3.1 Personalised Recommendation Based on BG Network Structure

In order to better solve the business resource allocation decision problem, the study introduces a RARA based on the BG network structure. $G = (V, E)$ represents the two-part graph, where $V$ stands for the node set and $E$ for the edge set. The node set contains node U and node I, which are independent of each other. The network structure of the BG is shown in Fig. 1. The boxes in the figure represent the user class nodes and the circles represent the item class nodes. Among them, project class nodes represent a specific type of entity or object, which plays a role in connecting nodes of different categories in the network. Project class nodes can represent entities of different categories, such as movies, books, products, etc. in recommendation systems.

Fig. 1. The network structure of BGs.

RAs based on BG networks rely only on the Boolean-type relationship between whether a user selects an item or not for recommendation, while the content of the nodes in the network is unrestricted and can be of any form ^[15]. The core goal of recommendation is to suggest items to the user that he/she has not yet selected but may be interested in. On this basis, the study introduces a substance diffusion RA based on a two-part graph. In a two-part graph network structure, the study sets there are $m$ users $U$, and $n$ items $I$, which are represented as shown in equation (1).

A neighborhood matrix $D$ represents the objects selected by the user. If a user has already selected an item, the corresponding position in the matrix has a value of 1, otherwise it is 0. If the user $u_{j} $ has selected the item $i_{k} $, the corresponding element in the adjacency matrix has a value of 1, otherwise it has a value of 0. Users have different preferences for different items, which represent their interests in certain aspects. Users' ratings of items directly reflect their preferences. Users' preferences can be abstracted into resource values (RVs) that can be passed on for allocation ^[16]. In a network, various choice relationships tie items to items, users to users, and projects to users, thus enabling RVs to flow through the relationships. When the project selected by the target user passes RVs to other unselected projects, it represents that the project selected by the target user has the ability to recommend other unselected projects to it ^[17]. In this regard, the schematic diagram of substance diffusion based on the two-part graph network structure is shown in Fig. 2.

Fig. 2. Schematic diagram of material diffusion based on bipartite network structure.

In Fig. 2, for the target user $U1$, the study analyses the resource allocation process based on two-part graphs, which mainly contains three core steps. The first step assigns initial RVs to the items. For the target user in the item class, the selected items are assigned an initial RV of 1, while the unselected items have an initial RV of 0. The specific resource determination calculation is shown in equation (2).

In equation (2), $a_{u,i} $ represents the initial RV of the user to the project. In the subsequent phase, the project's RVs are allocated to nearby user nodes based on the selection relationship. The set of users that obtain the RVs is defined as shown in equation (3).

The calculation of resources obtained by any user from the target user is shown in equation (4).

In equation (4), $r_{v} $ represents the resources obtained by any user $v$ from the items that have been selected by the target user $u$. $d_{i} $ denotes the number of items $i$ selected, i.e., the degree of the item. In the third step, the recommended RVs of the user nodes in the P-set are assigned to their neighbouring project class nodes according to the selection relationship. In this process, all the project nodes obtain the RVs. The RV obtained by the project class node is the sum of the RVs of all users in the P-set divided by the degree of the user node ^[18]. The calculation of obtaining recommended resources for any project is shown in equation (5).

In equation (5), $d_{v} $ is the items that any user $v$ has selected, i.e., the degree of the user. The purpose of RAs is to recommend items that users have not selected and may be interested in to them. After demonstrating the material diffusion process based on BGs, further analysis was conducted on the process of recommending materials to users using the BG network structure based material diffusion recommendation algorithm. The recommendation process was optimized through directional and weighted information. The flow schematic of the substance diffusion RA based on two-part graph network structure is shown in Fig. 3.

Fig. 3. Schematic diagram of the RA process.

