Research on optimisation of electronic information engineering course structure and modular design based on graph neural network

One of the main advantages of Graph Neural Networks (GNNS) applied to recommender systems is the ability to take into account the information of the graph structure, which improves the effectiveness of recommendations [28]. A graph is a data representation that describes complex transactions and consists of nodes and edges. Mathematically, it is generally formulated as graph G=(V, E). Where V represents nodes, which can be understood as things. E represents edges, which describe the relationship between two things.

GNNs capture the relationships between nodes and patterns in the graph structure by learning the representation vectors of each node. These models typically use a computational approach similar to that of convolutional neural networks, which extract useful features from the graph by performing a series of filter operations on the graph.

With the development of GNN, many new types of GNNs are emerging, as represented by Graph Convolutional Neural Networks (GCNs) [29]. GCNs are models that have evolved through spectral neural networks and Chebyshev polynomials. A spectrogram convolution operation is performed on the graph data, and the eigenvalues of the graph Laplacian are computed using the Fourier transform. The convolution of the method is defined as follows: (1) gθ*x=Ugθ(Λ)UTx

Where U denotes the eigenvectors of the normalized graph Laplacian matrix Lsym=I−D−−2AD−−2 , D is the degree matrix, Λ denotes the eigenvalue matrix of the Laplacian matrix, and g_θ(Λ) denotes the convolution kernel of graph convolution

The second generation GCN, which uses the first K terms of the Chebyshev polynomials to approximate the power operation of the Laplacian, yields the following equation: (2) gθ*x=U(∑k=0KθkTk(N))UTx

g_θ(Λ) in the above equation (1) is a polynomial function of Λ, i.e., g_θ(Λ)=θ₀Λ⁰ + θ₁Λ¹ +⋯+θ_nΛ_n. as n increases, the problem of vanishing gradient or gradient explosion occurs, so Chebyshev polynomial is used. The Chebyshev polynomial is defined as T_n(x)=2xT_n–1(x)–T_n–2(x), where T₀=1,T₁(x)=x. This polynomial has the property of T_n(cosθ)=cosθ, which results in a certain interval regardless of the size of n, and also needs to satisfy the eigenvalue size between [-1, 1], which can be deduced from Equation (3): (3) gθ*x=∑k=0KθkTk(Lsym−I)x

When K=1, Equation (4) can be derived: (4) gθ*x≈θ0T0(Lsym−I)x+θ1T1(Lsym−I)x

and T₀(x)=1,T₁(x)=x, which can be simplified to give Eq. (5): (5) gθ*x=θ0x−θ1D−12AD−12x (6) gθ*x=θ0x(D−12AD−12)

Where θ₀ is negligible, while the authors found through experiments that using the reorganization trick, i.e., adding a self-loop to the adjacency matrix, can lead to better results. The final formula after simplification is as follows: (7) GCN=D^−12AD−12x

Where A^=I+A,D^ denotes the degree matrix of the graph after adding the self-loop.

Some of the research on GCN after this was work on extending the Chebyshev first-order approximation to higher orders.The model of GCN is shown in Figure 1.

Figure 1.

GCN model

The core of semantic matching based knowledge graph technology is to map entities, attributes and their interrelationships to a specific semantic space, calculate their similarity, and then optimize the embedding vectors of entities, attributes and their interrelationships, and finally represent and reason about the knowledge graph effectively [30].

The matrix decomposition model is an important low-order embedding vector technique, that is widely used in recommender systems, and one of its most classic models is RESCAL. RESCAL model uses tensor decomposition to construct a knowledge graph; the triad (h,r,t) in the knowledge graph constitutes a tensor D, and the triad exists if Dhrt=1, and it does not exist if Dhrt=0. The RESCAL model aims to decompose the tensor D into relational embeddings and entity embeddings and finally let Dhrt ≈ hMrt. When given a ternary (h, r, t), his scoring functional equation is as follows: (8) fr(h,t)=hTMrt=∑i=0d−1∑j=0d−1[Mr]ij⋅[h]i⋅[t]i

The ternary group diagram of the knowledge map area of the EE course is shown in 2.

Figure 2.

