Integrated anchor and social link predictions across multiple social networks

Abstract

In recent years, various online social networks offering specific services have gained great popularity and success. To enjoy more online social services, some users can be involved in multiple social networks simultaneously. A challenging problem in social network studies is to identify the common users across networks to gain better understanding of user behavior. This is referred to as the anchor link prediction problem. Meanwhile, across these partially aligned social networks, users can be connected by different kinds of links, e.g., social links among users in one single network and anchor links between accounts of the shared users in different networks. Many different link prediction methods have been proposed so far to predict each type of links separately. In this paper, we want to predict the formation of social links among users in the target network as well as anchor links aligning the target network with other external social networks. The problem is formally defined as the “collective link identification” problem. Predicting the formation of links in social networks with traditional link prediction methods, e.g., classification-based methods, can be very challenging. The reason is that, from the network, we can only obtain the formed links (i.e., positive links) but no information about the links that will never be formed (i.e., negative links). To solve the collective link identification problem, a unified link prediction framework, collective link fusion (CLF) is proposed in this paper, which consists of two phases: step (1) collective link prediction of anchor and social links with positive and unlabeled learning techniques, and step (2) propagation of predicted links across the partially aligned “probabilistic networks” with collective random walk. Extensive experiments conducted on two real-world partially aligned networks demonstrate that CLF can perform very well in predicting social and anchor links concurrently.

Appendix

Social features of anchor links have been introduced in previous part, in this part, we will introduce the social features of social links and spatial distribution features, temporal distribution features and text usage features of both anchor links and social links.

1.1 6.1. Social features

See Table 3.

Table 3 Social features defined for social link (u, v)

$\Gamma (u)$ is the set of neighbors of user u.

In addition to social information, we also extract features from users’ location check-ins. For a certain anchor/social link (u, v), we can get the locations that u and v have been to $\Phi (u)$ and $\Phi (v)$, respectively. Since each user can visit a location many times, we construct vector l(u) and l(v) for u and v, respectively, each cell in which record the times that u and v visit a certain location in $\Phi (u) \cup \Phi (v)$.

1.2 6.2. Spatial distribution features

See Table 4.

Table 4 Spatial distribution features for link (u, v)

Similarly, we can get the set of locations that u has visited from the networks, $\Phi (u)$. For a certain anchor/social link (u, v), we can extract the spatial distribution features for it with those summarized in Table 3 except the “Adamic/Adar” measure based on $\Phi (u)$ and $\Phi (u)$.

1.3 6.3. Temporal distribution features

See Table 5.

Table 5 Other frequently features for link (u, v)

Users’ temporal activity information is also used to extract features for link (u, v). Each day is divided into 24 h slots, and the number of online posts published at certain hours is stored in vector ${\mathbf {x}}(u)$ and ${\mathbf {x}}(v)$, from which we can extract $IP({\mathbf {x}}(u), {\mathbf {x}}(v))$, $ED({\mathbf {x}}(u), {\mathbf {x}}(v))$ and $CS({\mathbf {x}}(u), {\mathbf {x}}(v))$ summarized in Table 5 as the temporal distribution features of link (u, v).

1.4 6.4. Text usage features

For a certain link (u, v), we can get the words that u and v have used in the past and group them as two bag-of-words vectors, ${\mathbf {x}}(u)$ and ${\mathbf {x}}(v)$, weighted by TF-IDF. From ${\mathbf {x}}(u)$ and ${\mathbf {x}}(v)$, we also extract $IP({\mathbf {x}}(u), {\mathbf {x}}(v))$, $ED({\mathbf {x}}(u), {\mathbf {x}}(v))$ and $CS({\mathbf {x}}(u), {\mathbf {x}}(v))$ summarized in Table 5 as the text usage features of link (u, v).