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Datasets collection

The data studied in this paper mainly comes from open educational platforms and databases, covering three types of datasets. Firstly, the dataset of educational resources is collected through MOOC platform and the national platform of higher education wisdom education. After cleaning, more than 11,000 records of online courses, teaching materials and teaching videos are kept. Secondly, the teaching model datasets of different majors come from China Higher Education Student Information Network, which covers the teaching plans and curriculum structure data of more than 200 majors in colleges and universities across the country. After standardization, they are combined for model analysis35. In addition, due to the limited access to the characteristic data of students’ behavior teaching, 8,000 students’ learning behavior data are captured and simulated through the teaching records made public by local ministries of education, and combined with information such as study habits, attendance rate and grades, a multi-dimensional student learning dataset is formed. After data cleaning, 37,892 valid records are finally retained, and the variables with correlation coefficient greater than 0.3 are screened by correlation analysis in the feature extraction stage. After data preprocessing, 28,6062 data are retained for model training and testing.

The data information of training and testing is shown in Table 1:

Table 1 Data used in training and testing.

Experimental environment

The training and testing of SEOM model is based on the core goal of model design, and its performance is comprehensively and objectively tested from multiple levels and angles. Firstly, in terms of the accuracy and generalization ability of the model, cross-validation (K = 10) and set-aside validation are adopted to test its ability to maintain high prediction accuracy and strong generalization under different data distributions36. Meanwhile, based on Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), the error of the model is quantified to verify its ability to deal with multi-dimensional educational resources and complex teaching models. Secondly, in the aspect of learning path optimization, by calculating Cmin/df, Goodness of Fit Index (GFI), Adjusted Goodness of Fit Index (AGFI), Comparative Fit Index (CFI), Root Mean Square Residual (RMR) and Approximate Root Mean Square Error (RMSEA), and analyze the recommendation effect of the model on personalized learning paths in different major categories (engineering, science, medicine, law, education, management, literature, economics, art and agriculture) in common teaching scenes37,38,39. In addition, by setting an abnormal network environment, Shapley value is used to analyze the contribution and delay sensitivity of resource allocation, and the intelligent effect of resource allocation in complex environment is tested40,41.

Among them, the evaluation criteria of each index in the analysis of learning path optimization effect are shown in Table 2:

Table 2 The index test standard in the analysis of learning path optimization effect.

Parameters setting

In this paper, the Graph Attention Network (GAT) is selected as the core type of GNN, and the features of neighboring nodes are given different weights through the attention mechanism to capture the uneven dependence between nodes more accurately. GAT is especially suitable for personalized learning path planning and educational resource optimization because of its strong expressive ability and adaptability to complex relationships between nodes. GAT is used to model the multi-level interaction between students and knowledge points, dynamically adjust the weights of adjacent nodes through attention mechanism, and generate a feature vector representation that is more suitable for the actual learning scene. Its architecture consists of three layers of attention, and each layer adopts a multi-head attention mechanism to improve the robustness and global nature of feature capture. In the application environment, GAT first receives the high-quality features screened by RFA as input and constructs the initial graph structure. Then, through iterative feature updating and aggregation, the dependency map of learning path is gradually optimized, and finally personalized recommendation results are generated. The main reason for choosing GAT is that it can effectively reduce the over-smoothing problem compared with the traditional GNN, especially in the dynamic education scene, and it can handle the complex interaction between students’ learning behavior and knowledge points more accurately through the propagation of node characteristics and the weighted update of edges. SEOM hyperparameters and training methods are arranged as shown in Table 3:

Table 3 SEOM hyperparameter and training method.

Relevant parameters of common teaching scenes in the analysis and verification of model learning path optimization effect are shown in Table 4:

Table 4 Relevant parameters of common teaching scenes.

The relevant parameters of sudden abnormal network environment in the analysis and verification of model educational resource allocation effect are shown in Table 5:

Table 5 Relevant parameters of sudden abnormal network environment.

Of course, in order to better highlight the advantages of SEOM in this paper, referring to the literature review in the previous paper, five baseline models that are most relevant to this paper are selected, compared and verified under the same data standard (10,000 data in the dataset are randomly selected). The selected baseline models are sorted out, and the results are shown in Table 6:

Table 6 Baseline model compiled in this paper.

The software and hardware environment parameters in the whole training and testing of the model are shown in Table 7:

Table 7 Software and hardware environment parameters.

Performance evaluation

Analysis of accuracy and generalization ability of the model

The analysis results of SEOM model accuracy and generalization ability are shown in Fig. 2:

Fig. 2
figure 2

SEOM accuracy and generalization capability analysis (a) Cross-validation (b) Leave validation.

In Fig. 2, SEOM model shows high accuracy and good generalization ability in cross-validation (K = 10) and set-aside validation. The RMSE value of cross-validation fluctuates between 0.2 and 0.5, and the MAE value is between 0.1 and 0.5, which shows the stability of the model in dealing with multi-dimensional educational resources and complex teaching models. Meanwhile, the accuracy of the model remains at 85-97%, indicating its reliability in optimizing educational resources and recommending learning paths. The comparison between RMSE and MAE is slightly higher, which keeps fluctuating between 0.2 and 0.6, but within the accuracy range of 80-90%, indicating that the model still has strong adaptability and wide application potential.

Effect analysis of model learning path optimization

The analysis result of SEOM model learning path optimization effect is shown in Fig. 3:

Fig. 3
figure 3

Analysis on the optimization effect of SEOM learning path (a) Engineering (b) Science (c) Medicine (d) Law (e) Education (f) Management (g) Literature (h) Economics (i) Art (j) Agronomy.

