## 2 Research Theory and Methods
### Mining Technology under Big Data
The loss function used by SVM after optimization is the hinge loss function, and its calculation is demonstrated in Equation (8):  
\[L(p)=\text{max}(0,\;1-p)\]Consistency studies on surrogate losses showed that when the surrogate loss is a continuous convex function and is an upper bound of the 0-1 loss function at any value, the result of solving the surrogate loss minimization is also the solution of the 0-1 loss minimization. The hinge loss function satisfies the above conditions. According to statistical learning theory, a classifier generates risk when it learns on and is applied to new data. The risk can be divided into empirical and structural risk types. The calculation is as follows:  
\[\epsilon=\sum_{i=1}^{N}L(p_{i})=\sum_{i=1}^{N}L[f(\mathbf{X}_{i},\mathbf{w}),y_{i}] \tag{9}\]  
\[\Omega(f)=\parallel\mathbf{w}\parallel^{p} \tag{10}\]  
where \(f\) refers to the classifier, \(N\) is the total number of samples, and \(i\) denotes the calculation sample. The equations show that empirical risk is defined by the loss function, and structural risk is defined by the classifier parameter matrix. Then, a classifier determines its model through two sublines, and the calculation of the model is indicated in Equations (11) and (12):  
\[\mathcal{L}=\parallel\mathbf{w}\parallel^{p}+C\sum_{i=1}^{N}L[f(\mathbf{X}_{i},\mathbf{w} ),y_{i}] \tag{11}\]  
\[\mathbf{w}=\underset{w}{\text{arg}min}\mathcal{L} \tag{12}\]  
where \(C\) is the regularization coefficient. The risk of the above model has been minimized. The improved algorithm for skewed data is written in Equation (13)  
\[C_{+1}N_{+1}=C_{-1}N_{-1} \tag{13}\]  
where \(+1\) and \(-1\) represent positive and negative examples, respectively. The improved calculation of probability SVM is illustrated in Equations (14) and (15):  
\[\hat{A},\hat{B}=\underset{A,B}{\text{arg}min}\frac{1}{N}\sum_{i=1}^{N}(y_{i}+ 1)\log(p_{i})+(1-y_{i})\log(1-p_{i}) \tag{14}\]  
\[p_{i}=\text{sigmoid}\left[\hat{A}\left(\mathbf{w}^{\top}\phi(\mathbf{X}_{i})+b\right) +\hat{B}\right] \tag{15}\]  
where \(\hat{A}\) and \(\hat{B}\) express the zoom and translation parameters, respectively. The solution of the model is as follows:  
\[h(\mathbf{\alpha},\beta)=-\sum_{i=1}^{N}\alpha_{i}+\frac{1}{2}\sum_{i=1}^{N}\sum_{ j=1}^{N}\left(\alpha_{i}Q\alpha_{j}\right)+\sum_{i=1}^{N}I(-\alpha_{i})+\sum_{i=1 }^{N}I(\alpha_{i}-C)+\beta\sum_{i=1}^{N}\alpha_{i}y_{i} \tag{16}\]  
\[I(x)=-\frac{1}{t}\log(-x),Q=y_{i}(\mathbf{X}_{i})^{\top}\big{(}\mathbf{X}_{j}\big{)}y_ {j} \tag{17}\]  
where \(I\) represents the logarithmic blocking function, which essentially uses a continuous function to approximate the inequality relationship in the constraints, and the meanings of the calculation parameters in all the above equations are the same. Based on the DM technology used with big data, the SVM algorithm was optimized, and the VET intelligent management platform was constructed. The algorithm comprehensively improved the efficiency and accuracy of data acquisition of the intelligent management platform, and provided more professional and accurate educational reference in-formation for the vocational education system. The platform can provide better professional information for the social industry system, promote the development of the social industry, and improve the efficiency of integrating teaching elements into its production process [47]. Figure 3 depicts the design method we used to improve the performance of the intelligent VET management platform by optimizing the SVM algorithm. Figure 3 shows that optimizing the SVM algorithm enhanced the performance of the intelligent management platform of industry-education cooperation using big data technology. Through the overall application of two-way data, the development of social industry systems can be promoted, and the teaching efficiency of the VET system can be increased.