# MVCG-SPS: A Multi-View Contrastive Graph Neural Network for Smart Ponzi Scheme Detection
## 4 MVCG-SPS Method
### Reinforcement-Learning-Driven Multi-View Aggregation  
The Reinforcement-Learning-Driven Multi-View Aggregation module is a key component in the MVCG-SPS framework, aimed at dynamically optimizing the aggregation of features from multiple views. This module leverages reinforcement learning (RL) to dynamically adjust the feature weights of each view, optimizing the performance of multi-view aggregation, effectively capturing potential correlations between views and avoiding information redundancy, thereby enhancing the representation learning of multi-view graphs. The module operates under the assumption that not all neighbors contribute positively to the feature aggregation process. Some neighbors may introduce noise, which can hinder the learning of accurate representations, particularly in the context of the complex structures inherent in multi-view graphs. To address this, the RL-based multi-view aggregation module includes two main functions: neighbor importance measurement and filtering threshold calculation. By integrating these components, the RL module enables the MVCG-SPS framework to adaptively learn the optimal filtering threshold for each view, thereby enhancing the feature aggregation and improving multi-view representation learning. 1. Multi-View Aggregation  
The process of multi-view feature aggregation is as follows:  
\[\mathbf{Z}_{\text{agg}}=\sum_{v\in\mathcal{V}}w_{v}\cdot\mathbf{Z}_{v}, \tag{1}\]  
where  
* \(\mathcal{V}\) represents the set of views,
* \(\mathbf{Z}_{v}\) is the node representation of view \(v\),
* \(w_{v}\) is the weight for view \(v\), dynamically optimized by the RL module. 2. Neighbor Importance Measurement  
In each view, the importance of a neighbor node to the central node is calculated based on edge weights and node feature similarity. This measure uses a fully connected neural network (FNN) to predict node labels and calculates the similarity between nodes based on their features. The importance score (IMP) for a neighbor node \(k^{\prime}\) to the central node \(k\) at layer \(l\) is computed as follows:  
\[IMP^{(l)}_{j}(k,k^{\prime})=\left\|A_{ij}(k,k^{\prime})\right\|\otimes\left(1 -DIST^{(l)}_{j}(k,k^{\prime})\right) \tag{2}\]  
where \(A_{i,j}(k,k^{\prime})\) denotes the edge weight, \(\otimes\) represents the multiplication operation, and \(DIST\) is the Euclidean distance between the central node and its neighboring node, computed based on the output of the FNN, as follows:  
\[DIST^{(l)}(k,k^{\prime})=\text{NORM}(\|\sigma(FNN(\mathbf{f}_{k}))-\sigma(FNN (\mathbf{f}_{k^{\prime}}))\|_{2}), \tag{3}\]  
where \(FNN\) is a single-layer fully connected neural network used to predict node labels and generate feature embeddings. 3. RL Module Design  
The core task of the RL module is to automatically compute the optimal filtering threshold for each view, to select the most valuable neighboring nodes. This is crucial, as different views may require different thresholds to optimally fuse features. The RL agent performs actions to increase or decrease the filtering threshold based on the reward signal, which is derived from the change in average neighbor importance between iterations. (1) Action Space  
The action of the RL agent is to adjust the threshold, and the action space is defined as \(\{+S,-S\}\), where \(S\) is the adjustment step size. (2) Reward Signal  
The reward signal is based on the change in average neighbor importance between the current and previous iterations, defined as  
\[REW^{(l)}_{j}[p]= \begin{cases}+1,&\text{if }AVG^{(l)}_{j}[p]>AVG^{(l)}_{j}[p-1]\\ -1,&\text{otherwise}\end{cases}  \tag{4}\]  
where \(AVG^{(l)}_{j}[p]\) represents the average neighbor importance at iteration \(p\). \[AVG_{j}^{(l)}[p]=\frac{\sum_{k\in N}\sum_{k^{\prime}\in N(k)}IMP(k,k^{\prime})}{ \sum_{k\in N}|N(k)|}. \tag{5}\]  
The reward function \(REW_{j}^{(l)}[p]\) measures changes in average neighbor importance, which directly reflects the multi-view aggregation quality.