Multi-grained alignment method based on stable topics in cross-social networks

The original theme

For the blog sets published by users, the Term Frequency-Inverse Document Frequency (TF-IDF) model is adopted to extract the sequence of users’ interested keywords, and K-means clustering (Macqueen, 1967) is carried out. Centroid words of each cluster are taken as the subject words, K original topics and their weights are obtained, and the users’ original interest matrix is formed, as shown in Eq. (1).

(1) $$A_{u_i}=\left(\begin{array}{c}{w}_1\cdot topi{c}_1^{u_i}\hfill \\ w_2\cdot topi{c}_2^{u_i}\hfill \\ ⋮\hfill \\ w_k\cdot topi{c}_k^{u_i}\hfill \end{array}\right)$$

The filter-out of short-time hot topics

Users are extremely vulnerable to the impact of hot events, and their attention to them is relatively concentrated (Nie et al., 2016) in time, which does not mean that users can stabilize the topic. Therefore, this article will find and filter out short-time hot topics with large jitter degrees according to the time slice.

First of all, the weights of the medium are decomposed based on the total number of time slices $A_{u_i}$ $topi{c}_j$ $w_j$ T and the length of each slice t, and the weights of the user topic in each time slice are obtained. The time jitter St of the user topic is defined in Eq. (2).

(2) $$S{t}_{topi{c}_j}^{u_i}={\displaystyle \frac{1}{T}\times \sum _{t=1}^T{\left(w_{j,t}^{u_i}-{\displaystyle \frac{1}{T}\times \sum _{t=1}^T{w}_{j,t}^{u_i}}\right)}^2}$$where $w_{j,t}^{u_i}$ represents the weight of the user's topic in the $u_i$ t time slice, T represents the total number of time slices, and t represents the number of time slices.

According to Eq. (2), the time jitter of all the users’ topics is obtained, which is arranged in ascending order. The higher the degree of the topic, the lower the weight is, and it is called the short-term hot interest that needs to be removed. The top kt topics are selected and the topics with a large jitter degree are cut. For statistical purposes, the weight of the reduced unstable topics is redistributed proportionally. Finally, the users' topic matrix is obtained as shown in Eq. (3), and the filtering process is presented in Algorithm 1.

(3) $${A_{u_i}}^{\mathrm{\prime }}=\left(\begin{array}{c}{w_1}^{\mathrm{\prime }}\cdot topi{c}_1^{u_i}\hfill \\ {w_2}^{\mathrm{\prime }}\cdot topi{c}_2^{u_i}\hfill \\ ⋮\hfill \\ {w_k}^{\mathrm{\prime }}\cdot topi{c}_{k\mathrm{t}}^{u_i}\hfill \end{array}\right)$$

The calculation of users’ topic similarity

The user, $u_i$, topic matrix is extracted and embedded into the ${A_{u_i}}^{\mathrm{\prime }}$ Word2Vec (Mikolov et al., 2013) model based on Chinese Wikipedia training, and weighted summation is employed to generate the user topic vector, as shown in Eq. (4).

(4) $$V_{u_i}=w_1^{\mathrm{\prime }}\cdot \overrightarrow{topi{c}_1^{u_i}}+w_2^{\mathrm{\prime }}\cdot \overrightarrow{topi{c}_2^{u_i}}+\cdots w_{k^{\mathrm{\prime }}}^{\mathrm{\prime }}\cdot \overrightarrow{topi{c}_{k^{\mathrm{\prime }}}^{u_i}}$$

According to the vector sum of users that utilize the theme and $u_i$ is obtained from Eq. (4), the similarity of the theme vector is calculated to obtain the user’s theme similarity, as shown in Eq. (5): $u_i$ $u_j\in U$ $V_{u_i}$ $V_{u_j}$ $Sim\mathrm{\_}Topic(u_i,u_j)$

(5) $$Sim\mathrm{\_}Topic(u_i,u_j)={\displaystyle \frac{V_{u_i}\cdot V_{u_j}}{\left|V_{u_i}\right|\cdot \left|V_{u_j}\right|}}$$

Data preprocessing

For a given social network G, there exists an edge between users in the original network diagram, which is a concerned relationship and cannot reflect the degree of correlation between the two subjects denoted as $u_i$ $u_j$. To better detect the hierarchical community of user topics, this article converts user edge E into a weighted edge, takes the user topic similarity used in Eq. (5) as the edge weight between users, and then transforms social network $\mathrm{\Delta }E$ $Sim\mathrm{\_}Topic(u_i,u_j)$ $u_i$ $u_j$ G into a weighted undirected network graph of users’ topics.

