3.1 Recommendation Model Building based on L2R2SN Algorithm

Traditional recommendation algorithms analyze the rating matrix of users and items to generate recommendations. This approach, which only considers the binary relationship between users and items, results in the recommended content relying mainly on machines, which affects the accuracy of the recommendation results. Sorting learning is a machine learning technique that predicts the order relationship between samples by sorting them. It is used primarily in the information retrieval field. Adding list-level sorting learning to recommendation algorithms can calculate the users' item preferences, prevent content recommendations that rely heavily on machines, and improve the rationality and accuracy of the recommendation results. Assuming there are $m$ users who have rated $n$ projects excessively, the project set is represented by $I=\left\{i1,i2,\ldots ,in\right\}$. The user set is represented by $U=\left\{u1,u2,\ldots ,um\right\}$, and the user's rating on the project is represented by $V$, where $rui$ represents any rating value in $V$. Fig. 1 shows the model for ranking learning.

Fig. 1. Schematic diagram of the sorting learning model.

The Plackett-Luce model is a classical list-level sorting learning (LLSL) algorithm that can directly optimize the sorting order of a list of items, describe the permutation probability distribution, and directly obtain a recommendation list that satisfies the user’s preferences by optimizing the evaluation metric or constructing a loss function. The Plackett-Luce model can capture the degree of user preference for different projects, and consider the relative relationship between projects and the overall ranking results. The model has good interpretability and robustness, and is suitable for innovative hanging recommendation and ranking tasks. In the Plackett-Luce model, for any permutation, the sum of the probabilities of one full permutation of all items selected is equal to one, and the probability of the permutation is expressed as Eq. (1).

where$\pi u$ denotes an arrangement of items; $wi$ denotes the probability of an item being selected; $\pi ui$ denotes the arrangement position of an item; $P(\pi u)$ denotes the probability of selecting $\pi u$. On the other hand, the list-level sorting-based learning algorithm does not model and incorporate the interactions in human society into the algorithm, so the recommendation results are inaccurate, and the time efficiency of the algorithm is constrained. The L$^{2}$R$^{2}$SN algorithm is a recommendation model based on LLSL that utilizes personalized networks to determine the relationship traits of users and friends from the interaction relationships, along with the resemblance traits of items. The acquired characteristics are then added to the fundamentals of the LLSL recommendation model. The L$^{2}$R$^{2}$SN algorithm is trained iteratively by constructing an efficient objective loss function and using a gradient descent strategy. In the L$^{2}$R$^{2}$SN algorithm, only items with the highest probability of being selected are chosen, as expressed in Eq. (2).

where $\phi (.)$ is chosen as the $\exp (.)$ exponential function. The social characteristics of users on social networks and the social information between items are considered in the L$^{2}$R$^{2}$SN algorithm to model the social relationships of users in everyday life. Social characteristics on social networks encompass personal profiles, posts, comments, likes, private messages, shared links, following status, and frequency of social activities. These characteristics can provide insight into an individual's personality, interests, and level of activity and interaction within the online world. Objective evaluation of these traits can be valuable when analyzing social behavior in cyberspace. Social information in course recommendations typically refers to users' behavior and interactions on social media platforms. This includes their social relationships with other users, interactions with courses, and the communication impact of such social information in social networks. The data can be used to improve the personalized level of course recommendations and enhance the overall appeal of the results. The social relationships among users were simulated using the user set $F(u)$ that comprises individuals within the same community as well as WeChat friends and other acquaintances of the target user $u$ within the social network. The user relationship is set when selecting the user trust set, and the difference between the ratings of two items is limited to less than 1 to represent the similarity between items. The user trust set and the item similarity set are expressed as Eq. (3).

where $v$ represents the user's rating of a project, $rvi$ and $rui$ denotes the trusting user’s rating of item $i$ and the target user’s rating of item $i$, respectively. Fig. 2 shows the user-item relationship scores.

Fig. 2. Example of a User Project Relationship Rating.

The closer the predicted value is to the genuine value, the smaller the loss function value. Eq. (4) depicts the target loss function of the L$^{2}$R$^{2}$SN algorithm.

