## 4 Experiments and Results
### Sensitivity Analysis in the Latent Space  
In view of the results presented in the previous subsection, it was considered of interest to study the variability of the results of each feature of the input space. For this purpose, this experiment uses the score of the SVC classifier defined in the latent space to estimate the sensitivity of the outcome to small variations of each feature in the original space. For these observations, we made small variations for each feature in every transaction individually by increasing and decreasing a small percentage of its features. Sensitivity was estimated as the ratio between the score obtained by applying a small percentage change in the input space and the score without the percentage change in the input space values. In Table 5, we can see the average sensitivity of each feature in the PaySim Dataset. This result shows that there is a large difference between the small variations in each feature, for example, the feature newbalanceOrig is more affected by small variations than step.  
From a graphical point of view, these results can be clearly observed to show that small variations in some features in input space can have a great impact on the latent space. We can see this effect in Figure 5, and we can observe that the same small variation in a feature in input space can have different response in latent space; for example, for the newbalanceOrig feature, this response is more visible than in type_transfer and type_payment features, where this response is not appreciable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Acc\_All\_Features (SVC)** & **Acc\_fs\_MIFF** & **Acc\_fs\_MIFF\_LS** \\ \hline Synthetic & \(0.9870\pm 0.003195\) & \(0.9872\pm 0.002951\) & \(0.9885\pm 0.00039\) \\ PaySim & \(0.9654\pm 0.00011\) & \(0.9678\pm 0.0002\) & \(0.9758\pm 0.00011\) \\ German & \(0.7580\pm 0.017017\) & \(0.7663\pm 0.020409\) & \(0.7778\pm 0.00238\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistical results for accuracy for different datasets. Mean and standard deviation of the results are shown for 100 resample analysis. In rows are the results for the different datasets. In columns are the analyses for the different set of features included in the process. Columns from left to right correspond to the inclusion of all available features, IVI with MIFF filter, and IVI with MIFF filter in the latent space (using autoencoder).  
In Figure 6, we can see the score distributions obtained in the latent spaces when we apply these small variations. For reasons of representability we have only represented two features, newbalanceOrig with high sensitivity and step with low sensitivity, according to the data in Table 5. In feature newbalanceOrig we can see how the distributions are shifted due to the sensitivity, while in feature step, having low sensitivity, it remains static. In addition, we can observe in these figures that they do not have normal-like distributions, but rather they are multimodal distributions. This type of distribution reinforces our hypothesis defined in Section 3.7.4, that each transaction can be affected differently in the latent space by the combinations of the values of the features in the real space, thus producing different weights in each feature used in the decision process.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Var. Name** & **Sensitivity** & **Var. Name** & **Sensitivity** \\ \hline newbalanceOrig & 1.118154 & bstep & 0.000600 \\ amount & 0.843496 & isFlaggedFraud & \(-\)0.000518 \\ newbalanceDest & 0.215071 & nameOrig\_code & \(-\)0.001186 \\ type\_transfer & 0.199242 & type\_CASH\_IN & \(-\)0.366544 \\ type\_payment & 0.104022 & type\_DEBIT & \(-\)0.753180 \\ type\_cash\_out & 0.012399 & oldbalanceOrg & \(-\)1.086948 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Mean of sensitivity for each feature in PaySim Dataset.  
Figure 5: Representation for one non-fraud transaction of how small variations for each feature in real space affect in the latent space with MIFF filter in the PaySim Dataset.