the Wrapper algorithm has a higher calculation accuracy (Padfield et al., 2019). In this study, the Filter and Wrapper algorithms were combined to form a new feature selection algorithm, which was named FAW-FS. The two algorithms of analysis of variance (ANOVA) and mutual information were adopted to calculate the data to filter out the feature subset, thereby obtaining the union as the new feature space.

ANOVA (Peng et al., 2020) is a common special statistical hypothesis testing model in data analysis. The total variance (TV), total variance between groups (BGV), and variance within groups (WGV) of ANOVA are expressed as the following equations. TV = ∑ i ∑ j ( Y i j − Y i − ) 2 (2) BGV = ∑ i n i ( Y i − − Y t − ) 2 (3) WGV = ∑ i ∑ j ( Y i j − Y i − ) 2 (4)

In the Eqs 2–4, i represents the group, and i = 1,2 , ⋯ , a ; Y i j means the j-th eigenvalue in the i-th dimension feature; j stands for the subscript of the observation value; Y t − expresses the mean of all eigenvalues; n i represents the total number of the i-th dimensional eigenvalues; Y i − indicates the mean of the i-th dimensional eigenvalues.

The mean square between groups (MSG) and mean square within groups (MSW) of ANOVA can be calculated as follows. MSG = BGV k − 1 = ∑ i n i ( Y i − − Y t − ) 2 k − 1 (5) MSW = WGV N − k = ∑ i ∑ j ( Y i j − Y i − ) 2 N − k (6)

In the Eq. 5 and Eq. 6, k and N stand for the dimension of the feature and the total number of eigenvalues, respectively.

Mutual information (MI) is mainly used to evaluate the joint probability distribution and marginal probability distribution between two variables (Wen et al., 2020). For discrete random variables, MI is defined as the following. I ( X ; Y ) = ∑ y ∈ Y ∑ x ∈ X p ( x , y ) log ( p ( x , y ) p ( x ) p ( y ) ) (7)

In the Eq. 7, p ( x , y ) represents the joint probability distribution function between the two variables X and Y, p ( x ) means the marginal probability distribution of X, and p ( y ) shows the marginal probability distribution of Y.

For continuous random variables, MI can be defined as the following. I ( X ; Y ) = ∫ Y ∫ X p ( x , y ) log ( p ( x , y ) p ( x ) p ( y ) ) d x d y (8)

In the Eq. 8, p ( x , y ) is the joint probability density function between the two variables X and Y, p ( x ) is the marginal probability density function of X, and p ( y ) is the marginal probability density function of Y.

Search strategy is the core of Wrapper’s selection method. In this study, the simulated annealing algorithm was introduced in the optimization process to improve the convergence of the Wrapper method and form a new genetic algorithm (GA). The simulated annealing algorithm can be expressed as follows. p = { 1 , i f e 1 < e 2 e − E ( e 1 − e 2 ) T , i f e 1 > e 2 (9)

In the Eq. 9, T, p, E, e 1 , and e 2 represent the temperature, the substitution probability, the internal energy, the objective function, and the objective function of the substitute object in turn.

Fitness is an important index to evaluate individual survivability in GA (Hasserjian, 2019). For the evaluation function f ( x ) , the fitness (Fit) function is F ( x ) , so the Fit of the individual x can be expressed as F i t = F [ f ( x ) ] . When the largest problem is solved, the Fit can be expressed as shown in the Eq. 10. What’s more, D means the minimum estimate of f ( x ) . F i t = F [ f ( x ) ] = { f ( x ) − D , f ( x ) > D 0 , f ( x ) ≤ D (10)

After introducing the simulated annealing algorithm, GA is improved and optimized. For the optimized GA, the parameters should be set, including the number of iterations of the population, the number of local search iterations, the initial size, the crossover probability, the probability of mutation, and the temperature. Multiple suitable individuals are used as the initial population, and the fitness of individuals in the population is calculated. If the termination condition is satisfied and the output optimal solution satisfies the termination condition, the algorithm ends. For the individuals that do not meet the termination conditions, crossover operation is carried out for each pair of matching individuals in the population according to the specified selection operator, and new populations are generated according to the local search strategy. Then, it is further verified whether the individuals meet the termination conditions and enter the next cycle. The optimized GA flow chart is shown in Figure 1.

