New chaos-integrated improved grey wolf optimization based models for automatic detection of depression in online social media and networks

Improved grey wolf optimizer

In the standard GWO; the α, β, and δ wolves with the best positions direct the remaining ω wolves to promised areas in the search space, and the decrease in diversity of population may cause the GWO to be stuck at the local optimum. To overcome these problems, a new search strategy is associated with the update and select step in the proposed I-GWO. I-GWO includes initialization, movement, and selection and update phases.

Initializing stage: In this stage, random N wolves are created in the search space, as shown in Eq. (8) (Nadimi-Shahraki, Taghian & Mirjalili, 2021). (8)${\displaystyle X_{ij}=l_j+ran{d}_j\left[0,1\right]\times \left(u_j-l_j\right),i\in \left[1,N\right],j\in \left[1,M\right]}$

M represents the size of the problem, l_j represents the lower limit that the j th decision variable can take, and u_j represents the upper limit. rand_j generates a random number between 0 and 1. The fitness value of $X_i\left(t\right)$, which represents the position of the ith wolf in the tth iteration, is evaluated according to the fitness function.

Movement stage: In addition to the group hunting strategy, a dimensional learning-based hunting (DLH) strategy was added for individual hunting at this stage. In the DLH stage, each wolf is learned by neighboring wolves as another candidate for the newly available position of $X_i\left(t\right)$ (Nadimi-Shahraki, Taghian & Mirjalili, 2021).

Canonical GWO search strategy: After determining the α, β, and δ wolves with the best fitness values in the population, the linear decreasing coefficient a and the coefficients A and C are computed by Eq. (3)–(5). As shown in Eqs. (5) and (6); X_α, X_β, and X_δ are used to find the surrounding prey. Finally, Eq. (8) is used to calculate the new position of $X_i\left(t\right)$.

DLH search strategy: In the GWO, location updates are made based on the three lead wolves in the population. This causes the algorithm to converge slowly and reduces the diversity in the population. To overcome these weaknesses of the algorithm, the proposed DLH search strategy considers other wolves in the population when updating the location. The position of the wolf $X_i\left(t\right)$ in the DLH search strategy is calculated using Eq. (11). When updating the location, a randomly selected wolf from the population and different neighbors are used. In this strategy, in addition to $X_{i-GWO}\left(t+1\right)$ for the wolf $X_i\left(t\right)$, another candidate solution, $X_{i-DLH}\left(t+1\right)$ is produced. First, the value of $R_i\left(t\right)$, which is the Euclidean distance between the candidate solution $X_i\left(t\right)$ and $X_{i-GWO}\left(t+1\right)$, is calculated using Eq. (9) (Nadimi-Shahraki, Taghian & Mirjalili, 2021). (9)${\displaystyle R_i\left(t\right)=∥X_i\left(t\right)-X_{i-GWO}\left(t+1\right)∥}$

Then, the neighbors of $X_i\left(t\right)$ denoted by $N_i\left(t\right)$ are found using Eq. (10) depending on the radius of $R_i\left(t\right)$. (10)${\displaystyle N_i\left(t\right)=\left\{X_j\left(t\right)|D_i\left(X_i\left(t\right),X_j\left(t\right)\right)\le R_i\left(t\right),X_j\left(t\right)\in Pop\right\}}$

Here, D_i represents the distance between X_i and X_j. After the neighborhood of $X_i\left(t\right)$ is created, and multineighbor learning is calculated using Eq. (11). The dth dimension of $X_{i-DLH}\left(t+1\right)$ is calculated using a randomly selected neighbor $X_{n,d}\left(t\right)$ from $N_i\left(t\right)$ and randomly selected $X_{r,d}\left(t\right)$ from the population. (11)${\displaystyle X_{i-DLH,d}\left(t+1\right)=X_{i,d}\left(t\right)+rand\times \left(X_{n,d}\left(t\right)-X_{r,d}\left(t\right)\right)}$

Selection and update stage: This is the stage where the most suitable individual is determined according to the fitness values of the two candidates, X_i−GWO and X_i−DLH. (12)${\displaystyle X_i\left(t+1\right)=\left\{\begin{array}{cc}{X}_{i-GWO}\left(t+1\right),\hfill & iff\left(X_{i-GWO}\right)<f\left(X_{i-DLH}\right)\hfill \\ X_{i-DLH}\left(t+1\right)\hfill & otherwise\hfill \end{array}\right.}$

After all, these operations, if the fitness value of $X_i\left(t+1\right)$ obtained is better than $X_i\left(t\right)$, the value of $X_i\left(t+1\right)$ is updated as the new position using Eq. (12). Otherwise, $X_i\left(t\right)$ remains unchanged. After all of these processes have been applied for each candidate solution in the population, the number of iterations is increased by one and the process repeats until the termination conditions are met (Nadimi-Shahraki, Taghian & Mirjalili, 2021).

New improved grey wolf optimizer (NI-GWO)

In this study, the NI-GWO algorithm, which is a new version of the I-GWO algorithm proposed by Akyol, Yildirim & Alatas (2023) was used. As seen in Eq. (3) in the I-GWO algorithm, the random number r₁ is used when calculating the A coefficient. To enhance the algorithm performance, a value that linearly decreases from alpha to 0 given in Eq. (13) is used instead of a random number. In this study, 2 was chosen as the constant alpha value and MaxIter represents the maximum iteration number. (13)${\displaystyle r_1=alpha-t\times \left(alpha/MaxIter\right).}$

Circle map

Circle map, one of the one-dimensional chaotic maps, was defined by Zheng (1994). This map, which belongs to the family of dynamical systems on the circle, is calculated as given in Eq. (14). (14)${\displaystyle z_{m+1}=z_m+y_2-\frac{y_1}{2\pi }sin\left(2\pi z_m\right)}$

Here, m is the generated chaotic number and z_m is the m th chaotic number in the range [0,1]. The y₁ and y₂ parameters also take the values of 0.5 and 0.2, respectively (Lucay & Jamett, 2021).

