# Evaluation and Prediction of Higher Education System Based on AHP-TOPSIS and LSTM Neural Network
## 5 Performance Evaluation
### Comparison with Other Models
However, the slopes of the four models tend to be constant, indicating that the prediction results tend to be homogeneous and idealized if only relying on the regression equation to fit the predictive line and ignoring the influences of practical factors. In addition, the predicted results of the model of [PERSON] et al. [35] are significantly higher than those of other models, considering that the initial value of the model is higher than that of other models. The reason may be that the data source is different from the other ones. At the same time, the slope of the curve of the model has a more evident change, and the growth rate gradually slows down in a later stage. Considering the complicity in reality with multiple factors, it is more reasonable to recognize that the growth rates fluctuate to a certain extent rather than being constant. Our predicted values without policy are quite close to the predicted values of the four models proposed by [PERSON] [34]. This reflects that the predicted results of our model are more idealized when there is no policy intervention. However, the predicted curves of our model with policy are unique in all curves. It appears that the curve starts from the lowest  
Figure 13: Comparison of different models. initial value and ends with the second highest predicted value in 2032. Moreover, the change in slope represents the influences of corresponding policies. From 2019, when the policies, which can improve the gross enrollment rate, are implemented, the slope increases significantly. Our model can not only predict the development trend of gross enrollment ratio in an idealized environment but also takes into account practical factors. Additionally, it can also have corresponding feedback for different policies, so it has a greater reference value for reality. After the accuracy is verified, we compare the complexity. The complexity of the model can be described by many indicators and has a certain subjectivity. In machine learning, model complexity usually refers to the number of features or terms contained in a given prediction model and whether the selected model is linear or nonlinear. It can also refer to algorithm learning complexity or computational complexity. There is a risk of over-fitting for a model with much complexity, and it may be more expensive in calculation, as is the case with LSTM. For example, Google translation only applies the LSTM network structure of seven to eight layers. The calculation complexity of each update of LSTM is:  
\[O(KH+KCS+HI+CSI)=O(W) \tag{23}\]  
\[W=KH+KCS+CSI+2 CI+HI=O(KH+KCS+CSI+HI) \tag{24}\]  
In the formula above, \(K\) represents the number of output units. \(C\) represents the number of memory units. \(S\) (\(S\) > 0) represents the size of memory units. \(H\) is the number of hidden units. \(I\) is the number of units directly connected with memory units, gate units and hidden units, and \(W\) is the number of weights. The complexity of the four rolling regression models designed by [PERSON] et al. [34] and the logarithmic prediction model proposed by [PERSON] et al. [35] is O(\(y^{3}\)) or less, and \(y\) represents the data of the training dataset. Thus, the model complexity of single-update LSTM is higher than that of other models, which leads to the disadvantage of LSTM in computing speed and depth calculation. However, due to the relatively small data range selected by our model, the risk of calculation-related, time-consuming and gradient problems is limited in our model.