## 4 Problem Statement and Methodology Definition
### The Datasets and the Graph Nature of the Data  
The data-gathering step is a particularly complicated task in the context of cryptocurrency transactions, even though raw transaction data are publicly available through different blockchain APIs. One of the main reasons for this is the difficulty of manually labelling transaction data, since this task requires exhaustive research to determine whether a given transaction is licit or not. Because of this, most available datasets are partially labelled. Another important factor is the great volume of transactions that are continuously being processed and the volatility of these data since they depend on different variables that are constantly changing, such as the price of the cryptocurrency on the market. Consequently, throughout this section, the different datasets used in the experimentation process of this research will be described, along with the handling of the data modelling. As mentioned previously, transaction data have the peculiarity of carrying underlying relational information that can be extracted and utilized by classification models to make more accurate predictions. To achieve this, the dataset needs to be modelled as a graph, and the most suitable way of doing this is by modelling the dataset as a homogeneous graph, \(\mathcal{G}=(V,E)\), where \(V\) is the transaction set and \(E\subseteq V\times V\) is the set of edges so that \(e=(s,t)\) represents the flow of cryptocurrencies or other assets from transaction \(s\in V\) to transaction \(t\in V\). This approach was utilized by researchers in [30] and applied to the Elliptic Bitcoin Dataset, a dataset with more than 200,000 Bitcoin transactions (approximately USD 6 billion) published by the Elliptic company in the same research work. Each of the transactions in this dataset is labelled as either licit (0), illicit (1) or unknown (2) and has 166 features. The first 94 features represent local information about the transaction, suchas the number of inputs and outputs, the transaction fee and the output volume, while the other 72 features are obtained by aggregating the local ones. Further details on the feature extraction process are not available due to the intellectual property policies of the Elliptic company. Following the previously explained mechanism, the dataset also contains a list of approximately 230,000 edges representing the Bitcoin Unspent Transaction Output (UTXO) flow between transactions. The dataset is described as being constructed from a set of transactions explicitly known to be licit and illicit and then extended with random transactions broadcast to the blockchain in evenly spaced time windows. Thus, one of the features of the transactions is a discrete temporal component ranging from 1 to 49, referred to as the timestep. For this reason, we believe that the Elliptic dataset constitutes a reliable representation of the Bitcoin transaction flow, and including different fraud categories in the illicit label made it ideal for the purpose of this study. Therefore, this dataset was widely used in a good part of the experiments in our work. Additionally, some popular datasets might also include features for both transactions and wallets, as well as the relations between them. In these cases, the transaction graph can be modelled as a heterogeneous graph, \(\mathcal{G}=(V_{tx},V_{ux},E_{tx}^{w},E_{w}^{tx})\), in which \(V_{tx}\) is the set of transactions (with its transaction-specific features), \(V_{ux}\) is the set of wallets (with its wallet-specific features) and \(E_{tx}^{w}\subseteq V_{ux}\subseteq V_{ux}\times V_{tx}\) are the sets of the Transaction\(\rightarrow\)Wallet and Wallet\(\rightarrow\)Transaction edges, respectively. This is the case for the Elliptic++ [12] dataset, presented in 2023 as an improved extension of the Elliptic dataset, containing a set of around 800,000 wallets with 55 features each and the relations between them as actors in the transactions of the original dataset.