## 2 Methodology and Materials
### Data Preprocessing
#### 2.2.2 Normalization Technique  
The second step is the normalization procedure. Normalization is a data preprocessing technique used to rescale variables to a common range, typically to address differences in size or units. This ensures that all variables are on a consistent scale, enhancing the performance and accuracy of certain algorithms [57]. The main purpose of normalization is to compress the values of each feature into a certain range. Usually, the data are scaled between 0 and 1, but other ranges can also be used. In this step, 4 different normalization \begin{table}
\begin{tabular}{c c c c c c} \hline
**Features (Input)** & **Variable** & **Max.** & **Min.** & **Mean** & **Std** \\ \hline T (\({}^{\circ}\)C) & Numeric & 1223 & 700 & 921.8853 & 85.5135 \\ \hline t (h) & Numeric & 16 & 0.2500 & 4.2940 & 2.2921 \\ \hline Boriding media & Categorical & - & - & - & - \\ \hline Boriding method & Categorical & - & - & - & - \\ \hline C (wt.\%) & Numeric & 1.5800 & 0 & 0.4371 & 0.3834 \\ \hline Mn (wt.\%) & Numeric & 2.0100 & 0.2700 & 0.8366 & 0.5130 \\ \hline Si (wt.\%) & Numeric & 1 & 0 & 0.4062 & 0.2890 \\ \hline Cr (wt.\%) & Numeric & 18.7500 & 0 & 5.9327 & 7.1440 \\ \hline Ni (wt.\%) & Numeric & 25.5000 & 0 & 2.8000 & 5.3122 \\ \hline V (wt.\%) & Numeric & 8.8700 & 0 & 0.2990 & 0.9009 \\ \hline W (wt.\%) & Numeric & 17.2000 & 0 & 0.6934 & 3.3741 \\ \hline Mo (wt.\%) & Numeric & 9.4000 & 0 & 0.6719 & 1.1361 \\ \hline Al (wt.\%) & Numeric & 0.1800 & 0 & 0.0076 & 0.0284 \\ \hline S (wt.\%) & Numeric & 0.3700 & 0 & 0.0268 & 0.0577 \\ \hline P (wt.\%) & Numeric & 0.0600 & 0 & 0.0176 & 0.0160 \\ \hline Cu (wt.\%) & Numeric & 0.4400 & 0 & 0.0416 & 0.1118 \\ \hline N (wt.\%) & Numeric & 0.0700 & 0 & 0.0045 & 0.0154 \\ \hline Ti (wt.\%) & Numeric & 2.1300 & 0 & 0.0517 & 0.3264 \\ \hline Fe (wt.\%) & Numeric & 99.0900 & 54.2200 & 87.8172 & 12.9740 \\ \hline Output & **Variable** & **Max.** & **Min.** & **Mean** & **Std** \\ \hline Boride thickness (\(\mu\)m) & Numeric & 455.5000 & 2.3000 & 73.7815 & 69.5855 \\ \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of the inputs and output of various parameters in the dataset. techniques are applied and their effects on the performance of ML algorithms are examined. These normalization techniques are Min-Max, Z-score, Robust and Quantile Transformer. The mathematical representations of these techniques can be summarized as follows:  
_Min-Max technique_: The data are scaled to be between the minimum and maximum values. In this method, the data are compressed between 0 and 1. The mathematical representation of Min-Max normalization is given in Equation (1) [58]. \(X_{n}\), \(X_{min}\), \(X_{max}\) and \(X\) are defined as the normalized value, the smallest value, the largest value in the attribute column, and any data point in the data, respectively, in Equation (1). \[X_{n}=\frac{X-X_{min}}{X_{max}-X_{min}} \tag{1}\]  
_Z-score technique_: It standardizes the data so that the mean is 0 and the standard deviation is 1. The standardization technique is given in Equation (2) [58]. Here, \(\mu\) represents the mean and \(\sigma\) represents the standard deviation. \(X\) and \(X_{n}\) are defined in Equation (1). \[X_{n}=\frac{X-\mu}{\sigma} \tag{2}\]  
_Robust technique_: It is a scaling method that is robust to extreme values in the dataset. This technique allows the data to be normalized using the median and interquartile range (IQR) instead of the mean and standard deviation. It is especially preferred in cases where there are extreme values in the dataset, because these values do not have much effect on the median and IQR. This method eliminates the excessive effect of extreme values while centering the data, which provides a more robust normalization that is not sensitive to extreme values. The mathematical representation of this technique is given in Equation (3) [59]. Here, while the median is the middle value of the dataset, the IQR represents the difference between the 75 th percentile and the 25 th percentile.