During the EEG acquisition process, different types of noise will have a certain impact on EEG. In this study, a band-pass filter is used to filter the data, and the EEG data are removed by the combination of Kalman filter and wavelet transform (Cabrera et al., 2018). The power spectrum entropy in nonlinear features is mainly applied to evaluate the strength of brain activity (Mendez-Balbuena et al., 2018). For the signal X ( w ) , the kilometer density is obtained after processing by the FAW-FS algorithm, and its power spectrum entropy can be expressed in the Eq. 11. H w = − ∑ i = o n p x ( w i ) log 2 [ p x ( w i ) ] (11)

Shannon entropy is employed to quantify EEG, and its calculation method is presented in the Eq. 12. H x = − x ⁡ log 2 ( x ) − ( 1 − x ) log 2 ( 1 − x ) (12)

The correlation dimension is mainly applied to describe the irregularity of EEG, and its calculation method is shown in the Eq. 13. In addition, ln ⁡ C ( r ) stands for the correlation function. C = lim r → 0 ln ⁡ C ( r ) ln ⁡ r (13)

Kolmogorov entropy describes the dynamic characteristics and signal complexity of the signal. The larger the Kolmogorov entropy, the more chaotic the dynamic characteristics, and the more complex the signal (Mutanen et al., 2018). The Kolmogorov calculation can be expressed in the Eq. 14. K = lim T → 0 lim ε → 0 lim N → ∞ 1 N T ∑ n = 0 N − 1 ( K n + 1 − K n ) (14)

C0 complexity is adopted to evaluate the degree of randomness of EEG, which can be calculated in the Eq. 15. The greater the C0 complexity value, the stronger the randomness of the EEG sequence. C 0 = ∑ n = 1 N | X ( n ) − Y ( n ) | 2 ∑ n = 1 N | X ( n ) | 2 (15)

In the above equation, X ( n ) represents the original EEG sequence, and Y ( n ) means the EEG sequence after Fourier transform.

The collected EEG data are used for filtering and electro-oculogram operation through the band-pass filter, Kalman filter, and wavelet transform. Then, the current and nonlinear characteristic EEG data are extracted, and finally, the FAW-FS algorithm is employed to select the EEG features. The flow chart of depression recognition based on meta heuristic algorithm is shown in Figure 2 below.

For each feature vector set output from the feature vector input module, it was first divided into a training set and a test set. Samples of the training set were derived from the public data set, with a sample size of 128. Each training set was divided into 1–5 of the 5 training subsets. Four training subsets out of the five training subsets were used for training in the deep forest each time, and the remaining one training subset was used as the verification set to verify the sub-model of training. The above sub-training process was repeated until every training subset in the whole training process made a verification set. After each verification of the trained sub-model, a set of feature vectors with a size of 12 was eventually obtained.

The data sets published in the public database (http://archive.ics.uci.edu/ml/index.php) were compared with the FAW-FS algorithm established in this study to verify the classification accuracy of the FAW-FS algorithm. The information of the 7 public data sets selected in this study was displayed in Table 1.

Accuracy was employed to evaluate the recognition results of depression EEG signals, and its specific calculation method was shown in the following equation. Accuracy = | X : X ∈ D t ∩ Y − ( X ) = Y ( X ) | | X : X ∈ D t | (16)

In the Eq. 16, D t stood for the test data, X was the test sample, Y ( X ) represented the real classification result of the test sample, and Y _ ( X ) indicated the classification result identified by the classification model.

The patients from both groups were given with paroxetine tablets (20 mg/time.d) for 3 weeks of drug treatment. On the basis of drug treatment, the control group was treated with routine psychological interventions, including sports, interest development, music listening, and social activities. The intervention group underwent the comprehensive psychological nursing intervention on the basis of routine psychological intervention. The content of comprehensive psychological intervention mainly included the following. First, patients were guided to make psychological adjustments with psychological counseling, psychological care, and psychological support, so as to reduce their depression and build confidence in treatment. Second, the medical staff should explain the clinical manifestations, treatment, and prognosis of AGA to patients, thereby establishing a proactive cognitive model. Third, the medical staff needed to help patients establish support from family members and friends.

The conditions of patients from the two groups were scored through the self-rating anxiety scale (SAS), self-rating depression scale (SDS), and Hamilton depression scale (HAMD) before and after treatment, respectively. SAS consists of 20 items in 1 dimension, which is scored from 1 to 4 levels; 50–59 points is considered as mild anxiety, 60–69 points as moderate anxiety, and 70 or above points as severe anxiety (Yue et al., 2020). There are also 20 items in 1 dimension of SDS, which are rated from 1 to 4 levels; 50–59 points is classified as mild depression, 60–69 points as moderate depression, and more than 70 points as severe depressions (Zou et al., 2016). The 1–4 levels were applied in the scoring of HAMD, with a total score of more than 35 points classified as severe depression; a score of 20–34 points indicates mild or moderate depression, and 8–20 points indicates mild depression (Zhao et al., 2019).

