Recommendation algorithm based on attributed multiplex heterogeneous network

Model architecture

Network G = (V, ξ, A), ξ = U_r∈R ξ_r is an attributed multiplex heterogeneous network, in which edges with edge types r ∈ R and |R| ≥ 1 form ξ_r together. We separate the network of each edge type or consider r ∈ R as G = (V, ξ_r, A). The Attributed Multiplex HEterogeneous Network (AMHEN) describes the model architecture diagram of users and projects. Model structures with different types of nodes and different numbers of edge types are also different. For networks with more edge types and nodes, the processing results of the model are better; as the edge type category increases, the number of nodes increases, and the recommendation effect of the model enhances. Of course, the more node types and edge types there are, the more complex the AMHEN model is. The more hidden information you choose, the wider the recommended directions for users, and the more accurate the recommendations will be. In the SSN_GATNE-T model, more than 15% of the node pairs in the two datasets we use will have more than one type of edge, and users may have multiple interaction information about the items. Our model accomplishes embedding of node as well as edge types through Base Embedding and Edge Embedding, where Base Embedding is accomplished by sharing between different types of edges contained in different nodes, and Edge Embedding is calculated by aggregating information about their neighbouring nodes through an attention mechanism. The base embedding is done by sharing between different types of edges contained in different nodes, while the edge embedding is computed by aggregating the relevant information about its neighbouring nodes through an attention mechanism. The two embedding methods are used to provide information on the interaction between the two types of nodes, user and project, and between the different edge types, and the nodes contain both user and project information. In the Youtube dataset, user input information includes gender, age and address, while item input information includes movie title and movie genre.

In order to better to describe the effectiveness of the SSN_GATNE-T model for large web embeddings and the effectiveness of recommendation performance, the model architecture of users and videos of the Youtube dataset is described in Fig. 1, which contains two node types and five edge types. The two node types are users and items with different attributes, with user inputs including information such as gender, age and address, and item inputs including information such as movie name and movie genre. The aim at combining the attribute reuse heterogeneous network model with the improved attention mechanism is to make better use of the five edge types, i.e. user-item interactions. The purpose of introducing the improved attention mechanism is to more explicitly labelling the access to useful information, to more fully grasp the connections between users, and to make recommendations between users who are closely connected, as the more similarities they have in common, the more similar their interests will be, and thus the better the recommendations will be. Our model SSN_GATNE-T uses mainly the interactive connection between the attributes of different nodes, determines the potential hobbies of the user and then recommends the model. In our SSN_GATNE-T model, we use some descriptive symbols. To explain the model more clearly, we use some symbols; Table 1 describes the meaning of each symbol.

In the YouTube dataset, our model collects the connections between nodes and edge types to determine whether there is a connection between users, whether they have shared friends, whether there are the same subscription videos, whether they are all subscribed users of the same video, and connections between them and whether there are five types of interactive information of common favourite videos, and our improved attention mechanism can help us to better label these five interactive relationships. If all five interactive relationships exist in the obtained annotation information, then the users can recommend videos to each other that they have not watched; then there are four users with the same interaction relationship, and then three, two, and the last, etc. The most important thing is if two of these five interaction relationships exist between users, their hobbies will be very similar. The potential interaction relationship is obtained through the node and edge types, and then the interaction correlation between the two is judged. The correlation between two of the five edge types is inferred, and then five more relevant videos are selected for recommendation. The same is true for the Amazon dataset; the difference is that the variables contained in the dataset are different.

To obtain a more accurate recommendation effect, we can only obtain the best model combination through continuous experiments so that our model can more accurately identify the user-item interaction relationship. Our model can help us better obtain the information of each attribute node in the user-item interaction through an attributed multiplex heterogeneous network, and the improved attention mechanism can help annotation obtain more useful information. To improve the attention mechanism, in this part, we apply the characteristics of the softsign and sigmoid functions to the attention mechanism to obtain more potential hobbies of users that can be accurately recommended for users. The formula is described as follows:

(1) $$a_{i,r}=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}{\left(w_r^T\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{i}\mathrm{d}\left(W_r{U}_i\right)\right)}^T$$

(2) $$a_{i,r}={\displaystyle \frac{{\left(w_r^T\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{i}\mathrm{d}\left(W_r{U}_i\right)\right)}^T}{1+|{\left(w_r^T\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{i}\mathrm{d}\left(W_r{U}_i\right)\right)}^T|}}$$

(3) $$a_{i,r}={\displaystyle \frac{{\left(w_r^T{\displaystyle \frac{W_r{U}_i}{1+e^{-\left(W_r{U}_i\right)}}}\right)}^T}{1+|{\left(w_r^T{\displaystyle \frac{W_r{U}_i}{1+e^{-\left(W_r{U}_i\right)}}}\right)}^T|}}$$

In addition, in the fully connected layer of the model, we apply the characteristics of the softsign function, which can better reduce the user potential that is discovered through the attributed multiplex heterogeneous network and the improved attention mechanism through the user interaction information for different node attributes. The loss of potential information that can be used for accurate recommendation has achieved good results in obtaining potential information. As a result of the information obtained by using the attribute multiplexing heterogeneous network, the network can more completely obtain the attribute node information in the user-item interaction, and our improved attention mechanism can help us to mark more useful information, mine more potential interests and potential interaction relationships of users, and then provide users with the most matching recommendations based on the potential information that is mined.

