## 2 Methodology
### Combining ResNet and MobileNet  
As stated in the above paragraph, the SynthSecureNet architecture is basically a combination of two architectures, namely, ResNetV2 and MobileNetV2 architectures. When initializing the model, MobileNetV2 and ResNet50V2 are initialized through pre-trained weights on ImageNet data. The pre-trained weights are a great starting point for feature extraction as they have learned useful representations from a large-scale image classification problem [34; 35].  
Both MobileNetV2 and ResNet50V2 models are used as feature extractors, which involves removing their classification layers and utilizing the outputs from their last convolutional layers as feature maps. For a better explanation, let \(f_{m}(x)\) and \(f_{r}(x)\) depict the feature maps extracted by MobileNetV2 and ResNet50V2, respectively, for an input x.  
Along the channel dimension, features extracted from MobileNetV2 and ResNet50V2 were concatenated. This concatenation ensures that the model learns from the non-duplicated information in both architectures. The aforementioned concatenated feature map \(f_{c}(x)\) can be mathematically shown as (1). The number of channels on the resulting feature map \(f_{c}(x)\) is greater than single feature maps [34; 36].  
\[f_{c}(x)=contat(f_{m}(x),\ f_{r}(x)) \tag{1}\]  
Then, the concatenated feature map \(f_{c}(x)\) is processed by extra layers to extract higher-level representations and perform classification. Additional layers include a flattened layer where the spatial feature map is converted into a one-dimensional vector. Additional layers also include dense layers, which are fully connected and learn non-linear combinations of features. Further, they also include dropout layers, which are a technique that performs regulation to prevent overfitting, where units are dropped out during the training duration [37].  
This can also be denoted as the output of those extra layers (2), as follows:  
\[y=g(f_{c}(x)) \tag{2}\]  
The function of \(g()\) corresponds to the mapping learned by additional layers, which takes the input as a concatenated feature map \(f_{c}(x)\) and the output as y.  
On the output layer, a sigmoid activation function is used in the final dense layer that produces binary output to classify whether the video contains violence or not [38; 39]. Here, the output is squashed between 0 and 1; hence, it can be considered as a probability value. The output of the SynthSecureNet model can be defined as follows (3):  
\[p(y\mid x)=\sigma(w\cdot g(f_{c}(x))+b) \tag{3}\]  
where  
\(w\) is a weight vector;  
\(b\) is a bias term;  
\(w\cdot g(fc(x))+b\) is a linear combination of the transformed features.  
We can consider the following sigma equation:  
\[\sigma(z)=\frac{1}{1+e^{-z}} \tag{4}\]  
Thus,  
\[p(y\mid x)=\frac{1}{1+e^{-(w\cdot g(f_{c}(x))+b)}} \tag{5}\]  
This equation models the probability \(p(y|x)\) as a sigmoid function of the linear transformation of the features obtained from the concatenated outputs of MobileNetV2 and ResNetV2 [38]. The function corresponds to the mapping learned by additional layers, which takes the input of concatenated features.  
The SynthSecureNet model was trained using the binary cross-entropy loss function, which measured the dissimilarity between the predicted probabilities and the true labels.  
The Adam optimizer was used to update the model's weights based on the gradients computed during backpropagation [40; 41].