## 5 Experiment Results and Performance Evaluation
### Predictive Models and Performance Metrics
* \(\
abla I(\theta_{t};x_{i},y_{i})\): gradient of loss function \(J\) with respect to parameters \(\theta_{t}\) by mini-batch of \(m\) samples \((x_{i},y_{i})\). We evaluate our predictive classifier models using the following performance metrics: accuracy, precision, recall, F1-score, computation time, and average loss. These metrics are evaluated based on the following parameters: true positive (TP), true negative (TN), false positive (FP), and false negative (FN). A true positive occurs when the predicted output is true and indeed true. Conversely, if the predicted output is false and indeed false, it is referred to as a true negative. A false positive arises when the predicted output is true, but in reality, it is false. Conversely, if the predicted output is false yet true, it is termed a false negative. The definitions and equations for each metric are as follows ([[https://www.javatpoint.com/performance-metrics-in-machine-learning](https://www.javatpoint.com/performance-metrics-in-machine-learning)]([https://www.javatpoint.com/performance-metrics-in-machine-learning](https://www.javatpoint.com/performance-metrics-in-machine-learning)) (accessed on 1 April 2024)):  
* Accuracy is the number of correct predictions to the total number of predictions. \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}\] (4)
* Precision is the ratio of true positive to the total positive predictions (true positive and false positive). \[Precision=\frac{TP}{TP+FP}\] (5)
* Recall (sensitivity) provides the accuracy for the positive instances (class 1) as fraudulent transactions. \[Recall=\frac{TP}{TP+FN}\] (6)
* F1-Score is the ratio of true positives to the total number of positives (true Positive and false negative). \[F1\text{-}score=2\times\frac{\text{{{{{{{{{{{{{{\text{\  
with the SGD, demonstrated high performance, achieving an accuracy, precision, recall, and F1-score of 0.97, 0.97, 0.96, and 0.97, respectively. Additionally, this model exhibited a computation time of 0.04 and an average loss of 0.10. Additionally, we implemented the RF algorithm integrated with the FL-blockchain (FL-blockchain-RF) framework, as shown in Table 6. We compared the performance of RF in our proposed detection system with our previous works [70; 74]. FL-blockchain-RF exhibited high performance, achieving an accuracy, precision, recall, and F1-score of 0.99, 0.99, 1, and 0.99, respectively, as illustrated in Figure 8.  
Table 7 presents performance comparison with other works. Based on the performance results, we observed that our proposed models exhibited good performance, achieving accuracy, precision, recall, and F1-score of 0.97, 0.97, 0.96, and 0.97, respectively. Our framework has demonstrated its efficiency; however, our goal is to increase the accuracy, recall, and F1-score to achieve a high probability of around 0.99. Due to the size of our dataset sample and resource limitations, we encountered some constraints during this experiment. Therefore, it is feasible to further enhance its classification performance and prediction accuracy through several factors, including online fraud detection systems,  
Figure 5: Performance evaluation with ADAM optimizer. Figure 6: Performance evaluation with SGD optimizer.