The detection method of users’ hierarchical community topic

The Louvain (Blondel et al., 2008) algorithm is an excellent hierarchical community detection method, that has leading performance in large-scale complex networks, but users without rights affect its effect in special application scenarios. To better detect topics in the hierarchical community, this article updates the user’s edge weights according to the similarity of the users’ topics. The Louvain algorithm (ST-L) is proposed based on stable topics and is divided into two parts: community optimization and community aggregation, respectively. The algorithm assesses which community is more suitable for the nodes in the network based on the community modularity. Q, community modularity, is shown in Eq. (6):

(6) $$Q=\frac{1}{2m}\cdot {\displaystyle \sum _{u_i,u_j\in U}\left[e_{ij}^{\text{'}}-\frac{d_i\cdot d_j}{2m}\right]}\delta \left(c_i,c_j\right)$$where Eq. (6) represents the topic similarity between users, the sum of the theme similarity of all users when connected, respectively, and belongs to, $c_i=c_j$ $\delta \left(c_i,c_j\right)=1$ $\delta \left(c_i,c_j\right)=0$ $e_{ij}^{\text{'}}$ $u_i$ $u_j$ $d_i$ $d_j$ $u_i$ $u_j$ $c_i,c_j$ $u_i$ $u_j$, m represents the sum of the similarity between all users in the network. The larger the value is $\left[-1,1\right]$, the better the structure is:

The core of the algorithm is to compare the modularity of a user before and after joining a community, and the modularity increment is derived from Eq. (6) and presented in Eq. (7): $u_i$ $c_i$ $\mathrm{\Delta }Q$

(7) $\begin{array}{rl}& \mathrm{\Delta }Q=\left[{\displaystyle \frac{d_{in}+d_{i,in}}{2m}-{\left({\displaystyle \frac{d_{ci}+d_i}{2m}}\right)}^2}\right]-\\ & \left[{\displaystyle \frac{d_{in}}{2m}-{\left({\displaystyle \frac{d_{ci}}{2m}}\right)}^2-{\left({\displaystyle \frac{d_i}{2m}}\right)}^2}\right]\\ & ={\displaystyle \frac{1}{2m}\left(d_{i,in}-{\displaystyle \frac{d_{in}\cdot d_{i,in}}{m}}\right)}\end{array}$where Eq. (7) presents the sum of the similarity of users in the community, the sum of the similarity of users connected to other users in the community, and the sum of the similarity of all users connected to each $d_{in}$ $c_i$ $d_{i,in}$ $u_i$ $c_i$ $d_{ci}$ $c_i$, respectively.

After obtaining the modularity increment, community optimization can be carried out. A different user group is initialized for each user on the network $\mathrm{\Delta }Q$. When partitions are initialized, the number of user groups will be as large as the number of users. Then, for each user and its neighbor users, the modularity increment is calculated by placing it in the user group that will be removed from its user group and placed in the user group with the largest modularity increment $u_i$ $u_j$ $u_i$ $u_j$ $u_i$. If so, the original user group stays there. When $\mathrm{\Delta }Q<0$ this process is repeated and applied sequentially for all users (the ordering of users has no significant effect (Blondel et al., 2008) on the obtained modularity increments) until completed.

Figure 2 depicts that seven user groups, c^0x, are supposedly obtained from the first part of the algorithm where x denotes the group serial number such as c⁰¹: {1,3,9,10,15}, c⁰²: {2,6,12}, c⁰³: {4,5,11,13,17}, c⁰⁴: {7,8,14,16}. Each number represents a user; the edge indicates that there is a relationship between users to be followed. The users in the same dotted box are considered to be divided into the same group, indicating that the user theme is similar. The structure in groups c⁰⁵, c⁰⁶, and c⁰⁷ and the connection relationships with other groups are omitted for the sake of simplification.

The next step is group aggregation; that is, the user group obtained in the first part is iterated upward, and the weight of the edge between them is the sum of the weight of the edge between the nodes in the corresponding two groups. Then, the algorithm for the first part is iterated on this new graph. After the algorithm of the first part is completed, the second part can be employed to generate a higher-level structure graph. The MGA adopts a three-layer structure, and the results of the top three layers are sparse (Blondel et al., 2008).