The items in the study's recommendation list (RL) that are displayed in Fig. 3 are all unselected by u1. In recommendation systems, RL refers to the number of items or items recommended to users. Reasonably setting RL can balance the personalization level of recommendations and the performance requirements of the system, thereby providing more satisfactory and effective recommendation services. The study placed the three items in descending order based on RV size to guarantee the efficacy and accuracy of the recommendation. The item recommended as a priority is the one with the highest RV. If the size of the RL is set to 1, the RL of the target user will contain only ${\{}$i${}_{5}$${\}}$. The study further transforms the two-part graph network structure into a one-dimensional projection, which in turn generates a directed graph reflecting the resource transfer relationship between items, as shown in Fig. 4.

Fig. 4. Directed graph of resource transfer between projects.

In Fig. 4, if two items are jointly selected by at least one user, it indicates the existence of a connectivity relationship. The numbers labelled on the edges represent the weighted influence that one item exerts on the initial RV when passing the recommended resource to the other item. The study represents the one-dimensional projection of the two-part graph on the item dimension by constructing an $n$-row, $n$-column matrix $W$. The matrix $W$ is a one-dimensional projection of the two-part graph on the item dimension. Where the elements of the ith row and jth column of the matrix $W$ represent the weighted values of the initial resources of item j when item $j$ passes the recommended resources to item $i$. The particular computation is presented in equation (6).

In equation (6), $d_{u} $ is the items selected by the target user $u$. Fig. 4 uses a matrix representation as equation (7).

Let the initial RV of project set I be expressed as equation (8).

The final RV for project set I is calculated as shown in equation (9).

3.2 Decision Recommendation Based on Improved BG Networks

Traditional BG-based RARAs tend to rely only on item degree and user degree for resource allocation ^[19]. For this reason, the study improves the algorithm by introducing an improved K-means clustering algorithm to deeply mine the potential information present in the clustering results. To help the target users locate their actual comparable neighbor users, the similarity computation between users has been enhanced to include item category information. In the two-part graph network structure RA, the excessive users and items in the recommendation system will lead to recommendation delay and affect the real-time performance of recommendation. To increase the system's recommendation efficiency, the paper presents the K-means clustering algorithm, which can split the network into several smaller BG networks. The core of the algorithm includes the determination of cluster centroids and the calculation of similarity between nodes. Taking movie recommendation as an example, this study uses K-means to cluster user and movie data in order to more accurately understand the relationship between user groups and movies, thereby improving the effectiveness of RAs. The specific process is shown in Fig. 5.

Fig. 5. Process diagram of improved clustering algorithm.

Since different datasets may have different numbers of optimal cluster classes, the k-value setting of the improved K-means algorithm has a significant impact on the clustering effect. Therefore, multiple clustering operations need to be performed on the set of film genre vectors, with a different k-value set each time, so as to identify the optimal k-value. The traditional way of resource allocation is uniform allocation, which gives equal treatment to all users and ignores the differences between users. This difference makes the way of resource allocation should be non-uniform, the more similar to the target user should be assigned more recommendation values ^[20]. Based on this, the study proposes a method that integrates the information of user degree, the difference in ratings between users, and designs an improved inter-user similarity calculation, which is expressed as shown in equation (10).

In equation (10), $Dsim(u,v)$ represents the similarity between any user and the target user. $d_{u,v} $ represents the number of items with the same rating between two users. After clustering the items, in order to measure the users' preference for the item categories, the study proposed two criteria. First, as indicated by equation (11), the ratio of the total number of items to the number of items assessed by users in the class cluster.

In equation (11), $A_{u,c} =\frac{\sum {}_{i\in I_{u,c} } r_{u,i} }{\left|I_{u,c} \right|} $ represents the percentage of the items that have been selected by the user in item class $c$. $\left|I_{u,c} \right|$ represents the set of items that have been selected by the user in item class $c$. $\left|I_{u} \right|$ represents the set of items that users have selected. Second, the mean value of users' ratings in the class cluster. Equation (12) depicts the expression.