Taking the YouTube dataset as an example, we made a structure diagram of the recommendation description process, as shown in Fig. 1. On the left side of Fig. 1, the user and video information is described, and five interaction relationships between the two are outlined. The right part depicts the AMHEN chart setting method. Through this network, the information of each attribute node in the user-item interaction can be better obtained; that is, the potential information existing in two nodes and five edge types can be mined, and the improved attention mechanism contained inside can help in tagging obtain more useful information. As more potential information is obtained from users, we have more information to provide users with more accurate recommendations. The lower side of Fig. 1 depicts the recommendation performance comparison of the SSN_GATNE-T model and the GATNE-T and GATNE-I models on the YouTube dataset.

Taking the Amazon dataset as an example, we made a structure diagram of the recommendation description process, as shown in Fig. 2. On the left side of Fig. 2, the user and video information is described, and two interaction relationships between the two are outlined. The right side depicts the setting of the attributed multiplex heterogeneous network (AMHEN) chart. Through this network, the information of each attribute node in the user-project interaction can be better obtained, that is, to explore the potential between the two nodes and the two types of edge types. The two types of edges, such as collaborative purchase and collaborative viewing of information, can help to dig out more potential interests of users, and the improved attention mechanism used can help labels obtain more useful nodes and edge types.

Sexual information. Since our model obtains and annotates more potential user information, we have more information to provide users with more accurate recommendations. The lower side of Fig. 2 depicts the recommendation performance comparison of the SSN_GATNE-T model and the GATNE-T and GATNE-I models on the YouTube dataset.

Figures 1 and 2 show examples of AMHEN. Figure 1 contains two node types and five edge types. The edge type includes whether there is a connection between users, whether they have shared friends, whether there are the same subscription videos, whether they all subscribe to the same video and whether there are common favourite videos among them. Figure 2 also contains two types of nodes and two types of edge types. The edge types include product attributes and synergy between products as well as view and collaborative purchase links. The two types of nodes in Figs. 1 and 2 are both users and items with different attributes.

SSN_GATNE-T network structure

The SSN_GATNE-T model is shown in Fig. 3. The application object of this model is an attributed multiplex heterogeneous network. This model uses two parts of “basic embedding” and “edge embedding” to complete the entire embedding, as shown in Fig. 3. The upper and lower parts of the middle are “base embedding” and “edge embedding”. The purpose of base embedding is to separate the topological features of the network. Edge embedding is the embedding representation of a specific node on different edge types. Take the orange node as an example. To calculate its edge embedding, there are several types of edges connected to it. From the graph, we can find that there are two types of edges connected to it: green and blue. Then, we separate the green and blue edges for this node. Two new network structures have been created.

In general, the SSN_GATNE-T model does not integrate node attributes for the embedding representation of each node. Instead, the model aggregates neighbouring nodes to generate their own edge embedding representations for different types of edge types connected to the node and then introduces improvements. The attention mechanism calculates their respective attention coefficients (that is, their different importance) to perform a fusion, thereby obtaining the overall embedding representation of the node.

Starting from the embedding learning of attribute-based multiple heterogeneous networks of the transduction environment, our model SSN_GATNE-T is given, as shown in Fig. 3. More specifically, in SSN_GATNE-T, node v_i on edge type r consists of two parts: edge embedding and foundation embedding. Each node v_i type is different and its foundation embedding can be shared. For node v_i on edge type R, its k-level edge embedding ${\mathbf{u}}_{i,r}^{(k)}\in R^s,(1\le k\le K)$ is aggregated by its neighbour’s edge embedding, as follows:

(4) $${\mathbf{u}}_{i,r}^{(k)}=\mathrm{a}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\left(\left\{u_{j,r}^{(k-1)},\mathrm{\forall }{v}_j\in N_{i,r}\right\}\right)$$where N_i,r is the neighbour of node v_i on edge type r. In our direct push model, the initial edge embedding ${\mathrm{U}}_{i,r}^{(0)}$ of nodes and edge types is randomly initialized. Moreover, the mean aggregator can also be used as the aggregation function, as follows:

(5) $$u_{i,r}^{(k)}=\sigma \left({\hat{W}}^{(k)}\cdot \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\left(\left\{u_{j,r}^{(k-1)},\mathrm{\forall }{v}_j\in N_{i,r}\right\}\right)\right)$$

Or use the max-pool aggregator:

(6) $${\mathbf{u}}_{i,r}^{(k)}=max(\left\{\sigma (\{{\hat{W}}_{pool}^{(k)}{u}_{j,r}^{k-1}+{\hat{b}}_{pool}^{(k)}),\mathrm{\forall }{v}_j\in N_{i,r}\}\right)$$

Among these functions, edge embedding v_i is represented by the K^th level edge embedding u_i,r, the activation function is represented by, and U_i is formed by embedding and connecting all edges of node v_i, and its size is m:

