## 4 Methodology
### Evaluation Metrics
#### 4.4.2 Quantitative Evaluation  
The regression score is used for comparing a model's external sources with and without the generated samples. For this, we used a five-layer RNN model. The RNN model comprises of five GRU layers with 32 units and a 6-unit dense layer. Although the RNN model is implemented using the Adam optimizer [39] as well, it uses mean absolute error (MAE), which will be discussed in more detail in the following section, for loss. For training, 6000 samples of 60 s (sequence length) from each data file were selected to construct the data. Then, these samples were divided into sets for training, testing, and validation. Of the data, 10% was in the test set and 15% was in the validation set. Training was done with the remaining 75% of the data. The real data samples and the synthesized samples are treated separately when applying this split. The RNN model is currently trained for 200 iterations and tested using datasets based on TRTS, TRTR, and TSTR.  
Two measures are used to assess the RNN model's performance. The average difference between the true and the anticipated values are measured by the first metric, called mean average error **(MAE)**. Any value between 0 and the MAE score is acceptable; however, the closer the value is to 0, the smaller the difference. In other words, a low MAE score is preferred because it indicates a more accurate prediction. The MAE score is calculated as follows using \(n\) as the number of values, \(y_{i}\) as the true value, and \(\widehat{y_{i}}\) as the anticipated value as shown in Equation (5):  
\[MAE=\frac{1}{n}\sum_{i-1}^{n}|y_{i}-\widehat{y_{i}}| \tag{5}\]  
The mean squared logarithmic error **(MSLE)**, which can be regarded as a measurement of the percentage difference between the true and projected values, is the second metric. In other words, minor differences between small true and predicted values are managed in a manner that is similar to how large discrepancies between large true and anticipated values are handled. The discrepancy between projected and true values is smaller the lower the MSLE score is, similar to the MAE score. Using the aforementioned definitions, the MSLE score is shown in Equation (6):  
\[MSLE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(log(y_{i}+1)-log(\widehat{y_{i}}+1))|^{2}} \tag{6}\]  
The MTS-TGAN model is assessed using comparisons between the MAE and MSLE on three training phases, namely, TRTR, TSTR, and TRTS methods (explained below).  
The RNN model ought to do well in terms of TSTR if it also catches the diversity in the real data. The goal of the evaluation varies depending on which version is used.  
* **Train Real Test Synthetic (TRTS)**: It refers to the process of training an external model using real data and then testing it on artificial data **(TRTS)**. By measuring how well the distributions within the genuine data were learned, this method explains how realistic the created data are.  
* **Train Real Test Real (TRTR):** The model is trained and tested on real data **(TRTR)**. This method only serves as a benchmark for Train Real Test Synthetic. Alone, it will not produce any useful results.
* **Train Synthetic Test Real (TSTR):** The model is tested on actual data after being trained on random data. This method's goal is to assess how well the differences in the real data are learned as well as how diverse the synthetic data are. The results of the above methods are shown in Section 5.