(4)

where $\xi $ represents the loss function; $g(.)$ denotes the $Sig\mathrm{mod}$ logic function, which can limit the range of predicted values. $\lambda $ is a regularization factor; $\alpha $ and $\beta $ represent parameters, and $\lambda (\left\| U\right\| _{F}^{2}+\left\| V\right\| _{F}^{2})$ can avoid overfitting. In summary, the L2R2SN algorithm effectively addresses the cold start issue by merging the user and social relationship traits. By analyzing the user characteristics, it predicts courses that may interest users and provides preliminary personalized suggestions. In addition, it uses social network data to bridge the gap in interactive data between the users and courses, solving the data sparsity problem to some extent.

3.2 TR-based DR Models for CE Courses

Recommendation engines (DR) analyze the user’s previous behavior to determine their preferences and forecast their likelihood of being interested in the material. The aim of DR is to provide personalized services to users by predicting what they are likely to be interested in. For example, Fig. 3 shows a generic process for personalized recommendation systems.

Fig. 3. General Model for Personalized Recommendation Systems.

Fig. 4. User Trust Mobile Network.

TR is considered to exist between two people when one person's behavior can influence another’s. In a trustworthy mobile network, users act as nodes, and trust is unidirectional. Fig. 4 shows a trustworthy mobile network. The nodes represent users, and the data on the node connections represent trust values.

Assuming a user set $U=\left\{u1,u2,\ldots ,uN\right\}$, project set $I=\left\{i1,i2,\ldots ,iM\right\}$, and user $u$'s project rating $i$ is used to represent $Ru,i$. The task of this study is to predict $Ru,i$. For any two items, the introduction of rules is considered in the calculation of item similarity, and the importance value between the two items is calculated by $\chi ^{2}test$ to eliminate the chance of rules, which is expressed as Eq. (5).

where $O11$ denotes the number of users who have a common rating for items $i$ and $j$; $O12$ and $O21$ denote the number of users who have a rating for item $i$ only and item $j$ only, respectively, and $O22$ denotes the number of users who have no rating for either item $i$ or $j$; $m$ represents the number of users. For each item, the most relevant item can be selected based on the importance value to construct its vector. The similarity between items can then be calculated using cosine similarity. The probability of user $u$ wandering to user $v$ node at step $k$ in the trust mobile network is expressed as Eq. (6).

where $P(S=v)$ denotes the selection of user $v$ as the next wandering node from the set of users with TR with user $t$. $tt,v$ denotes the trust value between user $t$ and user $v$. Staying at this node with probability $\phi v,i,k$ and selecting an alternative item score to return, the decision to continue selecting the next user as a wandering node is made with probability $1-\phi v,i,k$. Each user on the wandering path has a certain probability of selecting it as an alternative user for this wandering, as shown in Eq. (7).

where $P(u\approx u',i\approx i')$ is the probability of selecting item $i'$ as an alternative item and user $u'$ as an alternative user. Eq. (8) expresses the rating of item $i'$ by user $u'$.

The probability of selecting an alternative item $i'$ on the selected alternative user $u'$ is expressed as Eq. (9).

where $sim(i,l)$ represents the similarity between the two items. The variance is calculated from the values returned by the model for each tour, as shown in Eq. (10).

When the variance converges, the wandering comes to an end. Several wandering processes are needed to predict the rating of item $i$ by user $u$. The ratings of alternative items by alternative users returned by each wandering are then weighted in accordance with the corresponding probabilities, and the outcome is the predicted rating, as expressed in Eq. (11).