(7) $${\mathrm{U}}_{\mathrm{i}}=\left(u_{i,1},u_{i,2},\dots ,u_{i,m}\right)$$

The self-attention mechanism (Cen et al., 2019) is used to calculate the coefficient a_i,r ∈ R^m of the linear combination of vectors U_i on edge types r, and the softsign function is applied thereto as follows:

(8) $$a_{i,r}=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}{\left(w_r^T\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{i}\mathrm{d}\left(W_r{U}_i\right)\right)}^T$$where w_r and W_r are trainable parameters of edge types of sizes d_a and d_a×s, respectively, and the transposition of the matrix is represented by superscript T. Therefore, the overall embedding of node v_i can be expressed as:

(9) $$v_{i,r}=b_i+{\alpha }_r{M}_r^T{U}_i{a}_{i,r}$$where b_i is the basic embedding of node v_i, α_r is the superparameter representing the importance of edge embedding to overall embedding, and M_r ∈ R^s×d is the trainable transformation matrix.

When using the attributed multiplex heterogeneous network, we also adopted a self-attention mechanism. The self-attention mechanism we use is a combination of the softsign function and the sigmoid function. That is, $a_{i,r}=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}{\left(w_r^T\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{i}\mathrm{d}\left(W_r{U}_i\right)\right)}^T$, The combination of the improved attention mechanism and the attribute multiplexing heterogeneous network has a very good effect on the three evaluation indexes of ROC-AUC, PR-AUC, and F1, while the improvement of the F1 index is greater. In addition, we also chose the softsign function of the activation function of the fully connected layer of the model because we found that using the softsign function here combined with the attention mechanism we adopted has unexpected results, which greatly improves the evaluation index F1, showing the effectiveness of the recommendation performance of our model. In order to better to describe our SSN_GATNE-T model, we describe our SSN_GATNE-T algorithm in Algorithm 1.

Model architecture

The SSN_GATNE-T model combines attributed multiplex heterogeneous networks with an attention mechanism that introduces softsign and sigmoid function properties attributed multiplex heterogeneous network can help to obtain more attributes of the user-item information, regardless of the number of nodes and type of model, our model can be good at handling, and improved attention mechanism can help labeling to obtain more useful information, the combination of the two can help to explore more potential information to improve the recommendation effect. In addition, the application of the softsign function in the fully connected layer of the model can better reduce the loss of potential information about the user that can be used for accurate recommendations, and we use the Adam optimizer to optimize our model in order to avoid the impact on the accuracy of the model recommendations due to the excessive node and edge type information obtained. The optimisation of the model can qualitatively improve the recommendation effect of the recommender system. The optimization methods include Adagrad, Momentum, RMSprop, GradientDescent and Adam. Through extensive experimental validation, we use the Adam optimiser for the model optimisation, which allows for faster convergence and also helps with the tuning of the model. The Adam optimizer is shown in the following equation.

(10) $$m^t=\mu \ast m_{t-1}+(1-\mu )\ast g_t$$

(11) $$n_t=v\ast n_{t-1}+(1-v{)}^{\ast }{g}_t^2$$

(12) $${\hat{m}}_t={\displaystyle \frac{m_t}{1-v^t}}$$

(13) $$\hat{n}={\displaystyle \frac{n_t}{1-v_t}}$$

(14) $$\mathrm{\Delta }{\theta }_t=-{\displaystyle \frac{{\hat{m}}_t}{\sqrt{{\hat{n}}_t}+\epsilon }\ast \eta }$$

Dataset and parameter settings

In this article, we use YouTube and Amazon datasets to complete the experiment. The Amazon product data set includes product metadata and links between products; the YouTube data set includes various types of interactions. Since some baselines cannot be extended to the entire graph and the total data volume of nodes and edges contained in the original data set is too large, we selected part of the data in the original data set as the sampling data, which is the sampling data set we adopt, and pass SSN_GATNE-T. The model evaluates the recommendation effect and performance of the sampled data set. Table 2 describes the information of the two sampled datasets, including the total number of nodes, the total number of edges, the number of node types, and the number of edge types. The n-type and e-type in Table 2 represent the node type and edge type, respectively.

Amazon. In the experiment, the two interactions of the product attributes contained in the data and the collaborative viewing between the products and the collaborative buying link were used, which can be observed and understood from Fig. 2.

YouTube. The YouTube dataset contains five types of interactions, including shared friends and shared subscriptions, which can be observed from Fig. 1.

In the model, to filter out the most suitable parameter settings for the SSN_GATNE-T model, we chose to experiment the settings and determine the parameters one-by-one. Taking the embedding size of the whole and the edge as an example, the number of parameters with setting changes are only two. The settings of other parameters do not change during the process of determining these two parameters, and the determination of these two parameters is to first determine one of them and then determine the other while maintaining the determined items. After many tuning experiments, we finally set the embedding size of the whole and the edge to 200 and 10, respectively; the walking length and times of the node to 10 and 20, respectively; and the window to 5. The number of negative samples L of each positive training sample fluctuates in the range of 5-50. For each edge type r, coefficients α_r and β_r are set to 1. In the experiment, if the ROC-AUC of the verification set reaches the optimal value before all iterations are completed, the model will be terminated early.