Triplet of curriculum knowledge graph

The core idea of the graph convolutional network recommendation model (KGCN) is to combine the rich semantic information in the knowledge graph with the convolutional operations in the GCN to generate more accurate recommendation results [31]. In KGCN, a knowledge graph is used to represent association and attribute information between users and items. In a knowledge graph, entities can represent users, items, and their attributes, while relationships describe the connection methods and semantic information between these entities. By representing entities and relations with embedding vectors in a low-dimensional space, KGCN can capture potential associations and semantic similarities between entities. The framework diagram of KGCN is shown in Fig. 3:

Figure 3.

KGCN frame diagram

The main step of KGCN is to aggregate the information of neighboring nodes by constant iteration and then update the current node. But there is another important step before aggregation, that is, the similarity between the relational embedding and the learnable embedding must be calculated first, and the calculation formula is shown in equation (9): (9) πru=g(u,r)

In the above equation, g() represents the inner product function, u is the learnable embedding and r is the relational embedding. After calculating the similarity between u and r, the similarity between the relational embedding and the learnable embedding is normalized using the softmax function before assigning different weights to different nodes, which is handled as shown in equation (10): (10) π˜rv,eu=exp(πrv,eu)Σe∈N(v)exp(πrv,eu)

After obtaining the similarity between the relational embedding and the learnable embedding, the neighborhood of the node can be obtained by weighted summation of the neighboring entities e, which is calculated as shown in equation (11): (11) vN(v)u=∑eϵN(v)π˜rv,eue

After aggregating the neighbors of a node with that node, the representation learning of that node can be updated.KGCN updates the node after performing the neighbor aggregation as shown in equation (12): (12) eu[h]←agg(eδ(e)u[h−1],eu[h−1])

In the above equation, h represents the number of layers of KGCN. If the maximum number of layers is H, then the final representation of item v is v^u=e^u[H] .Finally the way to calculate the interaction probability of user u with item v is shown in equation (13): (13) y^uv=f(u,vu)

Experimental environment: CPU: Intel(R) Core(TM) i5-9600K CPU @ 3.70 GHz 3.70 GHz

Memory: 16G

Hard disk: 1T

Operating system: Windows 10

Experimental software: PyCharm, Jupyter Notebook

Programming language: Python 3.7, Tensorflow 1.8, Pytorch 1.6

Data set: MOOCCube

2.4.1

Model training and ablation experiments

In this section, the MOOCCube dataset is divided into a training set as well as a validation set in the ratio of 7:3, and the model is input for training as well as validation.

During the training process, the model adjusts the weights by comparing the loss of the model recognition output with the true value, and after 100 rounds of training, the Loss and Precision results of the model training and testing are shown in Fig. 4.

Figure 4.

Model training and testing of loss-precision results

The data in the figure shows the difference in loss between predicted and true during training.Obviously, the loss gradually decreases until it is smooth, so it can initially be considered that the model achieves the fitting effect.

After each round of model training, the weight parameters of the current training are loaded and tested against the prepared validation data, thus verifying the model’s effectiveness.As can be seen from the figure, the model’s testing effect on the validation data is basically the same as that on the training data, and the model converges to about 0.89 after 40 rounds of iterations of both Precision and the subsequent training to about 60 rounds of training, the Loss decreases to about 0.13, which tends to stabilize.

In this paper, further ablation experiments are done to verify that graph convolutional neural network and knowledge graph can improve the model performance, comparing the graph neural network, graph convolutional neural network, graph neural network + knowledge graph, and graph convolutional neural network + knowledge graph in this paper, which are denoted as models 1-4 in order, and the test performance of the four models in the above dataset. The MOOCCube dataset is used in Figure 5 to display the results of the ablation experiments. As can be seen from the figure, the test results of this paper’s model on Precision, Recall, and F1 are 0.922, 0.947, and 0.893, respectively, which are higher than the comparison models.

Figure 5.

Experimental results of ablation based on MOOCCube data set

2.4.2

Recommended effects

In this section, the built learning platform is validated for recommendation effect, and the MOOCCube dataset is also selected for validation experiments. Five models, FM, NFM, ECFKG, RippleNet, and KG-CR, are selected as comparisons. Figure 6 shows the results of the recommendation effect comparison experiment.

