# User Trust Inference in Online Social Networks: A Message Passing Perspective
## 3 The Proposed Model
### Prerequisites
* It might be possible that [PERSON] would trust [PERSON] at some time later, but at the time we observe the social network or capture a snapshot of the network as a dataset, [PERSON] does not know [PERSON] yet or [PERSON] does not claim to trust [PERSON] yet, so the trust relationship from [PERSON] to [PERSON] does not exist. * [PERSON] does trust [PERSON] and the trust relationship does exist in the real network, but it is missing from the dataset we observe. The cause could be the inability of capturing the whole network or capturing their relationship data being prohibited by the privacy preference settings of relevant users. This uniqueness of trust in OSNs makes trust inference in OSNs quite different from general link prediction problems and general binary classification tasks. Since we only focus on inferring trust relationships in online social networks without any distrust information, as a binary classification task, the goal of our proposed model is to find as many trust relations as possible, and in the meantime, maintain considerable overall accuracy. Further discussion on this assumption is beyond the scope of this paper, and it will be left for future work. **Assumption 5**. : _Trust is propagative but not fully transitive, so it will be beneficial for us to learn under what criteria trust can be transferable from one user to another._  
For example, if [PERSON] trusts [PERSON] and [PERSON] trusts [PERSON], [PERSON] can derive some amount of trust on [PERSON] based on how much she trusts [PERSON] and how much [PERSON] trusts [PERSON], but [PERSON] may not trust [PERSON] or even she does not know [PERSON]. However, under some particular circumstance which is what we need to learn, [PERSON] will trust [PERSON]. Based on this assumption, we propose two primary trust propagation strategies below so that our model can learn from more complex trust relationship topology that commonly exists in real-world datasets:  
* Direct trust propagation may exist from [PERSON] to [PERSON] when [PERSON] trusts [PERSON] and [PERSON] trusts [PERSON]. * Transposed trust propagation may exist from [PERSON] to [PERSON] when [PERSON] trusts [PERSON] and [PERSON] also trusts [PERSON]. The proposed trust propagation strategies are demonstrated in Figure 1. Some more complex propagation schemes can be derived from the above two primary ones. For example, if [PERSON] trusts [PERSON] and [PERSON], and [PERSON] also trusts [PERSON] and [PERSON], there might be an increase in the trust between [PERSON] and [PERSON], which is a cascaded result of two transposed trust propagation instances. In the field of citation network analysis, this very same scheme is called _co-citation_ and has been greatly studied. It is worth noting that the co-citation propagation conforms to Assumption 3, but, differently from it, we derived the \"co-citation\"-equivalent trust propagation from the topology perspective. The same above-mentioned trust propagation strategies of direct trust propagation and transposed trust propagation were also leveraged in [28], which helped the researchers build a better trust prediction model.