## 6 Conclusions  
With the growth of cryptocurrency, the fight against fraudulent activities has become a challenge. After introducing the background on cryptocurrency fraud and analyzing the related works, this article addressed the problem of identifying fraud in a large set of transactions extracted from the Bitcoin network. The goal was to find reliable methods to label Bitcoin transactions, taking into account their features. This study analyzed the effectiveness of a variety of ML methods with different approaches to the task of identifying fraud on the Bitcoin cryptocurrency network. Although the work could be generalized to other currencies such as Ethereum by following a similar method, a large enough dataset is needed. Moreover, the transaction graph for each network should be adapted to the intrinsic features of that specific currency. For example, not all cryptocurrencies follow the UTXO model used by Bitcoin, which is the mechanism that was used to build the edges between transactions in the Elliptic dataset. At the same time, the Elliptic dataset also has some limitations, such as the fact that its authors do not provide detailed information about the feature selection, the transaction gathering or the graph construction processes and if graph-specific properties like the density or node degree distribution were taken into account. On one hand, the results obtained with unsupervised learning methods have shown the usefulness of these approaches for detecting illicit transactions in the absence of a manually labelled dataset, despite still being far from the performance of supervised methods. Unfortunately, these methods also involve a series of potential drawbacks and limitations, such as the absence of labelled data for validation, difficulty in distinguishing between fraudulent patterns and other anomalous but licit activities, and sensitivity to noise and irrelevant data. On the other hand, the experiments carried out using the HGT framework revalidated the capability of deep learning methods in supervised approaches, particularly graph-based methods. The importance of data heterogeneity was shown in the results, although no further experiments were performed to isolate which specific components of the HGT model were responsible for this. Combining both unsupervised and supervised approaches in a more ambitious experiment could bring several benefits, such as enhancing the anomaly detection process, filtering out outliers before the use of deep learning models, handling newer and unknown fraud patterns or improving the explainability of the results. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Illicit Transactions**} \\  & **Precision** & **Recall** & **F1 Score** \\ \hline Graph Convolutional Network (GCN) \({}^{\mathit{Elliptic}}\)[30] & 0.81 & 0.51 & 0.63 \\ Graph Attention Network (GAT) \({}^{\mathit{Elliptic}}\)[46] & 0.92 & 0.86 & 0.89 \\ Heterogeneous Graph Transformer (HGT) \({}^{\mathit{Elliptic}++TX}\) & 0.63 & 0.61 & 0.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: A comparison of the HGT with other models. The first two were trained and evaluated using the standard Elliptic dataset, while the HGT was applied to the entire heterogeneous Elliptic++ dataset, and only the metrics for illicit transactions are shown. The results emphasize the importance of integrating both the structural information and the intrinsic features of the data, particularly in the context of transactional data due to their relational nature. Aggregating the information of a given transaction with that of its neighbouring transactions is a crucial step to decide whether it might be illicit or not, since the commission of the fraud itself can occur several hops before or after the given transaction. This aligns with related works that applied graph frameworks to supervised learning methods, obtaining remarkable improvements.