1) Node

As shown in Figure 2, the six objects are as follows: students (S), academic performance (P), economic conditions (E), preferred major (M), activity experience (A) and activity category (C). Academic performance (P) refers to the learning situation of a student in a specific course. The academic performance of a student is quantified by dividing the grades in each course. As shown in Figure 2, John’s performance in math class is average; that is, John’s score in math class is 0-70. This type of node helps us integrate information about the student’s academic performance into the network. Economic condition (E) refers to the monthly cost of living of a certain student. We delimit the range of monthly cost of living and indicate it with different nodes to include the student’s economic condition in the network. Major (M) refers to the major that most students prefer when majors are divided, activity (A) refers to the activities that students have participated in during the whole freshman year, and category (C) refers to all types of activities. From the perspective of student ability assessment, activities are divided into five categories: innovation, scientific research, study, practice and social interaction.

2) Edge

As shown in Figure 2, green is used to identify a relation with constraints, and black represents a normal relation. In the relation between students and majors, different attribute values are used to represent different meanings. For example, John’s first preference major is software engineering (SE), so the highest weight is assigned. The second preference, information security (IS), corresponds to the second-highest weight. The relation between students and activities indicates the degree to which a student is interested in an activity. The more students that are interested in the activity, the closer the weight is to 1, and vice versa.

3) When

The WHEN can be represented as $G_{WHEN}=(V,E,M)$ , where $V$ is the object set, $E$ is the relation set, and $M$ is the attribute value set on the relation. In the constructed WHEN, $V=S \cup A \cup M \cup P \cup E \cup C$ and $S$ , $A$ , $M$ , $P$ , $E$ and $C$ are the object sets of six types: student, activity, major, academic performance, economic state and activity category, respectively. For a relation type $R$ connecting object types $X$ and $Y$ , i.e., $X \stackrel {R / R^{-1}}{\longleftrightarrow } Y$ , we can use $E^{X \leftrightarrow Y}$ to denote its relation sets. Therefore, in the constructed WHEN, $E=E^{S \leftrightarrow A} \cup E^{S \leftrightarrow M} \cup E^{S \leftrightarrow P} \cup E^{S \leftrightarrow E} \cup E^{A \leftrightarrow C}$ represents a heterogeneous set of relations in $G_{WHEN}$ . In a recommendation system, we need to focus on user-item relations. In our recommendation framework, the user-item relation can be represented as $S \stackrel {R / R^{-1}}{\longleftrightarrow } A$ and $S \stackrel {R / R^{-1}}{\longleftrightarrow } M$ . We use $\left \langle{ u,i }\right \rangle$ for user-item pairs and $r_{\left \langle{ u,i }\right \rangle }$ for user-item ratings. Given a user-item pair $\left \langle{ u,i }\right \rangle$ , $r_{\left \langle{ u,i }\right \rangle }$ reflects how interested user $u$ is in item $i$ , and the higher $r_{\left \langle{ u,i }\right \rangle }$ is, the more interesting it is. For example, in the constructed WHEN, discrete values are used to indicate students’ ratings for major and activity, with 3 for the most interesting major, 2 for the second most interesting major, and so on. Given ${r_{\left \langle{ s,m }\right \rangle }}{\in M_{1}=\{1,2,3\}}$ , ${r_{\left \langle{ s,a }\right \rangle }}{\in M_{2}=\{1\}}$ , then $M=M_{1} \cup M_{2}$ represents the set of scoring records on different types of relations in the WHEN.

4) When Schema

The schema of the constructed WHEN shown in Figure 3(a) can be defined as $S_{WHEN}=(A,R,W)$ , where $A$ , $R$ , and $W$ represent sets of object types, relation types, and attribute value types, respectively. The schema $S$ is a meta template for WHEN $G=(V,E,M)$ with an object type mapping function $\phi: V \rightarrow A$ , a relation type mapping function $\psi: E \rightarrow R$ , and an attribute value type mapping function between functions $\theta: M \rightarrow W$ . Specifically, $A=\{S,A,M,P,E,C\}$ , $S$ , $A$ , $M$ , $P$ , $E$ and $C$ represent the six node types, $R=\{R_{1},R_{2},R_{3},R_{4},R_{5}\}$ , $R_{1}$ , $R_{2}$ , $R_{3}$ , $R_{4}$ and $R_{5}$ represent the five edge types between nodes of different types, and $W=\{W_{1},W_{2}\}$ , $W_{1}$ and $W_{2}$ represent attribute value constraints on different types of weighted links. It is worth noting that if $|W|=0$ , then the network is called an unweighted HEN. A specific instance of a WHEN is shown in Figure 2.