Evaluation index

In this article, to better understand the recommended performance of the model, we use the ROC-AUC, PR-AUC and F1 (F1-score), which are three evaluation indicators.

The ROC-AUC is an evaluation index that comprehensively considers the ROC and AUC. The two indexes of sensitivity and specificity are not affected by unbalanced data.

ROC-AUC makes an evaluation indicator that takes into account both ROC and AUC. F1 is an evaluation indicator that takes into account both precision and recall values.

F1 is an evaluation index that fully considers the precision value and the recall value:

(15) $$F\text{-score}={\displaystyle \frac{2}{{\displaystyle \frac{1}{\mathrm{P}}+{\displaystyle \frac{1}{\mathrm{R}}}}}={\displaystyle \frac{2\mathrm{P}\mathrm{R}}{\mathrm{P}+\mathrm{R}}}}$$where P stands for Precision and R stands for Recall.

(16) $$\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}=\frac{\mathrm{t}\mathrm{p}}{\mathrm{t}\mathrm{p}+\mathrm{f}\mathrm{p}}$$

(17) $$\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}=\frac{\mathrm{t}\mathrm{p}}{\mathrm{t}\mathrm{p}+\mathrm{f}\mathrm{n}}$$

To solve the single-point limitation of the P, R, and F-measures, we use PR-AUC/AP (average precision), which can reflect the overall evaluation index. The larger the PR-AUC value is, the better the performance of the model.

(18) $$PR-AUC/AP={\int }_0^{1}p(r)d(r)$$

Comparison of model accuracy

In this section, we compare our model SSN_GATNE-T with ANRL, PMNE (n) (He et al., 2021), PMNE(r), PMNE(c), MVE(Multi-View Network) (Berahmand, Nasiri & Li, 2021), MNE (Li et al., 2021), GATNE-T, GATNE-I, FAME, FANEm and other models for the evaluation of the Youtube and Amazon datasets, and express them in line graph to analyse in detail the impact on our model on these two datasets and where its advantages lie. For this model comparison, we demonstrate the effectiveness of our model for large network data by comparing the SSN_GATNE-T model with other models on two large network datasets containing different nodes and different edge types, Amazon and Youtube, and then demonstrate that the potential information on the different edge types of user nodes and project nodes obtained by improving the performance of the model for large networks can be used to improve the effectiveness of the recommendation performance.

In the experiment, we divided the dataset into a training set, a validation set and a test set and used the area under the ROC curve (ROC-AUC), the area under the PR curve (PR-AUC) and the F1 score as the evaluation indicators for model evaluation. The accuracy of our model and the pros and cons of its recommendation effect are judged through the impact of these three evaluation indexes on the two YouTube and Amazon datasets via different models, as shown in Table 3. When evaluating, we compare our model SSN_GATNE-T with models including metapath2vec, ANRL, PMNE(n), PMNE(r), PMNE(c), MVE, MNE, GATNE-TGATNE-I, FAME and FANEm. Our model has different effects on different datasets, and each model has different effects on these three evaluation indexes. Compared with other models, our model SSN_GATNE-T aggregates neighbour nodes to generate their own edge embedding representations for different types of edge types connected to nodes and then introduces an improved attention mechanism to calculate their respective attention. The coefficient to performs a fusion, thereby obtaining the overall embedding representation of the node. Compared with other models, our model can better obtain the interaction relationship between nodes and edge types, thereby digging out more potential user interests. In addition, our improved attention mechanism can also help us obtain and label node and edge types. The potential correlation information between the node and edge types is precisely because our model can obtain more important information that can be used for recommendations compared with other models, which makes our model have a great improvement in recommendation performance. Compared with the DeepWalk, LINE, node2vec, NetMF, and GraphSAGE network embedding models, our SSN_GATNE-T model can obtain not only node information but also the potential interaction relationship between nodes and edge types and the relationship between nodes and edges. The more types and quantities there are, the more options that can be used to provide users with accurate recommendations. Compared with HEN, PTE, metapath2vec and HERec, which are heterogeneous network embedding methods, our model mines the potential information in the network more easily than the heterogeneous network, which is full of people, to obtain the combination of content and structure. It also makes a great contribution to the scalability of the network. Our model can not only be used for the processing of small networks but can also perfectly mine its potential information for large networks containing billions of nodes and edge types. Compared with PMNE, MVE, MNE, and Mvn2vec, which are eager for multichannel heterogeneous network embedding methods, compared to the limitation of capturing a single view of the network and the effectiveness of obtaining node and edge type embedding information, our model is superior; the edge type correlation information mining and labelling are more comprehensive. Compared with TADW, LANE, and ANRL, which are these types of attribute network embedding methods, attribute network embedding is a low-dimensional vector representation of nodes looking for and retaining the network topology and the proximity of node attributes, and our model can not only do this, it is also possible to mine more potential attribute information for recommendation through the correlation between node and edge types. Compared with the existing recommendation algorithms, our SSN_GATNE-T model can either obtain the correlation information between labelled nodes and edge types, obtain the attribute information of nodes and edge types, or process billions of nodes and edges. In the processing of large-scale networks of nodes and edges, our model can use more or more relevant information for recommendations, and the recommendation effect is greatly improved.

