# A New Approach for Deepfake Detection with the Choquet Fuzzy Integral
## 4 Experimental Results
In Table 4, \(x_{1}\) represents the output of algorithm 1, \(x_{2}\) represents the output of algorithm 2, and \(x_{3}\) represents the output of algorithm 3. The required fuzzy measure must be calculated for the Choquet fuzzy integral module. The test results of each algorithm were recorded and used as a training set in the Choquet fuzzy integral network. First, we run the deepfake detection algorithms (DDA) separately, and later, they are run in combination, using the Choquet fuzzy integral. The confusion matrices for the experiments on the custom dataset are given in Figure 10. Accuracy values for the methods used for the custom dataset are given in Table 5. As can be seen from Table 5, the Choquet fuzzy integral has better performance. To demonstrate the computational efficiency of the proposed method, we run the inference process for different sizes of inputs. The elapsed times for inference associated with DDA1, DDA2, DDA3, and the proposed method are given in Table 6. Because the proposed algorithm uses two methods, in addition to their hybrid use, it has no need to calculate an additional instance of a given method's output. It can be seen in the table that the proposed method's run time is no longer than two instances of each method. Because the inputs are resized before inference, only the resizing process affects the performance. The experimental studies used to obtain the values in Table 6 are performed with a computer equipped with an Intel Core i7 processor, AsusRTX 3060 GPU, and 32 GB RAM. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Set** & **Fuzzy Measure Values** & **Set** & **Fuzzy Measure Values** \\ \hline \(g\{\varnothing\}\) & 0 & \(g\{x_{1},x_{2}\}\) & 0.7173912 \\ \hline \(g\{x_{1}\}\) & 0.0833336 & \(g\{x_{1},x_{3}\}\) & 0.9444430 \\ \hline \(g\{x_{2}\}\) & 0.0175454 & \(g\{x_{2},x_{3}\}\) & 0.8823529 \\ \hline \(g\{x_{3}\}\) & 0.3000000 & \(g\{x_{1},x_{2},x_{3}\}\) & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fuzzy measure values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Dataset & \multicolumn{2}{c}{DDA 1} & \multicolumn{2}{c}{DDA 2} & \multicolumn{2}{c}{DDA 3} & \multicolumn{2}{c}{Proposed Method} \\ \hline  & ACC & F1 & ACC & F1 & ACC & F1 & ACC & F1 \\ \hline Custom & \multirow{2}{*}{65.08} & \multirow{2}{*}{71.67} & \multirow{2}{*}{56.91} & \multirow{2}{*}{65.56} & \multirow{2}{*}{72.91} & \multirow{2}{*}{84.15} & \multirow{2}{*}{75.91} & \multirow{2}{*}{85.28} \\ dataset & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accuracy values and F1 scores of algorithms on custom dataset. In order to compare the results of the study, DDA1, DDA2, DDA3, and the proposed method were tested on the DFDC, CELEB-DF, FF-DF, DF-TIMIT datasets. AUC values of the methods are given in Table 7, in comparison with studies in the literature. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Input Description**} & \multicolumn{6}{c}{**Elapsed Time (sec)**} \\ \hline \multirow{2}{*}{**Resolution**} & **Length** & **FPS** & **File Size** & **DDA 1** & **DDA 2** & **DDA 3** & **Proposed** **Method** \\ \cline{2-7}  & **(sec)** & **FPS** & **File Size** & **DDA 1** & **DDA 2** & **DDA 3** & **Proposed** **Method** \\ \hline
1080 \(\times\) 1920 & 10.02 & 30 & 13 Mb & 2.42 & 4.13 & 2.57 & 4.52 \\ \hline
942 \(\times\) 500 & 15.47 & 30 & 4.4 Mb & 3.25 & 5.54 & 3.21 & 5.95 \\ \hline
432 \(\times\) 500 & 13.63 & 30 & 592 kB & 2.73 & 4.86 & 2.82 & 5.03 \\ \hline
942 \(\times\) 500 & 10.47 & 30 & 1.68 Mb & 2.20 & 3.61 & 2.28 & 3.98 \\ \hline
512 \(\times\) 384 & 5.40 & 25 & 290 kB & 0.82 & 1.52 & 0.85 & 1.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Elapsed times for inference. Figure 10: Confusion matrices for custom dataset: (**a**) DDA 1, (**b**) DDA 2, (**c**) DDA 3, and (**d**) Proposed Choquet fuzzy integral.