FIGURE 3.

Metapath selection.

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1) Projected Subnetwork

For a network schema, denoted as $S=(A,R)$ , its projected subnetwork schema [38] can be represented as $S'=(A', R')$ , where $A'\subset A$ , $R{'}\subset R$ . We use $P$ for pivotal-type nodes and $S$ for supportive-type nodes. Nodes in $S$ are associated with nodes in $P$ . $A'$ includes one pivotal type of node and several supportive types of nodes, and $R'$ contains heterogeneous links between different nodes.

$P-S$ is used to denote a projected subnetwork. As shown in Figure 3(b), by continuously selecting a sequence of pivotal nodes $\{C,A,S\}$ , WHEN is projected into an ordered subnet set, represented as (1) $C-\{A\}$ , (2) $A-\{S,C\}$ , and (3) $S-\{P,E,M,A\}$ . As shown in each subnet, we marked the pivotal-type nodes in red. From the perspective of network structure, subnet (1) is a bipartite graph structure, and subnet (3) is similar to the stellate network structure. It is worth mentioning that in network projection, a WHEN may be projected into a set of sequences of WHENs and unweighted HENs. For example, subnet (2) and subnet (3) are WHENs, and subnet (1) is an unweighted HEN. Next, we describe the process of selecting a metapath from each subnet.

2) Extended Metapath

The extended metapath [39] can be expressed as $\rho: A_{1} \stackrel {\delta _{1}\left ({R_{1}}\right)}{\longleftrightarrow } A_{2} \stackrel {\delta _{2}\left ({R_{2}}\right)}{\longleftrightarrow } A_{3} \cdots \stackrel {\delta _{l-1}\left ({R_{1-1}}\right)}{\longleftrightarrow } A_{l}$ , which shows the attribute value constraints on the relations. If there is an attribute value on the relation, the attribute value function $\delta \left ({R}\right)$ represents the range of the attribute value; otherwise, it is an empty set. If the attribute value function $\delta \left ({R}\right)$ on a metapath is not empty, then the metapath is called a weighted metapath. If the attribute value functions $\delta \left ({R}\right)$ on a metapath are an empty set, then the metapath is called an unweighted metapath.

Figure 3(c) shows partial metapaths selected from three projected subnetworks, including three weighted metapaths and three unweighted metapaths. Taking the weighted metapath in Figure 3(c) as an example, the scoring range between $S$ and $M$ is $\{1,2,3\}$ , $S_{1} \stackrel {3}{\leftrightarrow } M_{1}$ denotes that major $M_{1}$ is the first choice of student $S_{1}$ , $S_{1} \stackrel {3}{\leftrightarrow } M_{1} \stackrel {3}{\leftrightarrow } S_{2}$ denotes that both student $S_{1}$ and student $S_{2}$ choose major $M_{1}$ as their first choice. In Table 1, we show all the extended metapaths selected and explain what they mean.

TABLE 1 Extended Metapath and Its Corresponding Semantics

1) Random Walk Strategy Based on an Extended Metapath

Generally, random walks based on metapaths are used to generate the sequence of nodes in the WHEN. For a given unweighted HEN, i.e., $G=(V,E)$ and a metapath, i.e., $\rho: A_{1}\stackrel {R_{1}}{\longrightarrow }\cdots A_{t}\stackrel {R_{t}}{\longrightarrow }A_{t+1}\cdots \stackrel {R_{l-1}}{\longrightarrow }A_{l}$ , the random walk path is generated by formula (2):

View Source\begin{align*} P(n_{t+1}=&x | n_{t}=v, \rho) \\=&\begin{cases} \dfrac {1}{\left |{N^{A_{t+1}}(v)}\right |}, & (v, x) \in E {~\text {and }} \varphi (x)=A_{t+1}\\ 0, & {~\text {otherwise }} \end{cases}\tag{2}\end{align*}

For a given WHEN denoted as $G=(V,E,M)$ and a symmetrical extended metapath denoted as $\rho: A_{1}\stackrel {R_{1}}{\longleftrightarrow }\cdots A_{t}\stackrel {R_{t}}{\longleftrightarrow }A_{t+1}\cdots A_{l-t}\stackrel {R_{l-t}}{\longleftrightarrow }A_{l-t+1}\cdots \stackrel {R_{l-1}}{\longleftrightarrow }A_{l} (A_{t+1}=A_{l-t})$ , the random walk path can be generated by formula (3):

