## 2 Materials and Methods
### Two Outliers Generation Methods
#### 2.3.2 Generation Module Method  
The remaining half of the number of outliers were generated using the bimodal probability distribution reflecting sexual dimorphism. BMI, FAT, MUSCLE, and WATER values corresponding to the calculated body weight criterion values were also generated according to sex. Figure 3 shows the overall flow for the generation module. 1. The generation module creates the number of outliers to be generated, minus the total number of outliers generated by the search module. 2. Divide the number of outliers to be generated in the generation module by the number of weeks to calculate the number to be generated per week. 3. Excluding the days selected in the search module, the number of day indices to be created per week is extracted. 4. The average of the normal distribution was obtained by multiplying the weekly average weight calculated for each week by an arbitrary ratio of 1.1, and the mean standard deviation was set to \"2\". The mean standard deviation, \"2\", may change depending on data characteristics. Here, the reason for multiplying by 1.1 was to minimize distortion due to the difference in weight values. For example, 5 kg for a 50 kg user and 5 kg for an 80 kg user is the same 5 kg but feels different. Therefore, rather than modifying the weight by addition, we applied a multiplicative scaling to increase fairness. \[\textit{Average}(A)=\textit{average}+\textit{(average}\times\textit{random ratio), which ratio = 0.1} \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline
**Data Variable** & **Variable Description and Range** \\ \hline Random Noise for body weight & Noise for search scope, any real value between (0, 2) \\ BMI Noise & Noise for BMI calculation, any real value between (0.5, 1.5) \\ Body Mass Noise & Noise for calculating body mass, any real value between (1.5, 3) \\ Muscle Mass Noise & Noise for muscle mass calculation, any real value between (0.5, 3) \\ Height Noise & Used for BMI calculation with noise for the set height \\ FAT & Any real value between (17, 32) for men + body mass noise, and random real value between (15, 30) for women + body mass noise \\ MUSCLE & Weight Value—Body Mass Value + Muscle Noise \\ Body Water Noise & Noise for body water calculation, any real value between (2.5, 3) \\ Weight & Weight Value + Weight Noise from full RAW data \\  & Weight (kg)/(Height (m) + Height Noise)\({}^{2}\) The height of 1.73 m for males and 1.61 m for females is the standard height used in calculations. \\ Water & Any real value between (50, 65) for male + body water noise, and random real value between (45, 60) for female + body water noise \\ \hline \end{tabular}
\end{table} 
Table 1: Description of the noise of each variable set to calculate different variables. Figure 3: The Generation module: this module uses a normal distribution based on gender physical differences. \[\text{Standard deviation(S)}=\pm\text{ 2} \tag{3}\]
5. Generate one body weight (BW) randomly from the graph (A, S) of normal distribution created in step 1. 6. Based on the weight reference value obtained in step 5, if it is greater than 70, it is assumed that it is a man, and if it is less than 70, it is created separately.The reason for this setting is that, as a result of the data set EDA (Exploratory Data Analysis), the maximum value of women's weight was less than 70. 6-1. For males, BMI was calculated by setting the height to 1.73 m, the average male height in Korea, and randomly extracting WATER and FAT from a uniform distribution in the ranges of (50, 65), (17, 32), respectively, then computing the MUSCLE value by subtracting FAT from the reference body weight value. Finally, random noise corresponding to each variable was added. (See Table 1). 6-2. For females, BMI was calculated by setting the height to 1.61 m, the average male height in Korea, and randomly extracting WATER and FAT from a uniform distribution in the ranges of (45, 60) and (15, 30), respectively, then computing the MUSCLE value by subtracting FAT from the reference body weight value.