# Analysis of Score-Level Fusion Rules for Deepfake Detection
## 4 Experimental Results
### Results
#### 4.2.1 Intra-Dataset Scenario
To explain the obtained results, we reported the distribution of scores for both real and fake samples in Figure 5. We can observe that the reasons for the low performance in the cases of the ResNet (Figure 5a,b) and the Max fusion rule (Figure 5c,d) are related to the high tendency toward high scores for both real and fake samples. This is particularly evident in the case of the ResNet, confirming the Cohen's d reported on the previous table (Table 2). The plots also suggest a less pronounced separation between the distribution of fake samples and the distribution of real ones through the accuracy-based average (Figure 5e,f) and the Complement NB (Figure 5g,h) with respect to the other methods of the respective approaches. However, the separation between the distributions is still visually evident, confirming the values of the previously obtained performance metrics, particularly concerning the Cohen's d (Table 2). It is important to underline that ResNet is the only model trained on a different dataset, and this is evident from the distribution of reals completely overlapping that of fakes. This evidence should lead the designer to exclude a model with this behavior. Furthermore, in a controlled application context, it should be easier for a designer to keep the real distribution  
Figure 4: ROC curves on the FF++ dataset comparing the single deepfake detectors with their fusion through non-parametric approaches (**a**), the approaches based on weighted averages (**b**), the ones based on machine-learning models (**c**) and comparing the most performing methods of each category with respect to the obtained AUC (**d**). curve under control, as he/she knows the dpi, size and compression of the images or videos on which the detector works. Figure 5: Real and Fake Score distributions related to the FF++ dataset from single methods (**a**,**b**), non-parametric fusion methods (**c**,**d**), weighted averages (**e**,**f**), and Machine Learning-based methods (**g**,**h**). The designer should therefore select a fusion rule that keeps the reals distribution mean close to zero, for instance MLP and Perceptron. The choice of the fusion rule should also be correlated with the operational point at which the system must work. For example, the SVM-based fusion rule would seem optimal from the point of view of the distribution mean, resulting in one of the lowest EER of the analyzed rules. However, using more stringent operational points, such as a threshold at 1% FPR or at 1% FNR, leads to higher error rates than other rules, such as weighted averages. This is due to the second mode of SVM distributions, which, albeit at low density, affects the results. Since different operating points could be required by a particular application context, such as the need to misclassify very few fakes or very few real ones, the designer must analyze all the modes of the distribution, their average, their variability and their density. An optimal fusion rule should lead to unimodal distributions with low variability and averaging 0 for reals and 1 for fakes. The fusion rules based on Perceptron and MLP are therefore optimal in the analyzed intra-dataset scenario. To investigate how these rules behave in the presence of unknown manipulations, a cross-dataset analysis is required.