The professional-attribute matrix is formed, and the professional category data is considered a vector on $p$-dimensional space. The similarity between the course vector and the professional category is calculated as shown in Eq. (12).

where $zj$ and $ci$ denote the professional class vector and the course vector, respectively. Using the cache algorithm, courses are divided into pools of professional courses based on similarity, and the similarity between courses and professional classes is calculated using Eq. (12). The similarity matrix is updated to group the courses into the pool with the highest similarity. User trust-based CR rating prediction first predicts the ratings within the course pool based on the current user’s rated data. In the absence of ratings, the prediction selects the current user whom the current user most trusts to wander one step to make a predicted rating (Eq. (13)).

where $a$ denotes the node on the path during the search from user $v$ to user $u$. User $v$‘s rating prediction for $i$ is expressed as Eq. (14).

where $\overline{r}v$ and $\overline{r}u$ denote the mean of all ratings of $v$ and $u$, respectively; $R$ denotes the set of users for whom maximum trust exists between users $v$ and $u$, and $ru,i$ denotes the rating of $i$ by user $u$. Fig. 5 presents the precise steps in the trust-based DR model developed for CE courses.

Fig. 5. Flow chart of a dynamic recommendation model for community education courses based on trust relationships.

4.1 Effectiveness of Recommendation Models based on the L2R2SN Algorithm

The experiments were conducted using the Flixster dataset and the Epings dataset, denoted as Dataset 1 and Dataset 2, respectively, to evaluate the efficacy of the L$^{2}$R$^{2}$SN algorithm. The L$^{2}$R$^{2}$SN algorithm was compared with two conventional list-level sorting learning recommendation algorithms: the CofiRank and ListRank algorithms. The study selected 80% as the training set and 20% as the test set and used the normalizing discount cumulative gain (NDCG) as a measure, with higher NDCG values indicating better recommendations. Setting $\lambda $ to 0.01, setting both $\alpha $ and $\beta $ to 0.3, setting the matrix dimension to 10, and setting the implied eigenfactor dimension to 10, 20, 30, and 40, the NDCG values for the three algorithms varied, as shown in Fig. 6. The L$^{2}$R$^{2}$SN method has a larger NDCG value than the other two algorithms, with a minimum and maximum of approximately 0.73 and 0.82, respectively. On dataset 1, the recommendation accuracy (RA) of the ListRank algorithm and the L$^{2}$R$^{2}$SN algorithm improved as the dimensionality of the implied feature factor increased, while the RA of the CofiRank algorithm did not change significantly. On dataset 2, the RA of the CofiRank algorithm improved significantly as the dimensionality of the implied feature factor increased, while the RA of the ListRank algorithm did not change significantly.

Fig. 6. Changes in the NDCG values of three algorithms.

The other parameters were kept constant, and the list length was set to 5, 10, 15, and 20, respectively. The NDCG values of the three algorithms varied, as shown in Fig. 7. The NDCG values of the L$^{2}$R$^{2}$SN algorithm ranged from 0.7 to 0.74, making them greater than those of the other two algorithms. Therefore, adding the interaction between items and users to the LLSL algorithm improves the recommendations. Moreover, the NDCG values of the three algorithms also become larger as the list length increases and the RA improves.

Fig. 7. Changes in the NDCG values of the three algorithms.

When the number of users was set to 3500, 5500, and 8500, the NDCG values of the three methods varied, as shown in Fig. 8. The other parameters were unchanged. The NDCG values of the L$^{2}$R$^{2}$SN algorithm were greater than those of the other two methods, with the minimum and maximum values being 0.694 and 0.757, respectively. The NDCG values of all three methods, however, did not change significantly as the user base grew, suggesting that the user base has little impact on the recommendation effect.

Fig. 8. Changes in the NDCG values of the three algorithms.

The accuracy and Root Mean Squared Error (RMSE) were used to validate the efficacy of recommendation models that use the L2R2SN algorithm. These results were compared with four other state-of-the-art recommendation algorithms: the neural factorization machine (NFM) model algorithm, which is typically used for sparse prediction analysis; the DeepFM algorithm, based on the click-through rate estimation recommendation system; the Feature Category Interaction Factorization Machine (FIFM) model algorithm; and the recommendation algorithms based on the user interests and collaborative filtering algorithms ^{(Jin 2023)}. Table 1 lists the findings. The L2R2SN algorithm outperformed the other four algorithms in accuracy, scoring 0.827 and an RMSE index of 0.382. The results demonstrate the favorable recommendation performance of the L2R2SN algorithm because it exhibits superior precision over the other algorithms, displaying feasibility and superiority.

