## 1 Introduction  
Cryptocurrency networks such as Bitcoin or Ethereum are extensively used due to their features and differences from traditional money. Although these networks are considerably robust from the perspective of a distributed system thanks to being supported by the blockchain algorithm, cryptocurrencies face a challenge: the commission of fraudulent activities in these networks, mainly because of the lack of a regulatory entity [1, 2].  
Significant progress has already been made in the context of fraud detection, especially featuring the use of Machine Learning (ML) methods that can process large amounts of transaction data produced by cryptocurrency networks and use them to make predictions about their illicitness. To cite a few of the most recent works, we can highlight the use of traditional ML approaches like Naive Bayes, SVMs, Logistic Regression, Gradient Boosting, Ada-Boost, Random Forests and other Ensemble Learning models [3, 4, 5, 6, 7, 8], but also Federation Learning [9], neural network approaches [10, 11, 12], anomaly detection [13] and more recent graph-based approaches like those that consider the relational nature of transactional data, like the Hybrid Graph Neural Network [14], graphs based on a Transformer Network [15],the subgraph-based contrastive learning algorithm for heterogeneous graphs [16] and graph anomaly detection [17].  
Creating better and bigger datasets and developing more sophisticated deep learning models opens up new possibilities in the context of cryptocurrency fraud detection. However, all these supervised learning methods share a common problem: the need for a large enough labelled dataset to train them. From another perspective, in the absence of a manually labelled dataset, using unsupervised learning methods that can extract information about the data is another research field that, as far as we know, has not been extensively explored for the case of cryptocurrency fraud detection. In this context, this work aimed to revalidate the effectiveness of supervised learning methods on a representative Bitcoin transaction dataset by testing the Heterogeneous Graph Transformer (HGT) [18], a novel framework aimed at leveraging relational data with a heterogeneous nature. In addition, this study also explored the possibilities of different unsupervised learning methods based on anomaly detection through the use of k-means clustering and several feature-based outlier detection algorithms, such as the Local Outlier Factor (LOF) [19]. The obtained results revealed that the performance achieved with non-supervised methods was still far from that of one of the supervised approaches, even though they represent a considerable alternative due to not needing a manually labelled dataset.  
Hence, the main contributions of our research can be summarized in the following points: (1) we provide a comprehensive evaluation of unsupervised and supervised methods using real-world datasets, discussing their limitations and potential improvements; (2) explore the potential of feature-based anomaly detection methods in the context of cryptocurrency networks and, as a result, propose a hybrid approach combining structural and intrinsic data features; and (3) put to the test a novel graph framework that leverages the heterogeneous nature of transactional data.  
The structure of the rest of this article will be as follows: Section 2 will introduce the background on cryptocurrency fraud and describe the current literature about the topic. Then, Section 3 will present the related works. Later, Section 4 will formally describe the problem, the datasets and the methodology. Following this, Section 5 will detail the different experiments carried out, grouped into four categories: exploratory data analysis, anomaly detection, clustering and graph deep learning. Finally, Section 6 will draw conclusions, summarize the results and provide suggestions for future works.