2.1

Heterogeneous networks

A heterogeneous network means that there is more than one type of node and edge, which can be G = (V,E,T) to represent that V is the set of nodes, E is a set of edges, and T is a set of all types in the network.

As an example, the network in Figure 1 is given as a network G^s = (V^S,E^S,T^S), where T^s = {t₁, t₂ ⋯t_p}, represents p the different node types, and , represents the n nodes in the network and each specifies the type of that node, . Figure 1 will also be used as an example in the next presentation.

Figure 1.

Two citation networks and predefined meta-paths.

2.2

Meta-path fusion vector

A meta-path is a path containing a sequence of relations, such as the relation A-P-V in Figure 1, which is: author A publishes a paper P in journal V. The meta-path fusion vector proposed in this paper refers to the use of attention mechanism to fuse the features of all nodes on a meta-path to the first node (the node usually represents the user node in social networks) as a way to obtain information about the locality.

Given a node , the set of other nodes on the meta-path is given by , the 𝑡𝑟 ∈ 𝑇 to denote. For any After one layer of initial linear transformation to obtain , the nodes that would be obtained after one layer of GAT The features of other nodes on the meta-path, i.e., the meta-path fusion vector, are denoted by to represent.

2.3

Global fusion vector

Given a user node that is obtained after the first layer , then use the attention and followed information between users, and use the attention mechanism in the second layer to put , the user neighbors of , and k ∈ all of them are fused, i.e., we get the global fusion vector .

2.4

User identity alignment

Given two heterogeneous social networksG^s = (V^S,E^S,T^S) andG^g = (V^g,E^g,T^g) that are also known to have anchor links denote G^s in and G^g in belong to the same natural person. The problem of user identity alignment is then given on the basis of which i ∈ n, the k ∈ (for G^g network as well), finding G^s and G^g two other users in the network that belong to the same natural person .

3.1

Meta-path fusion vector

The meta-path fusion vector is generated by the first layer of GAT. Here we take G^s network as an example, for each node we first go through a layer of initialization to reduce it to a representation of f. For nodes with textual content (e.g., tweets and user profiles) we use Word2Vec to initialize their dimension feature vectors, and for nodes that are not textual, we use random initialization to represent them.

For each feature vector node, as shown in Figure 2, a linear transformation is first performed to obtain the weight matrix W ∈ R^fxf’, which can turn the initial feature vector into a higher latitude vector, denoted by to represent. At this point, a point is selected to be shown in Figure 2 . For example, its high-latitude feature vector is , according to the predefined meta-path, to direct the attention mechanism of this layer to notice only the feature vectors on the meta-path, and to fuse these vectors into . According to the predefined meta-path: (t₁, t₂, t₃), it is possible to find need to pay attention to the node , and from equation (1) it is possible to sum each node vector on the meta-path with the attention coefficients when performing fusion.

Figure 2.

MGUIL: Extraction of the final representation by two layers of GAT.

where are the dimension f input feature vector, W is f × f’ the dimension weight matrix, after the eigenvectors are combined, thus is the dimension vector of 2 x f’.

Then we have to calculate · for the final attention coefficients since we want to calculate the impact of each meta-path node on (including the effect of itself), so a normalization operation is performed on the attention coefficients.

After that, the feature fusion operation can be performed, and each feature on the meta-path is fused according to the attention factor according to equation (3), including self-attention.

In this paper, in order to enhance the fusion of relevant features, a multiple attention head mechanism is used for the meta-path fusion vector, where K represents the number of attention heads, thus can be expressed as equation (4).

Where and and W^k represent the k’th attention coefficient and weight matrix.

3.2

Global fusion vector

After the first layer of GAT, we get the meta-path fusion vector that fuses all of its own features. In the second layer, it will focus on fusing the features between user type nodes, and since the meta-path fusion vector already carries all of the user’s information, it can be concluded that the second layer is a global feature fusion. Then the influence between each user type node is shown in equation (5), and the final attention coefficient is shown in equation (6).

where are the dimension f’ input feature vector, and M is the f’ x f” the dimension weight matrix, the after the eigenvectors are combined, so is the 2 × f” the vector of dimension.