The differences of SAS, SDS, and HAMD scores before and after treatment were compared between the two groups. Besides, the changes in the depressive symptoms, treatment compliance, and quality of life of patients from the two groups were observed before and after treatment. The efficacy of depressive symptoms was evaluated by Jang et al. (2019). After treatment, the patient’s HAMD score reduction rate was greater than 75%, which means that the patient was cured; 50% < HAMD score reduction rate ≤75% indicated that the efficacy was markedly effective; 25% < HAMD score reduction rate ≤50% showed effectiveness; HAMD score reduction rate was less than 25%, meaning that the efficacy was ineffective. In addition, the total effect included clinical recovery, marked effect, and effectiveness.

The method of Kraepelien et al. (2019) was referred to assess the compliance to the treatment of depression. Those who strictly followed the doctor’s advice during treatment were complete compliance; those who basically followed the doctor’s advice were basic compliance; those who often did not follow the doctor’s advice or interrupt the treatment were regarded as non-compliance. Total compliance contained complete compliance and basic compliance.

Referring to the method of Teles et al. (2018), the quality of life of patients was evaluated before and after intervention for depression, and GQOLI-74 was adopted to analyze the 4 sub-items of the patient’s body, psychology, society, and substance.

The experimental data were processed by SPSS19.0 statistical software, and the measurement data were expressed as mean ± standard deviation ( x ¯ ± s ). The count data were represented by percentage (%), and the χ² test was used. In addition, p < 0.05 indicated that the difference was statistically substantial.

The classification accuracy of FAW-FS algorithm established in this study was compared with Correlation Attribute Eval (CA), Gain Ratio Attribute Eval (GR), Relief FAttribute Eval (RF), simulated annealing (SA) algorithm, and GA in the feature selection of logistic regression (Figure 3). In different public data sets, the classification accuracy of different algorithms changed in the same trend, while the classification accuracy of the same algorithm in different data sets varied greatly. In 7 different data sets, the classification accuracy of the FAW-FS algorithm was higher substantially than the accuracy of other algorithms, and its classification accuracy was 54.72–98.45%, with the mean classification accuracy of 80.87%.

There was a comparison on the classification accuracy of the 6 algorithms under the classification features of DT (Figure 4). Among the 7 different data sets, all algorithms had the lowest classification accuracy in the PMS data set. The classification accuracy of FAW-FS algorithm rose obviously compared with other algorithms. Moreover, its classification accuracy was in the range of 43.28–98.81%, and the mean classification accuracy was 79.24%.

The classification accuracy of the 6 algorithms was compared under the K-nearest neighbor algorithm (Figure 5). In the 7 different data sets, all algorithms had the highest classification accuracy in the BCW data set. The classification accuracy of FAW-FS algorithm elevated obviously in contrast to the accuracy of other algorithms. Its classification accuracy was distributed in the range of 42.94–99.12%, and the mean classification accuracy was 80.42%.

Figure 6 indicated that the classification accuracy of the 6 algorithms was compared under the features of SVM. In the 7 different data sets, the classification accuracy of the FAW-FS algorithm was higher hugely than that of other algorithms, and its classification accuracy was within 62.33–99.07%, with the mean classification accuracy of 83.07%.

The classification accuracy of the six algorithms was compared under the characteristics of RF, and the results were presented in Figure 7. In the seven different data sets, the classification accuracy of the FAW-FS algorithm was higher greatly than the accuracy of other algorithms, and its classification accuracy was 61.93–99.26%, with the mean classification accuracy of 81.45%.

In this study, a combination of Kalman filter and wavelet transform was used to preprocess EEG to remove electro-oculogram noise before the FAW-FS algorithm was adopted to extract and select EEG features, and the results were shown in Figure 8. Before electro-oculogram noise was removed, EEG had more electro-oculogram artifacts. After removing electro-oculogram noise, a pure EEG was obtained.

During the processing of the EEG raw data (Figure 9A), the EEG data were initially processed with a down-sampling method of 1,000–250 Hz, so that the original signal was separated from the noise and the original data was enhanced (Figure 9B). A band-pass filter was applied to filter the data to remove the EEG artifacts in the EEG data (Figure 9C). Finally, the Kalman filter and wavelet transform were combined to remove the electro-oculogram artifacts in the EEG data, and the pure EEG data were obtained after extraction by the FAW-FS algorithm established in this study (Figure 9D).