In equation (12), $A_{u,c} $ denotes the mean value of user's ratings in item class $c$. The user's preference for item class $c$ is calculated as shown in equation (13).

where the larger the $P_{u,c} $ value, the more favourite the item is by the user in that category. The study initially establishes the initial RV of the item as the size of the user's rating of the item in the non-uniform resource allocation procedure. Equation (14), when user $u$ is the target user, displays the initial RV of the item he has selected.

In equation (14), $b_{u,i} $ is the initial RV obtained from item $i$ that has been selected by user $u$, and $r_{u,i} $ is the rating of $i$ by $u$. Next, the resource gained by user $v$ from user $u$ is computed using equation (15), and the item degree is integrated into the first stage of the resource allocation process.

Subsequently, the study used the ratio of the user rating to the maximum value of the user rating as the resource allocation factor, and the second step of resource allocation was calculated as shown in equation (16).

In equation (16), $r_{j} $ represents the recommended resources obtained by item $j$. The maximum value of the recommended resources obtained by item $j$ is the maximum value of user $v$'s rating. $Max(v)$ is the maximum value of user $v$'s rating. In order to eliminate the potential interference of item categories on the calculation of inter-user similarity, the study proposes a method of inter-user similarity calculation independently for a single item category based on the clustering results. When the calculation is carried out in the whole item space, the calculation of inter-user similarity avoids being affected by the undesirable effects between different item categories. The flow of the resource allocation decision RA based on the improved two-part graph network is shown in Fig. 6.

Fig. 6. Flow chart of resource allocation decision RA based on improved BG network.

In the time complexity analysis of the algorithm, there are $m$ users and $n$ items in the BG recommendation system. The time complexity of traditional prediction algorithms is $O(n^{3} )$, while the computational complexity of resource allocation RAs based on improved BG networks is $O(K)$, where $K$ represents the number of nearest neighbor sets, which is less than $n$. Compared to others, the algorithm proposed by the research institute has lower time complexity and higher computational efficiency.

4.1 Recommendation Performance Analysis with Different Number of Clusters

To confirm the efficacy of the RARA based on enhanced BG networks, three levels of analysis are performed on the experiments: originality, diversity, and accuracy. The data for the experiment comes from the Movie Lens site, a film recommendation website that incorporates online communities. The recommendation system needs to consider the user's rating behavior and the recommended resource $r$ obtained when optimizing resource allocation. The maximum value $Max(v)$ of user ratings plays an important role in resource allocation, which not only affects the actual allocation of resources, but also indirectly affects the quality of recommendation results by affecting the prediction accuracy of the recommendation system. The recommendation quality of a recommendation system is measured using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Both are used to determine the accuracy of recommendations by calculating the deviation between the predicted item set and the actual item rating set. The smaller the error value, the better the recommendation accuracy. Assuming that the predicted user rating set is represented as $\{p_{1} $, $p_{2} $, ..., $p_{N} \}$ and the actual user rating set is $\{q_{1} $, $q_{2} $, ..., $q_{N} \}$, the MAE calculation of the algorithm is shown in equation (17).

The calculation of RMSE is shown in equation (18).

The dataset selected for the experiment includes 74364 users, 10228 movies, and 10 million user rating data for movies, with a rating range of 0-5 points. In the meantime, 70% and 30% of the user rating dataset are split up into training and testing sets by the study. Table 1 displays the experiment's environment setting. In Table 1, big data processing tools such as Spark and Hadoop typically require specific versions of Java to run, with JDK version 1.7.0_85 ensuring that all Java programs and libraries used in the experiment can run correctly and be compatible in that environment. The 64 bit CentOS 6.5 is suitable for big data processing environments and supports distributed processing frameworks such as Spark and Hadoop. Spark version 1.5.0 provides rich APIs and features to efficiently process large datasets containing tens of millions of rating data. Hadoop is used in experiments for distributed file storage and data processing. It provides a Distributed File System (HDFS) and MapReduce programming model, which, when combined with Spark, can achieve efficient data processing and analysis. Zookeeper is used in distributed environments to manage and monitor the status and configuration of services. It is mainly used to coordinate the node and task management of Spark clusters, ensuring the reliability and stability of the cluster.

