# Enhancing Predictive Expert Method for Link Prediction in Heterogeneous Information Social Networks
## 4 Methodology
### Trustworthiness Investor  
When the model generates the corresponding enhancing predictive expert for each type of link, it also needs to fully utilize the additional feature information of the specific type of link representation from other types of experts. By fusing the prediction labels of different types of experts for this type of link, the prediction accuracy can be improved. Each enhancing predictive expert network layer is followed by a fully connected layer with a softmax function to predict the existence likelihoods of unobserved links.The predictive existence label provided by the \(k\)th enhancing predictive expert \(y^{k}(l)\) is obtained as follow. \[P_{init}(l)=softmax(MLP(R_{l})) \tag{13}\]  
\[y^{k}(l)=\left\{ \begin{array}{l}1,P_{init}(l)\geq\alpha\\ 0,P_{init}(l)<\alpha\end{array} \right. \tag{14}\]  
where \(P_{init}(l)\) denotes the initial predictive likelihood value of link \(l\) according to individual feature projection process, and \(\alpha\) denotes the threshold that determines the predictive existence label of link \(l\) of the \(k\)th predictive expert. Each predictive expert uniformly assigns trustworthiness to estimated existence likelihoods of unobserved links, as predicted by enhancing predictive experts. Trustworthiness ratings are iteratively exchanged between the experts and the unobserved links' existence labels. The trustworthiness of an expert depends on a weighted combination of the trustworthiness of previously estimated existence labels and the expert's own trustworthiness. This iterative trustworthiness exchange process continues until all unobserved links have been reevaluated. Under our assumption, each enhancing predictive expert equally trusts all existence likelihoods of its predicted unobserved links. Trustworthiness of an existence label for an unobserved link grows non-linearly. Predictions from highly trusted experts are considered more credible, thus enhancing the trustworthiness of those experts. Let \(y^{k}(l)\) represent the predicted existence label by the \(k\)th expert for unobserved link \(l\). If \(y^{k}(l)=1\), the link's existence likelihood is high, while \(y^{k}(l)=0\) denotes low likelihood. Initial trustworthiness of an expert's existence label prediction is set at \(O^{0}(l)=1/|U^{k}|\), where \(|U^{k}|\) is the count of unobserved links predicted as 1 by the \(k\)th expert. In each iteration, an expert's trustworthiness is updated using a weighted sum of trustworthiness from previous labels. The updated existence label trustworthiness \(O^{i}(l)\) is determined uniformly from the expert's trustworthiness. This iterative process continues until convergence. \[H^{i}(k)=\frac{\sum\limits_{l\in\mathcal{U}^{k}}O^{i-1}(l)}{|\mathcal{U}^{k}|} \tag{15}\]  
The trustworthiness of the existence likelihood of each unobserved link is obtained by (16). \[O^{i}(l)=1-\prod\limits_{k\in Ex^{k}}\left(1-H^{i}(k)\right) \tag{16}\]  
The notation \(Ex^{k}\) is used to denote the set of all enhancing predictive experts that predict the existence of link \(l\). Formula (16) represents an \"investment\" approach. The reason for selecting this weight allocation method is that the prediction of the presence or absence of links is binary, similar to the outcome of an investment being either a win or a loss. This allocation method is logically straightforward and effective. It is worth mentioning that for the trustworthiness calculation Formulas (15) and (16), the convergence goal is to ensure that the difference between adjacent trustworthiness values is less than a threshold \(\epsilon\). In our experiments, we used a threshold of \(\epsilon=0.01\), which ensures the accuracy of the algorithm in obtaining trustworthiness values and facilitates a quick convergence. Once the trustworthiness of each enhancing predictive expert has been determined, the final feature \(P(l)\) of link \(l\) can be represented by Equation (17).