View Source\begin{align*} P(n_{t+1}=&x | n_{t}=v, \rho) \\=&\begin{cases} \dfrac {1}{\left |{N_{w_{t}}^{A_{t+1}}(v)}\right |}, & (v, x) \in E {, } \varphi (x)=A_{t+1} {, }\\ & w_{t}=w_{l-t} {, } w_{t} \in \delta _{t}\left ({R_{\mathrm {t}}}\right) \\ 0, & {~\text {otherwise }} \end{cases}\tag{3}\end{align*}

2) Optimization Objective

Ignoring weighted information, the network can be expressed as $G=(V,E)$ . The corresponding meta template is $S=(A,R)$ with the object type mapping function $\phi: V \rightarrow A$ and link type mapping function $\psi: E \rightarrow R$ . Following metapath2vec, to learn the feature representation of a given vertex $v \in A$ , we maximize the heterogeneous context $N_{t} (v)$ of the node by formula (4) and formula (5):

View Source\begin{align*}&\hspace {-3.2pc}\arg \max _{\theta } \sum _{v \in V}~\sum _{t \in A} \sum _{c_{t} \in N_{t}(v)} \log \mathrm {p}\left ({c_{t} | v; \theta }\right) \tag{4}\\&\log \mathrm {p}\left ({c_{t} | v; \theta }\right)=\frac {e^{x_{c_{t}} \cdot x_{v}}}{\sum _{u \in V} e^{x_{u} \cdot x_{v}}}\tag{5}\end{align*}

In each iteration of optimization, all nodes are traversed, which leads to low efficiency of the whole model. Therefore, we refer to word2vec [27] and adopt the negative sampling method to update only a small part of the model weight in each sample training to reduce the calculation burden and improve the quality of node embeddings. Given a negative sample size $M$ , the optimization objective can be updated to formula (6):

View Source\begin{align*}&\hspace {-2.2pc}\log \sigma \left ({X_{c_{t}} \cdot X_{v}}\right)+\sum _{m=1}^{M} E_{u^{m} \sim P(u)}\left [{\log \sigma \left ({-X_{u^{m}} \cdot X_{v}}\right)}\right] \tag{6}\\&\sigma (x)=\frac {1}{1+e^{-x}}\tag{7}\end{align*}

3) Embedding Fusion on Multiple Metapaths

After optimization, the same node from different input sequences is mapped into different vector spaces. In the directed graph, i.e., $G=(V,E)$ , there is a vertex $v\in V$ . $P$ represents the selected metapath set containing vertex $v$ , while $e_{v}^{(l)}$ denotes the embedding of vertex $v$ on the $l^{th}$ metapath. Thus, $\{e_{v}^{(l)}\}_{l=1}^{|P|}$ represents the set of embeddings on each metapath for vertex $v$ . To make full use of these node embeddings to enhance the recommendation performance, a fusion function $g(x)$ is adopted to fuse the node embedding set into one representation:

View Source\begin{equation*} e_{v}=g\left ({\left \{{e_{v}^{(l)}}\right \}_{l=1}^{|P|}}\right)\tag{8}\end{equation*}

1) Metapaths

To validate the effectiveness of the constructed metapaths, a contrast experiment is designed to compare the activity recommendation performance by adding different metapaths one by one. We use precision, recall, and F1-score as metrics to evaluate recommendation performance.