Figure 3 depicts that after the first part of the algorithm is completed, the second part is iterated to the upper layer. The first iteration is presented as follows: for the user group c⁰²⁰¹, c⁰³, c⁰⁴, c¹², and c⁰⁷ communities c¹¹, c⁰⁵, c⁰⁶, and C¹³, respectively. The second iteration of community c¹¹, c¹², c¹³ constitutes community c²¹.

The extraction of topic features

For the communities in the source social and the target social networks, the two communities can be regarded as the anchor communities denoted $G$ $G^{\prime }$ (Sun et al., 2020) after they are aligned. The communities connected with the anchor community pair are respectively in the middle and are called the connected community pair, that is, the community pair to be aligned denoted $G$ $G^{\prime }$.

After the first round of community detection is completed, users form a group, continue to conduct community detection, and aggregate into the upper community. In this process, each group will produce a group theme feature because it is close to the group member theme vector. The user theme vector is also very close to the community theme feature points, and there are a large number of edge points, which are in the middle of the two feature points. If it is directly forced to be classified into one class and the feature points are updated at this distance, the accuracy will be reduced $V_{c^{jh}}$. The fuzzy centre-based clustering (FCM) algorithm (Naderipour, Fazel Zarandi & Bastani, 2022) proposed the idea of fuzzy classification, and the clustering result was expressed as the sample belonging to all kinds of probability matrices, which effectively improves the classification effect of edge users. Therefore, the article introduced the correlation degree matrix between the user theme vector and the community feature points, as shown in Eq. (8).

(8) $$S^{\beta }=\left(\begin{array}{c}d\left(V_{u_1},CTopi{c}_1^{V_1^{jh}}\right),\cdots d\left(V_{u_1},CTopi{c}_z^{V_1^{jh}}\right)\hfill \\ d\left(V_{u_2},CTopi{c}_1^{V_2^{jh}}\right),\cdots d\left(V_{u_1},CTopi{c}_z^{V_2^{jh}}\right)\hfill \\ ⋮\hfill \\ d\left(V_{u_a},CTopi{c}_1^{V_a^{jh}}\right),\cdots d\left(V_{u_a},CTopi{c}_z^{V_a^{jh}}\right)\hfill \end{array}\right)$$

The correlation matrix is optimized and updated by a gradient descent algorithm to obtain the best features $V_{c^{jh}}$. It is a multi-dimensional topic vector, which can represent the theme features of a whole group or community to the greatest extent $V_{c^{jh}}$. Equation (9) presents it.

(9) $$V_{c^{jh}}=\left(\begin{array}{c}CTopi{c}_1^{c_i^{jh}}\hfill \\ CTopi{c}_2^{c_i^{jh}}\hfill \\ ⋮\hfill \\ CTopi{c}_z^{c_i^{jh}}\hfill \end{array}\right)$$

To achieve the optimality, the objective function presented in Eq. (10) is constructed as $V_{c^{jh}}$.

(10) $$f(\beta )=\{\begin{array}{c}\sum _{a=1}^N{\sum _{b=1}^Z{S}_{ab}^{\beta }\Vert V_{u_a}-CTopi{c}_b^{c^{jh}}\Vert }^2\hfill \\ \sum _{b=1}^Z{S}_{ab}^{\beta }\ge 1\hfill \end{array}$$where the user is the weighted constant, the topic vector of the user, and a topic feature point in the topic feature are denoted by $\beta$ $u_a\left(1\le a\le N\right)\in c^{jh}$ $V_{ua}$ $u_a$ $CTopi{c}_1^{c_i^{jh}}$ $c^{jh}$ $V_{c^{jh}}$, respectively, b is the number of the feature points, indicating the correlation degree between the user’s topic vector and the feature points, the problem is transformed into a minimum problem $S_{ab}^{\beta }$ $f(\beta )$. The sum of the correlation degree of each user’s theme vector is adjusted to the condition that it is greater than or equal to 1, and arranged to attain Eq. (11) as shown $u_a$ $V_{ua}$ $CTopi{c}_1^{c_i^{jh}}$.

(11) $$\begin{array}{rl}& f(\beta )=\sum _{a=1}^N{\sum _{b=1}^Z{S}_{ab}^{\beta }\Vert V_{u_a}-CTopi{c}_b^{c^{jh}}\Vert }^2+\\ & \sum _{b=1}^Z{\mu }_b\left(1-\sum _{a=1}^N{S}_{ab}^{\beta }\right)\end{array}$$where ${\mu }_b$ represents any coefficient and the partial derivative of Eq. (10) is equal to 0, and its iterative equation is obtained as shown in Eqs. (12) and (13) $S_{ab}^{\beta }$ $CTopi{c}_b^{c^{jh}}$.