Our SSN_GATNE-T model has the most obvious improvement effect on the YouTube dataset, and it has a corresponding improvement for Amazon. Although both of these datasets contain two nodes, users and projects, because the Amazon dataset contains only two edge-type interactions, while the YouTube data set contains five edge-type interactions, the nodes contained in the two data sets are related to the number of edges being different, which is also the reason for the different recommendation effects of the two. Since there are five types of edges in the YouTube dataset and there are only two types of edges in the Amazon dataset, our SSN_GATNE-T model can mine more user potential information for recommendations in the correlation between nodes and edge types. Yes, compared to other advanced recommendation models, our model shows a greater improvement on the YouTube dataset than on the Amazon dataset. However, the YouTube dataset contains a total of 2,000 nodes and 1,310,617 edges, and the Amazon dataset contains 10,116 nodes and 148,865 edges. In contrast, the Amazon dataset contains more nodes but fewer edges. The network constructed by the Amazon dataset is simpler than the network constructed by the YouTube dataset in the information it obtains and annotates. Compared with the YouTube dataset, there is less irrelevant information to be excluded. Although the improvement in the Amazon dataset is less than the improvement in the YouTube dataset compared to other models, the final recommendation effect is the best. Yes, we can conclude from its evaluation indexes ROC-AUC, PR-AUC, and F 1 that our model reached 0.9754, 0.9717, and 0.9386, respectively, while only reaching 0.8583, 0.8437, and 0.7812 on the YouTube dataset. In addition, our model has improved the three evaluation indexes of ROC-AUC, PR-AUC, and F1, but the improvement for F1 is more obvious. To this end, we have made separate line graphs of the evaluation metrics of our model and other models for the Amazon and Youtube datasets, as shown in Figs. 4 and 5, to give you a clearer picture.

For the Youtube dataset, it contains user nodes and project nodes, with the user nodes having attributes such as gender, age and address, and the project inputs having information such as movie name and movie genre, and also consisting of five edge types of interaction between different nodes. The user’s hobbies and interests obtained from different interactions in the YouTube dataset are also different and should be treated differently. Our model SSN_GATNE-T will not ignore these node attribute user-item interactions. Compared with the four models (DEEPWalk, metapath2vec, MVE, and PMNE(c)), our model pays more attention to the attributes of nodes and user-item interactions. The five interaction relationships that exist in the YouTube dataset will affect our model. The recognition rate of user-item interactions has increased. Heterogeneous networks can collect more information between users through attribute reuse, and a self-attention mechanism can better mark and obtain the information we need to make more changes for users as good and more suitable recommendations, so its evaluation index has been greatly improved. In comparison with the observations in Table 3, the evaluation index of the LINE model is not very good. Compared with the LINE model, ROC-AUC has improved by +33.61%, PR-AUC by +33.39% and F1 by +25.29%. All three assessment indices of the SSN_GATNE-T model gained a greater or lesser improvement compared to other models outside the LINE model. Therefore, our model SSN_GATNE-T has a good recommendation effect on the YouTube dataset and has a good effect on the three evaluation indexes.

The Amazon dataset includes collaborative viewing and collaborative purchasing links between product attributes and products, which are often overlooked. Our model SSN_GATNE-T does not ignore these node attribute user-item interactions. Compared with the four models DEEPWalk, metapath2vec, MVE, and PMNE(c), our model pays more attention to the node attributes and user-item interactions. Since the interaction relationship contained in the Amazon data set is only the collaborative viewing and collaborative purchase links between product attributes and products, the four models of DEEPWalk, metapath2vec, MVE, and PMNE(c) have good evaluation results on the Amazon data set. Therefore, its evaluation index is less effective than YouTube, a dataset with five interaction relationships. However, our model is still greatly improved compared to the four models of DEEPWalk, metapath2vec, MVE, and PMNE(c). In comparison with the observations in Table 3, the evaluation index of the ANRL model is not very good. Its recommended performance is the worst. Compared with the ANRL model, the SSN_GATNE-T model has increased ROC-AUC by +36.08%, PR-AUC by +38.21%, and F1 by +38.60%. All three assessment indices of the SSN_GATNE-T model received a greater or lesser improvement compared to other models outside the ANRL model. Therefore, our model SSN_GATNE-T has a good recommendation effect on the Amazon dataset, especially the evaluation index F1.

