# Countering Social Media Cybercrime Using Deep Learning: Instagram Fake Accounts Detection
## 4 Proposed Framework
### Stage3: Framework Structure
The following expressions help to further elaborate:  
\[\mathrm{i_{t}} =\sigma(\mathrm{W_{i}}\times\mathrm{x_{t}}+\mathrm{U_{i}}\times \mathrm{h_{t-1}}+\mathrm{b_{i}}) \tag{4}\] \[\overline{\mathrm{C_{t}}} =\sigma(\mathrm{W_{c}}\times\mathrm{x_{t}}+\mathrm{U_{c}}\times \mathrm{h_{t-1}}+\mathrm{b_{c}}) \tag{5}\]  
Figure 5: LSTM cell structure [48]. These expressions represent the input gate at time (t); the weights \(W_{i}\), \(U_{i}\), \(W_{c}\), and \(U_{c}\); and the bias factors (\(b_{c}\)) and \(b_{i}\). The following expressions are used to update the state of the cell at a given time:  
\[C_{t}=f_{t}\times C_{t-1}+i_{t}\times\overline{C_{t}} \tag{6}\]  
The output information in the current time step is primarily produced in the third layer. It is written as  
\[O_{t}=\sigma(W_{o}\times x_{t}+U_{o}\times h_{t-1}+b_{o}) \tag{7}\]  
The output threshold at time t is denoted by \(O_{t}\), the weights are \(W_{o}\) and \(U_{o}\), and the bias term is \(b_{o}\). The cell's output value can then be written as follows:  
\[h_{t}=O_{t}\times tanh(C_{t}) \tag{8}\]  
where \(h_{t}\) represents the cell's output value at time t, \(tanh\) represents the activation function, and \(C_{t}\) represents the cell's state at time t. When data are sent through the gates, the important information is labeled as output, while the invalid data are labeled as forgotten [48]. LSTM Parameters and Performance Measures  
The framework uses a series of hyperparameters that help to enhance the results. Five parameters, the optimizer, batch size, epochs, loss function, and learning rate, are employed and summarized in Table 4 to assess the performance of the proposed framework. There are numerous optimizers that could distinguish between different frameworks; some of these optimizers are displayed in \[\text{sigmoid layer }\sigma(\mathrm{x})=\frac{1}{1+e^{-x}} \tag{1}\]0 \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Description** \\ \hline Optimizer & Refers to adjusting the framework parameters to minimize the framework error in the training step. \\ Loss function: & Used to optimize your framework. It is the function that is minimized by the optimizer. \\ Batch Size & The number of data samples that are sent via the network before the parameters are updated. \\ Epoch & Refers to an iterative process of the training framework that occurs at each iteration \\ Learning Rate & A hyperparameter that controls how much to change the model in response to the estimated error each time the model weights are updated \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of LSTM. \begin{table}
\begin{tabular}{c c} \hline \hline
**Optimizers** & **Description** \\ \hline RMSProp & RMSProd effectively eliminates the influence of historical gradient by substituting an exponentially decaying moving average for the summation of squared gradient in \\ AdaGrad [49]. & Adam is a learning method created exclusively for deep neural network training. Adam has the advantages of being more memory efficient and using less compute resources [50]. \\ AdaGrad & With its more complex AdaGrad algorithm, learning rates are scaled inversely in relation to the square root of the cumulative squared gradient [50]. \\ Stochastic gradient & Due to SGD’s frequent updates and large variation, the objective function highly fluctuates [51]. \\ descent (SGD) & Due to SGD’s learning method, the objective function highly fluctuates [51]. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: LSTM Optimizers.