(12) $$S_{ab}^{\beta }={\left(\sum _{k=1}^Z\left({\displaystyle \frac{\Vert V_{ua}-CTopi{c}_b^{c^{jh}}\Vert }{\Vert V_{ua}-CTopi{c}_k^{c^{jh}}\Vert }}\right)\right)}^{-1}$$

(13) $$CTopi{c}_b^{c^{jh}}={\displaystyle \frac{\sum _{a=1}^N{S}_{ab}^{\beta }\cdot V_{ua}}{\sum _{a=1}^N{S}_{ab}^{\beta }}}$$where k denotes the number of iterations. When the iteration is terminated, it means that the iterative change of the user theme vector and the correlation degree of feature points is small, and no further optimization is required. Algorithm 2 presents the steps of $\mathrm{\nabla }{S}_{ab}^{\beta }<\epsilon$.

The alignment method of multi-granular community

For the communities and groups in source social network G and target social network, the topic features are obtained in the same vector space based on Algorithm 2, and pair-to-pair alignment is carried out at the same level, as shown in Eq. (14) $G^{\mathrm{\prime }}$.

(14) $$Sim\mathrm{\_}{V}_c=\frac{{\displaystyle \sum _{b=1}^z(CTopi{c}_b^{c^{jh}}\times {CTopi{c}_b^{c^{jh}}}^{\mathrm{\prime }})}}{\sum _{b=1}^z\left|CTopi{c}_b^{c^{jh}}\right|\times \sum _{b=1}^z{\left|CTopi{c}_b^{c^{jh}}\right|}^{\mathrm{\prime }}}$$

Because the calculation is conducted on the same dimensional matrix, the distance operation with () $V_{c^{jh}}$ ${V_{c^{jh}}}^{\prime }$ $V_{c^{jh}}$ ${V_{c^{jh}}}^{\prime }$ T can be performed to obtain a square matrix; the module of the square matrix is the similarity of two communities or two user groups, respectively.

This article adopts the alignment method of multi-granularity iteration from the upper large community with coarser granularity to the lower level concerning running order. Figure 3 shows the community structure. Figure 4 depicts that C²¹ and C²¹ are the highest-level communities and have completed the alignment. When the iteration reaches 21, the insides of C ²¹ and C are aligned with their internal sub-communities. In this round, C ¹²¹² and C are aligned, and the iteration continues to its internal user group. The user group C ^05'05 is aligned with C and continues iterating into two user groups for user matching.

User alignment

When user groups are aligned in the source social network G and the target social network, user members can match users based on users’ attribute data. For two groups of small users with highly similar themes, the attribute difference is an efficient way to distinguish them $G^{\mathrm{\prime }}$. Similar user names (Yuan et al., 2021) and user profiles such as profile, education, unit, etc. (Zeng et al., 2021) are important representations of users’ characteristics. Therefore, based on the document similarity algorithm (Kusner et al., 2015), this article employs the combination of user name similarity and personal data similarity to treat users and score matched users. Equation (15) gives the calculation of user attribute similarity.

(15) $$Sim\mathrm{\_}A(u,u^{\prime })=\underset{P\ge 0}{min}\sum _{i,j=1}^n{P}_{ij}{D}_{ij}$$where Eq. (15) represents the best conversion matrix and the word shift distance $P_{ij}$ $D_{ij}$.

Evaluation index of the original and stable topic number of users

The contour coefficient is used to evaluate the clustering effect of user topics represented by Eq. (16).

(16) $$s(i)={\displaystyle \frac{b(i)-a(i)}{max(a(i),b(i))}}$$where Eq. (16) represents the average distance between $a(i)$ i and other samples of the same cluster and the minimum average distance between $b(i)$ i and other clusters, respectively.

Topic jitter time is used to evaluate the effect of stable topic selection, as shown in Eq. (16).

Evaluation index of feature points

Feature density (Naderipour, Fazel Zarandi & Bastani, 2022) is used to evaluate the effect of feature extraction on community themes represented by Eq. (17).

(17) $$\mathrm{\Delta }dense=avg({\displaystyle \frac{\left|\left\{(p,q)|p,q\in i{n}_i,(p,q)\in i{n}_i\right\}\right|}{\left|\left\{i{n}_i\right\}+\left\{ou{t}_i\right\}\right|})}$$where Eq. (17) represents the sample point, the edge collection of feature points within the link cluster, and the edge collection of feature points outside the link cluster $p,q$ $i{n}_i$ $ou{t}_i$, respectively.