For large network datasets using network embedding methods of the acquisition of correlation information about different nodes and different edge types the models that work relatively well are GATNE-T, GATNE-I, FAME, FANEm and our SSN_GATNE-T model, the evaluation indices of each model are shown in Table 3. The GATNE-T and GATNE-I models are accomplished by dividing the overall embedding of the model into base embedding and edge embedding, and the GATNE-I model also incorporates attribute embedding. Compare with the GATNE-T and GANTE-I models, the edge embedding of SSN_GATNE-T is more powerful because our improved attention mechanism can better aggregate the neighbourhood node information and then obtain more relevant information between the node and edge types for recommendation to improve the accuracy of the recommendation model. Compared to the GATNE-T and GATNE-I models, the SSN_GATNE-T model obtained significant improvements in all three evaluation indices, ROC-AUC, PR-AUC, and F 1, especially the F1 index, for the Amazon and YouTube datasets. On the Amazon dataset, the assessment index F1 improved by +1.07% compared to GATNE-T and by +2.74% compared to GATNE-I; on the YouTube dataset, the assessment index F1 improved by +1.68% compared to GATNE-T and by +1.68% compared to GATNE-I. The FAME and FAMEm models to achieve fast and effective node representation learning by cleverly integrating spectral graph transformations and node attribute features into a sparse random projection system, and although it takes less time to obtain interaction information on nodes and edge types than the SSN_GATNE-T model, the number of interactions it obtains is less than that of the SSN_GATNE-T model. The ultimate goal of acquiring information is to improve the effectiveness of the recommendation performance, and the SSN_GATNE-T model is more capable of acquiring information about potential interactions between different nodes and edge types, which in turn leads to more accurate recommendations. Compared to the FAME and FAMEm models on the Amazon dataset, the SSN_GATNE-T model also achieved significant improvements in the ROC-AUC, PR-AUC and F 1 evaluation indices, with the ROC-AUC improving by 1.71% and 3.88% respectively, the PR-AUC improving by 2.28% and 3.70% respectively, and the F 1 improving by 4.29% and 5.82% respectively. The ROC-AUC increased by 1.71% and 3.88%, the PR-AUC by 2.28% and 3.70% and the F 1 by 4.29% and 5.82%. This can be verified from the comparative information on the evaluation indices between the models in Table 3. Therefore, compared to the GATNE-T, GATNE-I, FAME and FAMEm models, our SSN_GATNE-T model, both for the Amazon dataset and the Youtube dataset, is able to aggregate the interaction information between different edge types of neighbouring nodes of each node very well, and due to the stronger edge embedding capability of our model, we can obtain more comprehensive. The potential interaction information between different nodes and edge types can be more comprehensively captured and used only for recommendation, thus improving the effectiveness of the model’s recommendation performance.

In order to get a clearer picture of the strengths and weaknesses for each model, we have made line graphs of the evaluation results of each model for the Amazon and Youtube datasets. These are shown in Figs. 4 and 5.

In order to get a clearer picture of the strengths and weaknesses for each model, we have made line graphs of the evaluation results of each model for the Amazon and Youtube datasets. These are shown in Figs. 4 and 5. The rising trend of the line graph shows the effectiveness of the SSN_GATNE-T model in processing the data onto the large network model in the Amazon dataset, which can further show that the SSN_GATNE-T is more efficient in acquiring information about the interactions between different nodes and different edge types, and the information obtained is more comprehensive, which in turn improves the effectiveness of the recommendation performance when the information obtained is used for recommendation. The evaluation index of our model SSN_GATNE-T is at the highest point of the line graph, which shows that our model has indeed improved. This shows that our model is more effective than other mainstream recommendation models in processing and analysing the YouTube and Amazon datasets and in making recommendations, which is a testament to the effectiveness of our model.

Since the Adam optimisation approach allows the model to converge faster and then achieve accurate recommendations faster and better, and is also very helpful for model tuning, we have adopted the Adam optimization approach from/to the SSN_GATNE-T model. In optimizing the model, we used not only Adam’s optimisation method but also Adagrad, Momentum, RMSprop and GradientDescent to optimize the model, and the evaluation indices of the recommendation system after optimization is shown in Table 4. Although each optimizer has its own advantages and disadvantages for different datasets, there is still a gap compared to the Adam optimization method, and the network and each parameter of the model are the same when choosing the model optimization method, so the Adam optimization method is chosen for our SSN_GATNE-T model.

Fridman test

In order to better describe the effectiveness of the model, we use the Fridman algorithm to analyse the effectiveness of our SSN_GANTE-T model in obtaining relevance information of small and large networks containing multiple types of nodes and multiple types of edges through attributed multiplex heterogeneous network and an improved attention mechanism, and verify the effectiveness of our model in obtaining the missing information on the interaction between different nodes and different edge types in a large network of hundreds of millions of nodes and the effectiveness of obtaining potential information, and then the effectiveness of the obtained information in improving the accuracy of recommendations when used in a recommendation system.