The accuracy of EEG feature selection of the FAW-FS algorithm under different data sets was analyzed under the resting state and five audio stimuli, as shown in Figure 10. It was found that among the five classification algorithms, the LR algorithm had the highest feature selection accuracy under the five audio types, and its mean feature selection accuracy was 82.94%, followed by KNN (73.72%) and RF (70.09%). The mean accuracy of feature selection for DT and SVM was 65.77 and 55.49%, respectively. The mean accuracy of feature selection of SVM was the lowest among the 5 algorithms. What’s more, 5 different algorithms all had the highest mean accuracy of feature selection on audio stimulus 1 in the 6 data sets of resting state EEG and audio stimulation EEG, and the lowest accuracy was on audio stimulus 3.

There was an analysis on the EEG accuracy of the FAW-FS algorithm under different data sets under the resting state and the five audio stimuli (Figure 11). It revealed that among the five classification algorithms, the RF algorithm had the highest classification accuracy under the five audio types, with a mean accuracy of 73.01%, followed by KNN (58.94%) and LR (52.76%). In addition, the mean accuracy of DT and SVM were 40.18 and 42.55% in turn. The mean accuracy of feature selection of DT was the lowest among the five algorithms. In the 6 data sets of resting state EEG and audio stimulation EEG, 5 different algorithms had the highest average accuracy on audio stimulation 1, and there was the lowest mean accuracy on audio stimulation 4.

The basic data of patients from the two groups were compared and analyzed, and the results were displayed in Table 2. There was no statistical difference in age, gender ratio, body mass index (BMI), weight, height, and course of disease between the two groups (p > 0.05).

The changes of EEG before and after psychological intervention in AGA patients with depression were analyzed (Figure 12). Before the intervention, the EEG power spectrum amplitude of AGA patients showed a smoothly downward trend with the continuous growth of the normalized frequency. The EEG power spectrum amplitude was distributed in the range of −0.5026–59.8248 dB, and the EEG mean power spectrum amplitude was 17.883 ± 8.190 dB. After the intervention, the EEG power spectrum amplitude of AGA patients rose first and then decreased with the continuous increase of the normalized frequency. The EEG power spectrum amplitude was distributed in the range of 21.0315–63.9881 dB, and the EEG mean power spectrum amplitude was 34.854 ± 3.465 dB.

The scores of SDS, SAS, and HAMD scales before and after psychological intervention between the two groups were compared (Figure 13). There was no marked difference in SDS, SAS, and HAMD scale scores between the two groups of patients before the intervention (p > 0.05). After the intervention, the SDS and SAS scores of patients from the two groups were lower steeply than those before the treatment, and the difference was statistically obvious (p < 0.05). After the intervention, the HAMD scale scores of patients from the two groups were dramatically different from those before the treatment (p < 0.01). The SDS, SAS, and HAMD scores of the intervention group reduced sharply in contrast to the scores of the control group (p < 0.05).

There was a comparison on the quality of life scores of patients from the control group and the intervention group before and after psychological intervention (Figure 14). Before the intervention, there was no significant difference in the physical function, psychological function, social function, and substance function between the two groups of patients (p > 0.05). After the intervention, the physical function, mental function, social function, and substance function of patients from the two groups increased hugely compared with before the intervention, with a statistically huge difference (p < 0.05). The scores of physical function, mental function, social function, and substance function of the intervention group were higher markedly than the scores of the control group (p < 0.05).

Figure 15 showed the statistical analysis on the improvement of the efficacy of depression after treatment in patients from the two groups. In the control group, there were 4 cured cases (14.81%), 5 cases (18.52%) with marked effect, 7 effective cases (25.93%), and 11 cases (40.74%) with no effect after the intervention, and the total number of effective cases was 16 (59.26%). In the intervention group, 12 cases (44.44%) were cured, 8 cases (29.63%) were markedly effective, 5 cases (18.52%) were effective, and 2 cases (7.41%) were ineffective, so the total number of effective cases was 25 (92.59%). The proportion of cured, markedly effective, and total effective patients in the intervention group was higher greatly than the proportion of the control group (p < 0.05). After the intervention, there were 4 cases (14.81%) with complete compliance, 7 cases (25.93%) with basic compliance, and 16 cases (59.26%) with no compliance in the control group, and the total number of cases with compliance was 11 (40.74%). In the intervention group, 15 patients (55.56%), 9 patients (33.33%), and 3 patients (11.112%) were completely compliant, basically compliant, and non-compliant, so there were 24 cases with compliance (88.89%). The proportion of patients with complete compliance and total compliance in the intervention group elevated substantially compared with the control group, and there was a significant difference between the two (p < 0.01).