Logistic map

The logistic map, introduced by May (2004), is one of the simplest one-dimensional chaotic maps and is described as shown in Eq. (15) (May, 1976; Lucay & Jamett, 2021). (15)${\displaystyle z_{m+1}=\mu z_m\left(1-z_m\right)}$

Here, the µvalue is taken as 4 (Lucay & Jamett, 2021).

Iterative map

Like the logistic map, Iterative Map was introduced by May. It is an Iterative Chaotic Map with infinite collapse and is expressed as shown in Eq. (16). (16)${\displaystyle z_{m+1}=sin\left(\frac{y\pi }{z_m}\right)}$

where y ∈ (0, 1) is a suitable parameter (May, 1976; Gandomi et al., 2013). The initial value of z₁ is taken as 0.7 for all three chaotic maps.

CNI-GWO1

The initiation step of NI-GWO can affect the success of convergence. Thus, various chaotic systems are used rather than random number sequences in the start step of NI-GWO. Therefore, a chaotically initiated NI-GWO termed chaotic NI-GWO (CNI-GWO1) is proposed in this study. In this way, the global convergence of NI-GWO is tried to be improved and kept away from being trapped in local solutions. Equation (17) is used instead of Eq. (8), which is used to create the initial population in the NI-GWO algorithm. (17)${\displaystyle X_{ij}=l_j+z_{m+1}\times \left(u_j-l_j\right),i\in \left[1,N\right],j\in \left[1,D\right]}$

The variable z_m+1 is calculated using Eqs. (14), (15) and (16). The pseudocode of the initial step is given in Fig. 3 and the flowchart of the CNI-GWO1 algorithm is shown in Fig. 4.

CNI-GWO2

Second, in this proposed method, the randomly generated C₁ value in the range [0, 2] in Eq. (5) in NI-GWO is generated with chaotic maps. The resulting new expression is defined in Eq. (18). (18)${\displaystyle D_{\alpha }=|\left(2\times z_{m+1}\right)-X_{\alpha }-X\left(t\right)|}$

CNI-GWO3

Third, in CNI-GWO3, the randomly generated C₂value used for the hunting phase of the β wolf in Eq. (5) is generated with chaotic maps. The resulting new expression is defined in Eq. (19). (19)${\displaystyle D_{\beta }=|\left(2\times z_{m+1}\right)-X_{\beta }-X\left(t\right)|}$

CNI-GWO4

Finally, in Eq. (5), chaotic maps are used instead of the C₃ value used to improve the hunting skills of the δ wolf. The updated version of the equation is given in Eq. (20). (20)${\displaystyle D_{\delta }=|\left(2\times z_{m+1}\right)-X_{\delta }-X\left(t\right)|}$

The flowchart of CNI-GWO2, CNI-GWO3, and CNI-GWO4 algorithms are shown in Fig. 5.

Preprocessing of the depression dataset

In this study, the dataset created by labeling the data from Reddit (Daru, 2023) as “depressive” or “non-depressive” was used. This dataset consists total of 4,737 data, of which 3,937 are depressed and 900 are “non-depressed”. This dataset is divided into two separate datasets, 80% training and 20% testing. A section from this dataset is shown in Fig. 7.

The dataset used in this study was preprocessed and a document matrix was obtained. The number of words extracted from the dataset because of preprocessing was 1,117. In the document matrix, the rows represent the comments, while the columns correspond to the words in all comments. If the word is mentioned in the comment on the relevant line, it takes the value 1, if not, it takes the value 0. A section of the document matrix is shown in Fig. 8.

Representation type (encoding)

The position vector of gray wolves for the focused depression detection problem is represented as follows: ${\displaystyle X_{N,M}=\left[\begin{array}{cccc}{X}_{1,1}\hfill & X_{1,2}\hfill & \cdots \hfill & X_{1,M}\hfill \\ X_{2,1}\hfill & X_{2,2}\hfill & \cdots \hfill & X_{2,M}\hfill \\ ⋮\hfill & ⋮\hfill & \ddots \hfill & ⋮\hfill \\ X_{N,1}\hfill & X_{N,2}\hfill & \cdots \hfill & X_{N,M}\hfill \end{array}\right]}$

In this encoding type, N is the number of wolves and M is used for representing the number of features extracted from the depression dataset. In other words, M represents the number of words extracted from the dataset, and N represents the number of population.

Fitness function

While calculating the fitness of each individual in the population, the accuracy value obtained from the KNN classifier was used. In addition, a feature selection process is performed so that only the necessary features are included in the model. Thus, a multiobjective approach is used. The fitness function consisting of the combination of these two objectives is calculated as shown in Eq. (21). (21)${\displaystyle fitness=w_1\times AccuracyObtainedfromKNN+w_2\times FeaturesRatio}$

Here, AccuracyObtainedfromKNN gives the accuracy rate obtained from the KNN classifier. FeaturesRatio gives the ratio of the number of features in the model to the total number of extracted features in the dataset. w₁ and w₂ represent the weights and their sum is equal to 1. In this study, the w₁ value was taken as 0.9 and the w₂ value as 0.1. Due to the direct usage of the selected features for classification, the proposed models seem to have explainable capability. While creating the model, it is aimed to include only the necessary features in the model with feature selection. In the fit function, the number of features to be included in the model is kept low with FeaturesRatio. It is known how many features are included in the proposed model and which of these features are. In this way, the model has the characteristics of being explainable, interpretable, and comparable.