For both the Youtube and Amazon datasets, we defined four variables, edge_type, node1, node2 and label, to perform non-parametric tests on the results we obtained to check the relevance of the interest implied. node1 and node2 represent user nodes and item nodes respectively. Whether it is the YouTube dataset or the Amazon dataset, we have defined four variables, edge-type, node1, node2, and label, to perform nonparametric tests on the results we obtained to test the relevance. During the analysis process, the five types of interactions of edge-type in the YouTube dataset, including shared friends and shared subscriptions, are represented by 1, 2, 3, 4, and 5, respectively. For the edge-type product attributes in the Amazon dataset and the collaboration between products, the two interactions of view and collaborative purchase links are represented by 1 and 2, respectively, and the label is represented by 1 and 0 to indicate yes or no. For the correlation information between the nodes existing in these two datasets and different types, we use edge-type and label to perform nonparametric tests on the relevant samples of node1 and node2. To this end, we performed a hypothesis test summary and related samples through the Wilcoxon signed rank test summary. Tables 5 and 6 describe the test of the YouTube dataset, and Tables 7 and 8 describe two items of the Amazon dataset. In Tables 5 and 6, which describe the summary statistics of the model on the Youtube dataset, we performed the relevant sample Wilcoxon signed rank test of the model results in the median of the difference between node1 and node2 equal to 0 as the original hypothesis. Test. The summary statistics of the model on the Youtube dataset are described in Tables 4 and 5. We used the median of the difference between node1 and node2 equal to 0 as the original hypothesis to perform the relevant sample Wilcoxon signed rank test on the model results. The total number of samples tested was 262,010, the test statistic was 25,120,694,864.000 and the significance level a was 0.05, when P > 0.05, the original hypothesis is retained, otherwise the original hypothesis is rejected. During the testing of the Youtube dataset, the significance P obtained from the test was 1.000 and the asymptotic significance P from the two-sided test was also 1.000, so the original hypothesis was retained. While Tables 7 and 8 depict the summary statistics of the model on the Amazon dataset, we performed the relevant sample Wilcoxon signed rank test on the model results with the original hypothesis that the median of the difference between node1 and node2 is not equal to 0. The total number of samples tested was 29,488, the test statistic was 234,912,151.00, the significance level a was 0.05, and the significance P obtained from the test is 0. The asymptotic significance P after the two-sided test is also 0, so the original hypothesis is rejected. In the hypothesis testing of the Youtube and Amazon datasets, we also used the Bonferroni adjustment with a more stringent significance level of 0.025 and 0.005 in order to reduce the error in the test results, and the results were the same as those obtained with a significance level of 0.05. The results are the same as those obtained by using a significance level of 0.05. It can be seen that our model provides a stronger boost to the recommendations provided by the processing analysis of the Youtube dataset compared to the Amazon dataset.

Taking the YouTube dataset as an example, we use edge-type and label as the basis to describe the correlation between node1 and node2 through the five interactions they contain and create a continuous field of node1 and node2 that changes with the frequency and total number of nodes. The information histogram is shown in Figs. 6 and 7.

Taking the Amazon dataset as an example, we processed the model on a case-by-case basis, as shown in Table 9. During this process, the missing values of the user and the system are both 0. In our model, this is due to the introduction of attribute reuse heterogeneous network, which indicates the problem of missing information in the process of obtaining potential correlation information between nodes and edge types, making the interactive information we obtain more comprehensive and showing the effectiveness of our model. In addition, we describe the distribution parameters for the estimation of the model as shown in Table 10. We also described the normal P-P graph and detrended normal P-P graph of node2 through edge_types based on node1 and label, as shown in Figs. 8 and 9.

The data and graphs obtained through the Friedman test show that our model has a very obvious effect on the acquisition of the correlation information between each node and different edge-types in the large and small networks, and more potential related information is obtained; moreover, the more effectively we can make accurate recommendations for users. Taking YouTube as an example, our model can identify and obtain more of the five interaction relationships between users and projects: sharing friends, sharing subscriptions, sharing subscribers, and sharing favourite videos, showing the effectiveness of the recommendation effect of our model.

The Friedman test, on the one hand, shows that our SSN_GATNE-T models/modelled does not suffer from missing node information due to the variety and number of nodes and edge types it contains when dealing with large web datasets such as Amazon and Youtube, as evidenced by the zero missing user and item values. On the other hand, the summary of the Wilcoxon signed-rank test and the summary of the node1 and node2 case processing, as well as the estimation of the distribution parameters, demonstrate that the model is more comprehensive in obtaining information about the potential interactions between different nodes and different edge types. Both the absence of missing nodes in the user’s project and the availability of more comprehensive information about the potential interactions between different nodes and different edge types can improve the effectiveness of the recommendation performance by providing the user with more relevant information for the recommendation.

Ablation experiment

In this research, we conducted many experiments on the YouTube and Amazon datasets and obtained the best model settings by improving the model step by step. In the experiments of this article, to obtain more effective information about users and projects and identify more potential interests of users, we first set the parameters of the entire model. The overall and edge-embedding sizes are set to 200 and 10, respectively, the node walking length and number of times are set to 10 and 20, respectively, and the window is set to 5. The number of negative samples L of each positive training sample fluctuates in the range of 5–50. For each edge type r, the coefficients α_r and β_r are set to 1. In addition, the model in this paper is optimized by the Adam optimizer. To prove the validity of the model proposed in this study, we performed ablation analysis on the model itself and compared this model with the model already proposed.