Evaluation index of community detection

Normalized mutual information (NMI) and modularity indexes are mainstream indicators (Wang, Hao & Guan, 2020) used to evaluate the performance of community detection, respectively. They are presented in Eqs. (18) and (19).

(18) $$NMI={\displaystyle \frac{2\ast I(U,V)}{H(U)+H(V)}}$$where U, V, I, and H represent real classification, the results of the classification, interactive information, and cross-entropy, respectively.

(19) $modularity=\sum _{i=1}^n\left[{\displaystyle \frac{L_i}{TL}-{\left({\displaystyle \frac{D_i}{TL}}\right)}^2}\right]$where $L_i$ represents the total number of edges in the community, i is the sum of vertex degrees in the community i, $D_i$ TL is the total number of edges, NMI measures the similarity between the algorithm’s running result and the preset label. Modularity measures the inner tightness of the community.

The evaluation indicators of the alignment performance

The Accuracy index is used to detect alignment accuracy (Chen et al., 2017) across network communities and user groups, represented by Eq. (20).

(20) $$Accuracy={\displaystyle \frac{1}{NC}{\sum }_0^{\mathrm{j}}{\sum }_0^{h}success\left(c^{jh},{c^{jh}}^{\prime }\right)}$$where NC represents the total number of communities and user groups; if the alignment of users exceeds 20% of the total number, one is returned. Otherwise, 0 is returned $c^{jh},{c^{jh}}^{\prime }$ $success\left(c^{jh},{c^{jh}}^{\prime }\right)$.

The metrics used for user alignment accuracy are called precision, recall, and F1 values, respectively.

Analysis of users’ original topic number k and users’ stable topic number kt

In this article, the TF-IDF model was used to analyze users’ interests, and then 50 keywords with the highest frequency and at least ten occurrences were selected after the stop words were removed. K-means clustering was performed on the keyword sequence to generate K original topics. Figure 5 shows the change in the average contour coefficient when the value of k topic numbers changed from [2, 20]. Figure 6 depicts that both Zhihu and Weibo users reach the local optimal average contour coefficient when k takes a value of 12. In subsequent experiments, users of the two networks are processed together to analyze parameter selection, and the original topic takes a value of 12 to carry out a short-time hot spot filtering discussion.

When short-term hot topics are filtered out, the change of the statistical trend for users’ topics tends to be flat (Ni, 2020) according to monthly observations. Therefore, the time slice t in this article takes a month as a unit, and a total time length of 12 months is selected. According to Eq. (2), the jitter degree of the 12 original topics of users is calculated and arranged in ascending order. Figure 6 shows the average jitter degree of users’ original topics. The average jitter degree of the 9th topic is significantly higher than that of the 8th topic. Concluded that kt = 8 can achieve the optimal experimental state, and the user topic becomes the most stable.

Z-analysis of community theme feature points

The number of feature points z for the theme feature is related to the accuracy of describing the community theme features. If the z value is too small, the feature is too general and not accurate enough; on the other hand, if it is too large, it is too sparse. In this article, weighted and termination constants, $\beta =2$ $\epsilon ={10}^{-17}$ (Hu & Chan, 2015), are selected when the performance of the fuzzy algorithm for theme features becomes relatively stable (Naderipour, Fazel Zarandi & Bastani, 2022). Figure 7 shows the density change of theme features when the number of feature points z ranges from 2 to 13. It is seen that when z is assigned to 6, the density of community theme features is 0.28 to achieve local optimization. When the number of community theme feature points reaches 6, the aggregation effect of users’ theme vectors in the community becomes the best. Therefore, the number of feature points z takes the value of 6 in the subsequent experiment.

Performance analysis of topic-based hierarchical community detection

To evaluate the performance of the ST-L algorithm, the following community detection models are used to compare.

GEMSEC (Rozemberczki et al., 2019): Community single-layer self-clustering based on machine learning to regularize users’ social attributes.

vGraph (Sun et al., 2019): Based on the probability generation model that implements users’ information to predict interaction probability, single-layer community detection.

UICD (Jiang et al., 2022): Based on UGC that obtains users’ interest through the LDA algorithm and uses interest for single-layer community detection.