Figure 3 shows that the Cmin/df of SEOM model is between 1.0 and 2.5 in different major categories and teaching scenes, indicating that the model has an ideal fitting degree in each scene. The indexes of GFI and AGFI are above 0.85, and CFI is close to 0.95, which shows that the model has high accuracy and rationality in capturing the dependence of knowledge points in different teaching modes. Meanwhile, RMR and RMSEA values are lower than 0.05, which shows that the residual of the model is small and the model has strong adaptability to the actual teaching scene. Especially in the personalized teaching scene, the recommendation effect of the model on the learning path is significantly improved, which further verifies SEOM’s intelligent optimization ability in the complex educational environment.

Effect analysis of model education resource allocation

The analysis results of educational resource allocation efficiency of SEOM model are shown in Fig. 4:

Fig. 4
figure 4

Analysis of the distribution effect of SEOM educational resources.

In Fig. 4, the Shapley value ranges from 0.1 to 0.4 in the abnormal network environment, indicating that there are significant differences in the contribution of different network environments to resource allocation. Among them, bandwidth bottleneck and network delay have great influence on the efficiency of resource allocation, and the delay sensitivity is high, up to 0.8, which shows that network delay has a strong interference effect on the allocation of teaching resources. The efficiency of resource allocation fluctuates between 60% and 95%, which depends on the stability of the network environment. The analysis results show that SEOM can intelligently optimize the allocation of educational resources under complex network conditions, especially in the environment of high delay and bandwidth bottleneck, and the model shows strong adaptability and resource allocation ability to ensure the effective completion of teaching tasks.

Comparative analysis of model with other baseline models

The comparative analysis results of SEOM model and other baseline models are shown in Fig. 5:

Fig. 5
figure 5

Comparative analysis of SEOM and other baseline models (a) 10,000 data (b) 2,000 data (c) 3,000 data (d) 4,000 data (e) 5,000 data (f) 6,000 data (g) 7,000 data.

As Fig. 5 shows, SEOM model has obvious advantages in many key indicators, especially when dealing with multi-dimensional educational resources optimization and personalized learning path recommendation, and its performance is superior to the traditional baseline model. In terms of model accuracy, the accuracy of SEOM is always above 95% when the data scale is gradually increased to 10,000, which is significantly higher than the stable values of GCN and SVM models of 88% and 83%, showing excellent generalization ability and robustness. At the same time, in the modeling of complex dependencies, SEOM effectively optimizes the distribution of feature weights by virtue of the attention mechanism of GATT. The RMR value is reduced to 0.035, which is significantly lower than the average value of 0.052 in other baseline models, reflecting that the fitting error of the model to multidimensional data is significantly reduced. In addition, in the optimization of resource allocation efficiency and learning path, SEOM maintains the allocation efficiency of more than 90% in the high data density environment through the dynamic weighted adjustment of Shapley value. Additionally, its resource adaptation ability is more prominent than that of KNN model, where the efficiency drops to 75%. This shows that SEOM optimizes the complex dependence among knowledge points in the personalized learning scene, and effectively realizes the intelligent allocation of teaching resources in the complex environment. This fully reflects its wide application potential in the intelligent reform of higher education.

Discussion

SEOM model combines RF, AdaBoost and GNN to build an intelligent optimization system for complex educational resources and personalized learning paths. RF improves the accuracy of multi-dimensional educational resources processing by means of adaptive enhancement mechanism, and GNN enhances the accuracy of the model in learning path prediction by constructing the dependency map between students and knowledge points. The model verification results show that the fitting indexes such as Cmin/df, GFI, AGFI and CFI are highly accurate, and the indexes of RMR and RMSEA are in a reasonable range, which indicates that SEOM has high fitting ability and small error. Especially in the abnormal network environment, SEOM shows excellent resource allocation optimization ability through Shapley value and delay sensitivity analysis. In addition, SEOM can intelligently recommend the optimal learning path according to students’ learning habits and knowledge points in personalized learning scenes, and realize the seamless docking of personalized teaching through real-time data update. In the aspect of educational resource management, SEOM intelligently allocates and transmits all kinds of resources by integrating with the management platform to ensure the efficient allocation of resources and the smooth progress of teaching tasks.

From the optimization point of view, SEOM effectively alleviates the bottleneck problem of feature extraction in traditional education model when dealing with high-dimensional and complex data through the deep combination of improved RF algorithm and adaptive enhancement mechanism. RF algorithm improves the robustness of feature selection through multi-tree structure, and adaptive enhancement mechanism further strengthens the comprehensive performance of weak classifiers, enabling SEOM to accurately capture key features in educational resources and optimize resource allocation strategies. On this basis, GNN, by virtue of its modeling ability of dynamic dependency, not only comprehensively depicts the complex interaction relationship, but also dynamically adjusts the weight of nodes by constructing the map structure between students and knowledge points. It effectively copes with the problem of nonlinear feature distribution and dynamic change in learning path recommendation. The verification results further illustrate this point. SEOM significantly reduces the error rate (RMSE value is reduced to 0.2–0.5) in high-noise data environment. Its efficient fitting ability is verified by Cmin/df and GFI, especially in complex network scenarios, which can accurately optimize the resource allocation efficiency through Shapley value and delay sensitivity analysis. Compared with the traditional model, the architecture design of SEOM has shown outstanding advantages in intelligent resource allocation, personalized learning path recommendation and adaptability of teaching scenarios, thus promoting the comprehensive realization of intelligent optimization of higher education.

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