For the hyper parameters of the SSN_GATNE-T model we chose epoch and batch size to tune the accuracy of the model recommendations. When the batch size and other parameters are fixed, the model is tuned by adjusting the epoch to 10, 30, 50, 100, 150 and 200, respectively, to run the model. It was found that the model was not optimal at the end of the run for epoches of 10, 30 and 50, whereas for epoches of 150 and 200, the model reached the optimal solution earlier and then stopped, but the model evaluation results was smaller than the optimal solution obtained for epoch 100. Therefore, if the epoch is chosen to be 100, the final result of the model will be obtained to the optimal solution, neither because the number of iterations is insufficient to reach the optimal solution nor because the model reaches the optimal solution early, which causes the model to be terminated early and the result is not accurate. When epoch was 100 and other parameters were fixed, we determined the size of batch-size to be 64 through experiments, and we also chose batch size of 16, 32 and 128 to adjust the model. The results obtained are not as good as those obtained when the batch size of 128 is chosen, although the convergence time is faster and the training times are faster than that of 64, the accuracy is lower and the evaluation results obtained are not satisfactory. Therefore, the hyper parameters epoch and batch size of SSN_GATNE-T model are 100 and 64 respectively.

In the ablation experiments, we performed the ablation study by deleting or replacing the modules in this model when the epoch and batch size was 100 and 64 respectively and the corresponding parameters were kept constant. In these two data sets, only the attributed multiplex heterogeneous network and the original attention mechanism (GATNE-T) are introduced, and the attributed multiplex heterogeneous network and our improved attention mechanism that introduces the softsign and sigmoid function characteristics (S_GATNE-T), attributes the multiplex heterogeneous network and introduces softsign and sigmoid function characteristics of attention mechanism and adds softsign function characteristics of the fully connected layer (SN_GATNE-T), which attributed multiplex heterogeneous networks and introduced softsign and sigmoid functions The characteristic attention mechanism and the fully connected layer with the softsign function characteristic and the Adam optimizer (SSN_GATNE-T) are used for optimization, and other parameter settings remain unchanged.

From the results of the various ablation experiments shown in Table 11, the attribute multiplexing heterogeneous network and the attention mechanism that introduces the softsign and sigmoid function characteristics, the fully connected layer that adds the softsign function characteristics, and the optimization by the Adam optimizer (SSN_GATNE-T) have an important impact on the recommendation model. The evaluation index ROC-AUC of the model reached 0.8583 and 0.9754 on the YouTube and Amazon datasets, respectively; PR-AUC reached 0.8437 and 0.9717, respectively; F1 reached 0.7812 and 0.9386, respectively. We tested our model on the YouTube dataset and found that compared to only introducing attributed multiplex heterogeneous networks and the original attention mechanism (GATNE-T), our model can better compare the obtained nodes. The relevant information between edge-types is better processed and analysed, so the three evaluation indexes of ROC-AUC, PR-AUC and F1 increased by 1.44%, 2.98% and 1.68%, respectively. Compared to the attribute multiplexing heterogeneous network, we improved the introduction of the attention mechanism (S_GATNE-T) with softsign and sigmoid function characteristics. Our model can better reduce the information mined by the model through the interaction of different node attributes and different edge-types, which can be used for accurate recommendation. The potential information loss is considered, and the recommended evaluation indexes have been increased by 0.96%, 1.98%, and 1.43%, respectively, compared to the attribute multiplexing heterogeneous network and the introduction of the softsign and sigmoid function characteristics of the attention mechanism and the addition of the softsign function. The characteristic fully connected layer (SN_GATNE-T), our model can converge faster and better, and its recommended evaluation indexes have been increased by 0.55%, 0.97% and 0.46%, respectively. Through our SSN_GATNE-T model to test the recommendation effect on the Amazon data set, we found that our SSN_GATNE-T model has improved three evaluation indexes compared with other ablation models, but compared with the improvement of the evaluation index F1, the other two have not improved. The improvement effect of the evaluation index is not as obvious as the improvement of F1. Compared with the GATNE-T, S_GATNE-T and SN_GATNE-T models, the evaluation index F1 of the SSN_GATNE-T model increased by 1.07%, 1.16% and 0.46%, respectively. Compared with other models, our SSN_GATNE-T model can not only better process and analyse the related information between the obtained nodes and edge types but also reduce the number of users that can be mined for accurate recommendation. The loss of potential information, in addition, can make the model converge better. Through the attribute multiplexing heterogeneous network and our improved attention mechanism, we can obtain the user’s potential interests and hobbies for the most suitable recommendations for the user, cooperate with the fully connected layer that introduces the softsign function to process the model, and then optimize the effectiveness of the recommendation model by the Adam optimizer for accurate recommendation effects.

To better describe the improvement in the recommendation performance of each module of our SSN_GATNE-T model in the YouTube and Amazon datasets, we made the experimental results of our model’s ablation experiment on the two datasets into Figs. 10 and 11. The line charts of Fig. 10 show that the progress of each module of our model has greatly improved the recommendation performance of the YouTube dataset. Figure 11 shows that in the Amazon dataset recommendation process, although our model has improved the three evaluation indexes of ROC-AUC, PR-AUC and F1, the most obvious improvement effect is F1, and the improvement of each module has been improved very well, showing the effectiveness of our model in the recommendation system.