HIOC (Zheng et al., 2019): Based on corpora fixed label classification, hierarchical community detection is carried out by user interest and label similarity.

ReinCom (Ding et al., 2021): Users’ characteristics are learned based on a deep learning model, optimizing community tree, and hierarchical community detection algorithm.

Since Weibo and Zhihu data sets have no preset classification, they cannot obtain the NMI index, so the NMI index is only discussed in the Aminer and Cora data sets. The detailed experimental data are shown in Table 1. The six algorithms have better effects on the Aminer and Cora data sets than on the Weibo and Zhihu data sets. Because Aminer and Cora are public data sets with preset classifications, users have high convergence according to classification. At the same time, for the four data sets, the NMI and modularity performance of the hierarchical community detection method is significantly superior to those of the single-layer community detection algorithm, indicating that the adoption of hierarchical community detection is effective. Among the hierarchical community detection algorithms, ST-L and ReinCom are superior to the HIOC algorithm, with fixed classification labels and multiple user detection in each data set. When compared with ReinCom in Aminer and Cora, respectively, the ST-L has increased the NMI index by 14.8% and 2.6%, while the modularity index has increased by 1.8% and 2.1%. In Weibo and Zhihu, the modularity index improved slightly. In general, the ST-L makes full use of subject features and adopts the non-fixed label layering mode to improve the performance of the data set.

The performance analysis of the community alignment

To better evaluate the community alignment performance of the MGA, this article compares it with the following algorithm on the microbot-Zhihu dataset.

CAlign (Chen et al., 2017): Based on user attributes, Dirichlet distributed clustering is used to build communities, and cross-network community alignment is performed.

PERFECT (Sun et al., 2020): The cross-network user information is embedded into the hyperbolic space based on the Poincare sphere model, clusters the users within the hyperbolic distance threshold into communities, and aligns the communities by the hyperbolic distance of each user.

Detailed experimental data are shown in Table 2. The MGA improves the accuracy of community alignment by 6.1% and 2.5%, respectively, when compared with CAlign and PERFECT algorithms, which proves that the MGA adopts multi-granularity fuzzy topic feature alignment and effectively reduces the influence of edge users on community alignment accuracy when compared to forced clustering method (Naderipour, Fazel Zarandi & Bastani, 2022).

The performance analysis of user alignment

To better evaluate the MGA user alignment performance, this article will use the mainstream user alignment algorithm to compare the micro-blog Zhihu dataset.

BSNA (Yuan et al., 2021): Based on the BP neural network, the user name is uniformly mapped, the problem is transformed into a vector mapping problem, and the user alignment is performed.

PERFECT (Sun et al., 2020): The cross-network user information is embedded into hyperbolic space based on the Poincare ball model and aligns users by hyperbolic distance between vectors.

UGCLink (Gao et al., 2021): UGC is modelled based on a convolutional neural network and aligns users by the relationship between content and time.

MEgo2Vec (Zhang et al., 2018): Self-centred network based on graph neural network mining user attributes and structure for user alignment.

MUIUI (Zeng et al., 2021): Based on the three characteristics of user attributes, generated content, and relationships, a fusion classifier carries out user alignment.

The precision, recall, and F1 values of each comparison algorithm and the MGA algorithm are shown in Table 3. It was found that the performance of the BSNA algorithm for vector mapping alignment based only on user name is inferior to other algorithms, indicating that the accuracy of the alignment method based on a single feature is low. Similarly, the UGCLink algorithm based on UGC combined with time features and the PERFECT algorithm based on user topology embeddings that are combined with a small number of attribute features have improved performance, but the MEgo2Vec and MUIUI algorithms are significantly superior to the previous two algorithms. When compared with MEgo2Vec and MUIUI, respectively, the proposed MGA algorithm has improved the accuracy rate by 4.5% and 3.4%, the recall rate by 2.7% and 2.1%, and the F1 value by 3.4% and 2.5%, respectively. As the MGA fully utilizes the topic features generated by UGC, performing community detection before user alignment reduces the interference of user pairs with similar attribute features to a certain extent. The MGA has richer granularity choices than the two multi-granularity alignment algorithms.

The experimental results demonstrate that the MGA algorithm fully leverages UGC and integrates time characteristics comprehensively. It acquires the user stability theme, conducts hierarchical community detection, and performs cross-network multi-granularity alignment. The algorithm successfully addresses the issue of excessive users at the community edge, leading to improved accuracy, recall rate, and F1 values in user alignment by incorporating user attribute characteristics.