In this experiment, SAS, SACAS, SMS_2, SMS_3, ACA, SES and SPS are fused in turn. During the fusion process, the changes in the precision, recall and F1-score curves are shown in Figure 5. As each metapath is incorporated, the precision of our method increases gradually, while the recall and F1-score fluctuate slightly. Among the 7 metapaths, there are 4 weighted metapaths SAS, SACAS, SMS_2 and SMS_3, corresponding to $S \stackrel {1}{\leftrightarrow } A \stackrel {1}{\leftrightarrow } S$ , $S \stackrel {1}{\leftrightarrow } A \leftrightarrow C \leftrightarrow A \stackrel {1}{\leftrightarrow } S$ , $S \stackrel {2}{\leftrightarrow } M \stackrel {2}{\leftrightarrow } S$ and $S \stackrel {3}{\leftrightarrow } M \stackrel {3}{\leftrightarrow } S$ , respectively. In addition, there are 3 unweighted metapaths ACA, SES and SPS, corresponding to $A \leftrightarrow C \leftrightarrow A$ , $S \leftrightarrow E \leftrightarrow S$ and $S \leftrightarrow P \leftrightarrow S$ , respectively. Focusing on the precision curve, it is obvious that the addition of each metapath can gradually improve the precision value. With a single metapath SAS, the precision value reaches 56.76%, the recall value reaches a maximum of 46.60% and the F1-score is 51.18%. After that, three weighted metapaths are incorporated in turn, increasing precision by 5.41, 4.06 and 4.05 percentage points, respectively. SCACS results in a slight decrease in recall, but the F1-score has a certain increase at the same time. SMS_2 causes a sharp decrease in the curve of recall and F1-score, while SMS_3 has the opposite effect. According to Table 1, SMS_3 and SMS_2 indicate that students have the same first and second preferences when choosing majors, respectively. For the strong contrast between the effects of SMS_2 and SMS_3 on the recall and F1-score curves, the possible explanation may be that students tend to focus more on primary choices of major rather than secondary choices, which results in SMS_2 containing more noisy information. With the incorporation of the other three unweighted metapaths, the precision value of the recommendation is further improved. ACA, SES and SPS improve precision by 6.76, 4.05 and 4.05 percentage points, respectively. ACA has the highest precision value among 7 incorporated metapaths, increasing the precision value from 70.17% to 77.03% while reducing the recall value from 41.70% to 38.80%, which ultimately results in a decrease in the F1-score from 52.34% to 51.61%. Although SES and SPS have relatively lower precision values, they both slightly improve the recall value and ultimately contribute to the improvement of the F1 score. SES increases the recall value from 38.80% to 39.27%, which in turn raises the F1 score from 51.61% to 52.91%. With the final metapath SPS incorporated, the precision reaches the maximum value of 85.13%, while the F1 score reaches the historical high of 58.39%, and the corresponding recall value is 44.44%. The experimental data show that SES and SPS have improved effects on all three values, while ACA has a greater improvement effect on precision. In our recommendation task, the most important thing is to recommend more accurate rather than comprehensive items because if students are not interested in the recommended activities, their time will be greatly wasted. Therefore, it is worthwhile to sacrifice the recall value in exchange for an increase in the precision value, with the F1 value showing an overall upward trend. Thus, experimental results demonstrate the effectiveness of the chosen metapaths.

FIGURE 5.

Metapath effectiveness.

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2) Graph Embedding Method

In this section, we evaluate the performance of the graph embedding method compared with other methods. We used a WHEN-based embedding method to embed each node of the heterogeneous network into a low-dimensional vector space. Five other graph embedding methods for comparison are briefly introduced as follows:

• Graph factorization (GF) [40]: The adjacency matrix is decomposed to obtain the low-dimensional dense representation of nodes.

• DeepWalk [28]: A method of learning the representation of nodes in a network, which introduces deep learning into the field of network embedding.

• Node2vec [29]: Based on DeepWalk, this method uses two biased random walks (i.e., BFS and DFS) to better explore neighborhoods.

• LINE [30]: This method explicitly preserves both first-order and second-order proximities. It is suitable for a variety of networks, including directed, undirected, binary or weighted edges.

• SDNE [41]: This method uses a deep learning model to capture the nonlinear relationship between nodes.

For the above methods, GF is a traditional method, while DeepWalk, node2vec and LINE belong to the shallow model, mainly using the random walk method. Our method also belongs to the shallow model. SDNE belongs to the deep model, which mainly adopts the deep neural network method. Different graph embedding methods are applied to two recommendation tasks, including student-activity recommendations and student-major recommendations.

As shown in Figure 6(a) and 6(b), the performance was compared in two aspects: student-activity and student-major recommendations. The detailed data are given in Table 3. Obviously, WHEN-based embedding performs better on both tasks than the baselines, ranging from GF to DeepWalk. In the student-activity recommendation task, compared with GF, our method improves RMSE by approximately 84% and MAE by approximately 82%, which is similar to DeepWalk. In the student-major recommendation task, compared with GF, our method improves RMSE and MAE by approximately 60% and 68%, respectively, while node2vec only improves RMSE and MAE by approximately 34% and 26%, respectively. DeepWalk and node2vec are more suitable for homogeneous networks, which contain only one type of node and edge. This means that these three methods ignore the semantics of metapaths shown in Table 1 when dealing with the WHEN. In contrast, our method is more interpretable. LINE and SDNE exploit the first-order proximity and second-order proximity to characterize the local and global network structure. Focusing on the similarity of the network structure, the above two methods cannot distinguish metapaths that have the same structure but contain different semantics, such as $S \stackrel {3}{\leftrightarrow } M \stackrel {3}{\leftrightarrow } S$ and $S \stackrel {3}{\leftrightarrow } M \stackrel {2}{\leftrightarrow } S$ . Taking full account of the weight information in WHEN, our method achieves better RMSE and MAE values than the baselines. Experimental results show that the graph embedding method used in our framework is effective.