The final global fusion vector is obtained by weighting all the node type vectors based on the calculated attention coefficients according to equation (7).

So far, in order to ensure that our extracted features can be well represented both locally and globally, the first GAT layer and the second GAT layer are combined together, i.e., the combined vector, as shown in Figure 2. In the case of G^s and G^g After performing the same operation, we can map the nodes in these two networks into a low-dimension space, and then we can perform user identity alignment in the low-dimension space. It is worth noting that in some cases the node types in the two networks do not coincide, in which case one should align to the one with more node types and initialize the feature vector of the missing node type in the other network to f dimension all zeros.

3.3

User alignment model

Based on the above two operations, the high latitude nodes of two networks can be mapped to the same low latitude space. At this point, we can determine whether the two final combined vectors are the same natural person based on their similarity/distance. Already existing anchor link , it is now necessary to map the anchor links from G^s and G^g network to find the user and they belong to the same natural person, so there is an anchor link . We should make the distance between two vectors belonging to the same natural person on the low-dimension space as small as possible, and make the distance between vectors not belong to a natural person on the low-dimension space as large as possible, so the loss function is as equation (8).

where d is a distance function, and the Chebyshev Distance is used in the text to calculate the distance between the metapath fusion vector and the global fusion vector of both, respectively. represents the distance between the user with which this node is related, i.e., from the combined vector of that user. w and λ are used as hyperparameters to balance the effect of the meta-path fusion vector and the global fusion vector on the results, and .

4.1

Datasets

Twitter-Foursquare is a heterogeneous pair of networks in which node types include users, tweets, and geographic locations^{17, 18}. Foursquare is a platform that encourages mobile phone users to share information such as their current location with others. The details of this dataset are listed in Table 1.

Table 1.

Twitter-foursquare dataset.

4.2

Baselines

To evaluate the performance of the proposed MGUIL, we compare our framework with the following state-of-the-art methods:

4.3

Comparison of experimental results

In the experiments, the hyperparameters of the proposed method MGUIL in this paper w = 0.6, K = 3. f’ = 256 and f” = 128. And the methods in BaseLines are set to be consistent with those in the original paper. Table 2 shows the performance of each method, using the evaluation metrics Precision@k (P@k) and MAP¹⁹.

Table 2.

Twitter-foursquare dataset.

Note: * Means the method works best.

From Table 2, it can be found that:

4.4

Hyperparameter setting experiment

After comparing with baselines’ method, we then set the values of the hyperparameters in MGUIL differently to evaluate the effect of different hyperparameter settings on the results of this model, as a way to find the best hyperparameters for MGUIL.

w and 𝜆 are hyperparameters used to balance the influence of meta-path fusion vectors and global fusion vectors on the final combined vector, and it can be seen from Figure 3a that MGUIL has the best effect when w = 0.6, which indicates that there is a balance point between the meta-path fusion vector and the global fusion vector and that the influence of the meta-path fusion vector on the combined vector is somewhat more important than that of the global fusion vector in terms of the percentage.

Figure 3.

Effect of equilibrium factor w, number of multiple attention heads k, embedding dimension on the results.

Since the multiple attention head mechanism is introduced in the first layer of GAT, the number of attention heads K also affects the final effect. As can be seen from Figure 3b, the full capability of the model can be best exploited at K=4. In short, setting a small K value may lead to incomplete feature fusion and not extracting deeper information. Setting a large K value may lead to too much noise introduced in the fusion process and affect the accuracy of the features.

The choice of the embedding dimension determines the complexity of the potential space, and in this paper, we choose 128 dimensions as the final dimension. As shown in Figure 3c, better results can be obtained at 128 dimensions.