## 5 Experimentation Process
### Exploratory Data Analysis  
This subsection will introduce several graphs and diagrams that illustrate the nature of the Elliptic and Elliptic++ datasets to extract useful information about their features, the class imbalance and the relational structure. An important thing to consider before diving into the experiments is the high dimensionality of the data being worked with. Specifically, the transactions dataset had a total of 183 features. Dealing effectively with this number of features was crucial for both the experiments and the visualization of the data, due to the noise they can produce. In later sections, dimensionality reduction methods oriented to experimentation, such as PCA, will be treated in detail. However, for the sake of a clear visualization of the data, other methods tend to be more suitable, such as t-Distributed Stochastic Neighbour Embedding (t-SNE). In this manner, a precise representation of the original data can be obtained in a reduced two- or three-dimensional space that can be represented on a concise plot. Accordingly, Figure 2 shows the output of the t-SNE algorithm applied in a three-dimensional space to the subset of transactions that occurred at the seventh timestep. The first subfigure includes the transactions with a known label, namely licit (in green) or illicit (in red). The second one also includes the transactions with an unknown label (in orange). Both of them give a hint about the imbalance that exists between the different labels of the dataset. To take a closer look at the imbalance, Figure 3 shows the number of transactions of every label (licit, illicit and unknown) at each timestep of the dataset, from 1 to 49. A high imbalance between different classes can be observed in the figure, and it is also remarkable that this imbalance varied from timestep to timestep with high volatility. Additionally, Figure 4 shows the proportion of licit and illicit transactions at each timestep, confirming this tendency. Equivalently, Figures 5 and 6 show that the set of wallets showed similar behaviour to that of the transactions set. Using a probability theory approach, the mutual information shared between the label and a feature, treated as two random variables, could be estimated by sampling both from the dataset. This provided a measure of their dependency, allowing us to draw conclusions about the extent to which a feature influenced the class. In this manner, Figures 7 and 8 show the amount of estimated mutual information of each feature concerning the class (licit or illicit) for both the 183 features of the transactions and the 55 features of the wallets, respectively. Figure 4: Imbalance between licit and illicit transactions per timestep. Figure 5: Number of wallets in each class per timestep. Figure 6: Imbalance between licit and illicit wallets per timestep. Figure 7: Mutual information of transaction features. As can be observed in the figures, especially for the transactions, there were slight patterns in some groups of features. This could be attributed to the fact that some features may have been obtained by aggregating other features. However, as stated in Section 4.2, the authors of the dataset do not provide such information. Although in both cases, the amount of mutual information was generally low, there existed slight differences between the features, which suggested that a component reduction algorithm could be beneficial for some models. On the first iteration, a feature ablation analysis was carried out by removing all the features below a threshold in the mutual information quantity. In order to select this threshold, a histogram was plotted for both transaction and wallet features to analyze the distribution of the mutual information values in both cases. Figure 9a,b show these histograms with the chosen threshold for both transactions and wallets, respectively. Figures 10 and 11 show the final result of the feature ablation compared to the previous mutual information plots.