## 3 Methods
### Application of Data Preprocessing Techniques  
Pre-processing of data in this study mainly involved data merging, data cleaning, and data conversion: to enable subsequent exploration and modeling, data from medical records and MRI imaging were merged together and the merged dataset was re-checked and cleaned for errors such as inconsistencies, repetitions, redundancies, and outliers. Then, the cleaned dataset was normalized with a sample of six patients, to ensure distribution in a specified range as well as to minimize effects from scale differences, using the following formula [23]:  
\[X^{\prime}=\frac{X-X_{A}^{min}}{X_{A}^{max}-X_{A}^{min}}\Big{(}X_{A,new}^{max}- X_{A,new}^{min}\Big{)}+X_{A,new}^{min} \tag{1}\]  
where \(A\) is the attribute data,  
\(X_{A}^{min},X_{A}^{max}\) are the minimum and maximum value of A, respectively,  
\(X^{\prime}\) is the new value of each entry in data,  
\(X\) is the old value of each entry in data,  
\(X_{A,new}^{max},X_{A,new}^{min}\) is the max and min value of the range (i.e., boundary value of range required), respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Input Variables**} \\ \hline \multicolumn{3}{c}{**Medical records**} \\ \hline \multirow{3}{*}{Demographic data} & Age & Continuous variable \\ \cline{2-3}  & Gender & Male or female \\ \cline{2-3}  & \multirow{3}{*}{Education} & No education, elementary school, \\  & & junior high school, senior high school, \\  & & university or higher \\ \hline \multirow{3}{*}{Physiological data} & Body mass index (BMI) & Continuous variable \\ \cline{2-3}  & Diastolic pressure & Continuous variable \\ \cline{2-3}  & Systolic pressure & Continuous variable \\ \hline \multirow{3}{*}{Lifestyle} & Smoking history & present or absent \\ \cline{2-3}  & Drinking history & present or absent \\ \hline \multirow{3}{*}{Physical examination} & Presence of other medical conditions & present or absent \\ \cline{2-3}  & \multirow{3}{*}{Walking distance on level ground} & Requires complete assistance, requires \\  & & partial assistance, can walk slowly for \\  & & approximately 50 m, or can walk \\  & & independently \\ \cline{2-3}  & Leg pain & present or absent \\ \cline{2-3}  & Joint pain & present or absent \\ \cline{2-3}  & Muscle pain & present or absent \\ \cline{2-3}  & Muscle weakness & present or absent \\ \cline{2-3}  & Mild paralysis/numbness & present or absent \\ \cline{2-3}  & Leg numbness & present or absent \\ \hline \multicolumn{3}{c}{**MRI diagnosis**} \\ \hline Reduction of intervertebral disc height & present or absent \\ \hline Intervertebral disc herniation & present or absent \\ \hline \multicolumn{3}{c}{**Output variable**} \\ \hline Surgery & Surgery performed or not performed \\ \hline \hline \end{tabular}
\end{table}
Table 1: Classification of the variables.  
On the basis of the two categories emerging from the data--surgical treatments performed (n = 81) and surgical treatments not performed (n = 22)--the researchers developed a synthetic minority oversampling technique (SMOTE) by using R. On the basis of the characteristics of a minority class, SMOTE manually synthesizes new and nonrepetitive minority class samples by using other minority class neighbors surrounding the original minority class. This helps ensure the balance between data category sample sizes. Originally, the number of unprocessed data listings was 103 and the distribution ratio of the two categories was 0.78:0.21. After categorical data were balanced, the number of data listings was 132, and the distribution ratio of the two categories was 0.5:0.5.