The study begins by verifying the performance of a RARA based on a modified BG network under different numbers of clusters. The selected metrics are recommendation hit rate, average ranking value, popularity, and Hamming distance. The number of clusters ranges from 6-10. An increase in the number of clusters usually increases the complexity and dimensionality of the data, so choosing from 6 to 10 can cover this change, from fewer clusters to more clusters. The recommendation hit rate and average ranking value of the proposed algorithm under different clusters are shown in Fig. 7. Ranking score describes the relative position of hit items in the recommendation list. The quality of RAs to a certain extent depends on whether the algorithm can accurately rank the items that users are interested in at the front of the recommendation list. If the items that users like are ranked at the front of the recommendation list, the average sorting value will be smaller, and the recommendation algorithm will be better. Hit rate is an important indicator for evaluating accuracy in RAs, which refers to the proportion of hit items in the recommendation list to the length of the recommendation list. The higher the hit rate, the more items the user has actually rated in the recommendation list, and the more satisfied the user is. In Fig. 7(a), the highest hit rate is obtained when the number of clusters is 8 when the length of the RL is up to 6, and its highest hit rate is as high as 43.2%. When the length of the RL is more than 6, the highest hit rate is obtained when the number of clusters is 6, and its highest hit rate is as high as 32.9%. As shown in Fig. 7(b), when the number of clusters is 10, the recommendation ranking of the movie with the highest hit rate is higher. When the length of the RL is 10, the average ranking value under this number of clusters is only 0.38. When the number of clusters is 6, the ranking of the movie with the highest hit rate is relatively lower.

Fig. 7. Recommended hit rate and average ranking value under different numbers of clusters.

The study continues to use Hamming distance to evaluate the diversity of RAs, which describes the differences between recommendation lists among users. When the Hamming distance is small, the items included in the recommendation list of two users have a higher similarity and may have similar preferences or behavior patterns. When the Hamming distance is large, the difference in recommendation lists between two users is significant, indicating that their interests or behavior patterns are different. The novelty index represents the average degree of all recommended items, and the smaller the value, the higher the novelty. The popularity and Hamming distance under different numbers of clusters are shown in Fig. 8. It is evident from Fig. 8(a) that the algorithm becomes less popular when there are eight clusters. When the length of the RL is 10, the popularity under this number of clusters is only 30.1, which is 47.3 lower than the case of the clusters is 6. It shows that the recommendation of the algorithm is more personalised and novel when the clusters is 8. From Fig. 8(b), the algorithm achieves a higher Hamming distance when the number of clusters is 8, indicating that its recommendations are more diverse. When the length of the RL is 15, the Hamming distance for this clusters is 0.94, which is improved by 0.09 compared to the case when the clusters is 7. Collectively, the clusters will have different impacts on the algorithm's hit rate, average ranking value, popularity, and Hamming distance. When the number of clusters is 8, the optimal hit rate, popularity, and Hamming distance can be obtained. When the number of clusters is 10, the recommended ranking for hit movies is better. In order to obtain more accurate and personalised resource allocation recommendations, the clustering centre and the number of clusters need to be reasonably determined according to the actual situation.

Fig. 8. Popularity and Hamming distance under different numbers of clusters.

