## 3 Materials and Methods
### Datasets  
One of the main problems in CFD literature is the lack of information due to the confidentiality of the data such that it is not easy to find representative, informative, and open datasets. For this reason, we have first used a synthetic dataset to validate our proposal [1], thus paving the way for a later analysis over real datasets. **Synthetic Dataset. ** The first dataset introduces a synthetic linear classification problem with a binary output variable, and it was developed in the original proposal of the IVI algorithm [13] with 485 input features. For this work, and for reasons of representability and execution time, we have used a subset of features while keeping the feature names. This subset was selected with the first features of each group. The dataset used for this work includes a set of 23 input features distributed as follows: 11 input features drawn from a normal distribution, 5 of them are used to linearly generate a binary output variable, specifically \(f0,f1,f2,f3\), and \(f4\). Therefore, these five features will be informative for the problem. A set of another 12 features are randomly created with no relation to the previous ones and so they could be considered as noisy and non-informative features. Additionally, a new group of 6 features are computed as redundant with the informative input features. **German Credit Dataset. ** This set is known as German Credit Fraud (Stattog) [39], and it contains real data used to evaluate credit applications in Germany. We used a version of this dataset that was produced by the Strathclyde University. The German Credit Dataset contains information on 1000 loan applicants. Each applicant is described by a set of 20 different features with a binary output variable. Among these 20 features, 17 of them are categorical while three are continuous. There are no missing values. To facilitate FS and in order to train the models, the values of the three continuous attributes were normalized, and for the discrete features they were converted to one hot encoding. After these preprocessing stages, the final dataset was 61-dimensional. Detailed information for each feature can be found in [39] and there is a short description in Table 2. \begin{table}
\begin{tabular}{p{113.8 pt} p{227.6 pt}} \hline \hline
**FS method** & **Summary** \\ \hline Filter methods & They use statistical techniques to evaluate the relationships among characteristics (i.e., Pearson’s correlation, chi-square) [35]. \\ Wrapper methods & They are based on the inferences that we draw from a previous model, and we decide to add or remove features from our subset (i.e., forward feature selection and backward feature selection) [36]. \\ Embedded methods & They combine the qualities of filter and wrapper methods. They are implemented by algorithms that have their own built-in feature selection methods (i.e., RFE) [37]. \\ IVI & It is capable of identifying the informative variables and their relationships. It transforms the input-variable space distribution into a coefficient-feature space [1; 13]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary table of feature selection methods (FS) present in the literature according to the basic techniques used [32; 38]. **PaySim Dataset. ** PaySim simulates mobile money transactions based on a sample of real transactions extracted from one month of financial logs from a mobile money service implemented in an African country [40]. The original logs were provided by a multinational company, who is the provider of the mobile financial service which is currently running in more than 14 countries all around the world. PaySim covers five of the most important transaction types: cash-in, cash-out, debit, payment, and transfer. The PaySim dataset contains information on 6,362,620 transactions. Each applicant is described by a set of 11 different features.