TABLE 3 Comparison Between WHEN-Based Embedding and Baselines on Two Recommendation Tasks. For Ease of Reading the Results, We Highlighted the Best Results of the Two Values of RMSE and MAE for Each Task in Bold

FIGURE 6.

Comparison of RMSE and MAE between WHEN-based embedding and baselines on two recommendation tasks. The data are presented in the form of a histogram for easy observation.

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3) Recommendation Method

To evaluate the performance of our model, we use precision, recall, F1-score, RMSE and MAE as evaluation criteria. More details about the compared methods are shown as follows:

• HERec [32]: A general heterogeneous network embedding-based approach for HIN based recommendation.

• User-based CF [42]: User-based collaborative filtering: This algorithm recommends to the user items that other users with similar interests like.

• Item-based CF [43]: Item-based collaborative filtering: This algorithm recommends items that are similar to the user’s previous favorite items.

• SVD [44]: A later factor model for dimensionality reduction, which solves the matrix sparsity and improves the operational efficiency.

• SVD++ [45]: An extension of SVD considering implicit ratings.

Detailed experimental data are given in Table 4. As shown in Figure 7, both user-based CF and item-based CF are classical recommendation algorithms. User-based CF has lower RMSE values and higher precision, recall and F1 score values than item-based CF. The WHEN is a student-centric network that describes similar users, leading user-based CF to outperform item-based CF. SVD and SVD++ are methods of matrix decomposition. The RMSE and MAE values of SVD++ are smaller than those of SVD, while SVD has a higher recall rate and F1 score than SVD++. Compared with SVD, the precision value of SVD++ is improved by 27%. This implies that implicit feedback can significantly improve the accuracy of recommendation results. HERec and our method are graph embedding-based recommendation methods. Our approach improves RMSE and MAE by 91% and 86%, respectively, which are better than HERec. The precision and recall value of our method are improved by 10 and 7 percentage points, respectively, which are also better than HERec. The F1-score value reaches 0.58, which is 17.76% higher than HERec. As mentioned previously, HERec is based on a heterogeneous information network. Its essence is to learn embeddings for users and items, while other types of objects are only used as a bridge to construct the homogeneous neighborhood. Therefore, HERec might lose some important information when building a homogeneous neighborhood. Moreover, our approach is to learn embeddings for different types of nodes directly from heterogeneous neighborhoods, which considers more heterogeneous information. Thus, the performance of matrix decomposition methods is better than that of collaborative filtering methods. In this way, graph embedding-based recommendation methods have the best performance compared to other methods. Compared with other methods, our method can achieve the highest precision, recall and F1-score values, reaching 85.13%, 44.44% and 58%, respectively. The precision value indicates that 85.13% of the activities recommended by the framework are in students’ preferences, or 14.87% are not in students’ preferences. The recall value indicates that 44.44% of the students’ preferred activities are in the recommended list, while 55.56% of their preferred activities are not. The F1-score is used to comprehensively consider precision and recall.

TABLE 4 Recommendation Method Performance Evaluation. The Lower MAE and RMSE and the Higher Precision, Recall and F1-Score Indicate Better Performance. The Best Results are Shown in Bold to Better Observe the Experimental Results

FIGURE 7.

Recommendation method performance evaluation. The data are presented in the form of a histogram for easy observation.

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In summary, our method is more suitable for the educational environment than other recommendation algorithms. By constructing the WHEN, we comprehensively considered various heterogeneous information for each student, including behaviors, interests and economic conditions. Through WHEN-based embedding, rich semantic information can be mined on the specific extended metapaths, which ultimately helps us improve the recommendation performance. Therefore, the new method proposed in this paper can not only help students find online learning resources by using the network according to the historical information of students but also help students who are not divided into majors choose their own majors. It is an effective method to help students fight COVID-19 by using advanced networking technologies.