4.2 Comparative Analysis of Different RAs

To verify the superiority of the proposed algorithm, the study uses the unimproved RARA based on BG as well as the collaborative RA for performance comparison. The comparison metrics include recommendation hit rate, average ranking value, popularity, and Hamming distance. Fig. 9 compares the average ranking value and hit rate of several algorithms. It is evident from Fig. 9(a) that the suggested RARA with enhanced BG has a greater hit rate. The success rate of the suggested approach reaches 32.5% when the length of the RL is 10, which is a 21.5% improvement over the CFA. At the same time, the algorithm improves 4.3% over the unimproved BG-based RARA. The reason is that the study of the proposed algorithm improves the calculation of similarity between users, which helps to accurately find similar users to the target user. In Fig. 9(b), the CFA has the lowest average ranking value when the length of the RL is within 9, and then it is gradually higher than the remaining two algorithms. Additionally, after the RL length surpasses 9, the unimproved RARA based on BG has the lowest average ranking value, indicating that the objects it hits are comparatively higher in the RL. However, the average ranking value of the studied proposed algorithm is not much different from that of the pre-improved RA, indicating that the algorithm has a strong recommendation advantage.

Fig. 9. The hit rate and average sorting value of different algorithms.

The specific findings are displayed in Fig. 10 as the investigation proceeds to confirm the acceptance and Hamming distance of the various algorithms. In Fig. 10(a), the item popularity of the proposed algorithm is significantly smaller than that of the BG RA as well as the CFA before the improvement. When the length of the RL is 10, the popularity of the proposed algorithm is only 39.1, compared with the CFA, the popularity has dropped by 69.3, which indicates that the items recommended by the proposed algorithm are more cold, and it is easy to find out the user's preferences. From Fig. 10(b), compared with the remaining two algorithms, the Hamming distance of the proposed algorithm is significantly better, and its mean Hamming distance is as high as 0.976, indicating that the items recommended by the proposed algorithm are more diverse. Comprehensively, the RARA based on improved two-part graph has more significant recommendation performance.

Fig. 10. Popularity and Hamming distance of different algorithms.

The study further validates the recommendation effectiveness of each algorithm for different number of nearest neighbours. The evaluation metrics used are MAE and RMSE. The number of nearest neighbours K is taken in the range of 10-50. The experimental results are shown in Fig. 11. As can be seen from Fig. 11(a), the MAE value of each RA decreases as the nearest neighbours increases. The research proposal algorithm has an MAE value that is noticeably lower than those of the other two methods. When $K = 30$, the MAE value of the proposed algorithm is only 0.741. In Fig. 11(b), the RMSE values of the proposed algorithms are all lower than the remaining two algorithms. In particular, when $K = 20$, the RMSE value of the proposed algorithm is only 0.959, which is 0.018 lower compared to the CFA. indicating that the proposed RA has a higher recommendation accuracy.

Fig. 11. MAE and RMSE values of different algorithms.

The study further selected the Amazon Product dataset for algorithm recommendation performance testing. This dataset is a product recommendation dataset provided by Amazon, which includes user ratings and purchasing behavior data for various products, and can be used to verify the effectiveness of the algorithm in product recommendation. The study also used the improved BG recommendation algorithm and commonly used collaborative RAs to compare their performance indicators. The comparison indicator is the MAE and RMSE values under different numbers of nearest neighbors. The MAE and RMSE values of different recommendation methods are shown in Fig. 12. As shown in Fig. 12(a), in the Amazon Product dataset, the MAE values of each recommendation algorithm decrease with the increase of the number of nearest neighbors. Among them, when $K = 20$, the MAE value of the resource allocation recommendation algorithm based on the improved BG network is only 0.613, which is significantly lower than the other two algorithms. When $K = 30$, the MAE value of the algorithm proposed in the study is only 0.605. As shown in Fig. 12(b), the RMSE values of the proposed algorithm are lower than those of the other two algorithms. Among them, when $K = 20$, the RMSE value of the algorithm proposed in the study is only 0.787, which is reduced by 0.108 compared to the collaborative filtering algorithm. In the Amazon Product dataset, the recommendation accuracy of the resource allocation recommendation algorithm based on the improved BG network is significantly better.

Fig. 12. MAE and RMSE values for different recommendation methods.