Overall, the L$^{2}$R$^{2}$SN recommendation model outperforms the conventional LLSL algorithm and has advantages over the most recent recommendation algorithms. This highlights the positive impact of including item-user interactions in the LLSL algorithm, which improves the precision of the system suggestions.

4.2 Analysis of the Effectiveness of the Application of the TR-based DR Model for CE Courses

The study compared the effectiveness of the TR-based CE course DR model with three methods in terms of coverage, RMSE, and aggregation diversity: the TidalTrust algorithm, the matrix decomposition, and the UC-BCF algorithm. A new dataset was produced to establish trust among users and solicit ratings for the proposed model because no suitable dataset was available for trust propagation. This approach eliminated any potential biases in the dataset and increased its legitimacy. Two sets of datasets featuring normally distributed user ratings for courses were generated to ensure the reliability of the dataset. Dataset 1 included 17598 items, 9857 users, 94893 TRs, and 89264 ratings. Dataset 2 comprised 31685 items, 11994 users, 110902 TRs and 150812 ratings. Fig. 9 presents the outcomes of the coverage comparison between the four techniques. The model constructed by the study performed well in terms of coverage rate. This is because the model fully utilizes the trust relationship between users and effectively manages trust propagation, resulting in a high coverage rate of approximately 0.75 while maintaining accuracy. In addition, the matrix decomposition has the lowest coverage rate of 0.6 among the four methods because it only utilizes the users’ item rating information.

Fig. 9. Comparison results of the coverage of the four methods.

Fig. 10 shows the outcomes of the RMSE comparison between the four techniques. The model developed in this study had the lowest RMSE value on both datasets, approximately 1.25-1.4, demonstrating the high accuracy and low error rate of the model. On the other hand, the accuracy of the method was low because of the inability of the Tidal Trust to handle effectively the noise problem that arises during trust propagation while considering the trust level.

Fig. 10. Comparison results of the RMSE of the four methods.

Fig. 11 compares the combined diversity of the four approaches. The model developed by the study outperformed the other three algorithms in terms of DR variety, as depicted in the figure, with a range of 2400 to 4100, which is richer. Even in sparsely populated data areas, the model produced richer DR results by considering user trust and computing item similarity based on the criteria.

Fig. 11. Comparison results of the aggregation diversity of the four methods (Ed note: I suggest replacing “our” with the actual name of the algorithm).

Data on courses and student evaluations were gathered and pre-processed to confirm the precision. Four thousand nine hundred students across 30 majors, 650 courses, and 791,483 behavioral statistics made up Data 1, the first of the two datasets that comprised the training set. The test set of Data 1 consisted of 11 majors, 250 courses, and 1436 students, whereas Data 2 consisted of 21,357 behavioral statistics. The courses were divided into course pools, as stated in Table 2, and the keyword count of the training set was set at 4, 6, 8, 10, 12, 14, and 16. As shown in Table 2, selecting "weak keywords" for course classification resulted in a better success rate for adding courses to the course pool than selecting "strong keywords." This success rate increased as the number of keywords increased. From 322 to 554, there were steadily more successes because there were more keywords. In addition, selecting keywords required careful consideration of the content settings. Choosing a broad "weak keyword" resulted in extensive coverage of courses and multiple placements of the same course in various pools. Strong keyword selection resulted in limited course category coverage and a significant long-tail distribution ^{(Nimrah and Saifullah 2022)}.

The results in Fig. 12 compare the TR-based CE course DR model developed by this study with the conventional random wandering TidalTrust technique. The mean Absolute Error (MAE) was used as an evaluation parameter to compare the CR results. The suggested model recommendation from this study had a greater success rate than the TidalTrust algorithm, as shown in the figure. All courses in the professional course pool cache were first divided into several broad categories to focus the search when looking up the courses and increase the search efficiency. In addition, when wandering in the event of unsuccessful cases, the users with the highest levels of trust were also considered, which increases the likelihood that successful recommendations will be made.

Fig. 12. MAE values of the two algorithms.