Figure 6.

The recommended results compare the results of the experiment

As can be seen from the figure, the lower the number of recommendations the better the performance of the recommendation. When the number of recommendations is 10, the model of this paper recommends an accuracy of 0.942, which is significantly higher than the other groups of models. When the number of recommendations rises to 40, the recommendation performance of each model decreases, while this paper’s model improves 21.3%~29.7%, 6.6%~12.4%, and 10.4%~32.8% in Precision, Recall, and F1, respectively, compared with the comparison model.

The reasons for the improved performance of this paper’s model in online EE course recommendations are further analyzed. First, compared to non-knowledge graph methods, the algorithm proposed in this paper utilizes graph convolutional neural networks to model the higher order connectivity in the graph structure, which can capture more information between learners and courses. And using semantic knowledge graphs as auxiliary information can enrich the course representation and reduce the sparsity of data.

In order to explore the influence of the hyperparameter learning rate, entity embedding dimension and aggregation method in the experiment on the above experimental results, this paper changes the learning rate, embedding dimension and aggregation method for the experiment. The results of the influence of different parameters on the recommendation effect of electronic information courses are shown in Table 1.

Table 1.

Effects of different parameters on recommended effects

Project	Size or way	Precision	Recall	F1
Learning rate	0.0001	0.35	0.26	0.33
	0.0005	0.41	0.31	0.37
	0.001	0.47	0.39	0.42
	0.005	0.54	0.46	0.49
	0.01	0.37	0.33	0.41
Entity embedded dimensions	32	0.31	0.28	0.34
	64	0.46	0.41	0.47
	128	0.34	0.36	0.33
Polymerization mode	Concatenate	0.59	0.49	0.46
	Sum	0.53	0.37	0.33
	Bi-interaction	0.63	0.55	0.57

From the table, it can be seen that for the influence of different parameters, with the increase of parameter values, the recommendation effect appears to increase and then reduce the trend. If the learning rate is too low, the experiment’s effect will not be good because too low a learning rate leads to the model convergence speed being too slow and may not achieve the optimal value. As the learning rate increases, the model becomes more and more effective. The best experimental results are obtained when the learning rate takes the value of 0.005. Precision, Recall, and F1 are 0.54, 0.46, and 0.49, respectively. The aggregation method is the best Bi-interaction, which makes full use of the way of summation and the way of the product of the elements, and the two ways complement each other.The aggregation approach is best with Bi-interaction, which makes full use of the summation approach as well as the elemental product approach, and the two approaches complement each other, thus performing the best.

The platform realizes the convenience of the user interface, the efficient processing of business logic, and the security and reliability of data access through B/S architecture. Specifically, the B/S architecture divides the platform into three levels, each of which undertakes specific functions and tasks. The online learning path recommendation platform’s overall architecture is depicted in Figure 7.

Figure 7.

Overall architecture of the learning path recommendation platform

The specific functions of the online learning platform are shown in Figure 8. This section further provides specific design and implementation details for each functional module to fully meet the diverse needs of users. The core modules of the learning path recommendation platform mainly include the learner module, the course knowledge mapping module, the learning path recommendation module and the platform management module, which together constitute the main framework of the platform.

Figure 8.

Platform function module diagram

The design process of the modular teaching mode of electronic information engineering courses mainly includes the following aspects: the first step is teaching analysis, including teaching content analysis, learner analysis, and teaching environment analysis; the second step is the design of course teaching objectives. The third step is to design the course module. The fourth step is the implementation of course modules. The fifth step is to design the module for teaching evaluation.

Analyzing this instructional design process shows that:

Teaching analysis is the foundation of the whole modular teaching design, which provides the basis for the subsequent modular teaching design according to the analysis of teaching content, analysis of learners, and analysis of the teaching environment.

In electronic information engineering courses, the implementation of modular teaching is the first thing to make corresponding adjustments to the teaching content, so the focus of modular teaching is to break the structure of the original course and the arrangement of the textbook, hands-on ability and the necessary computer literacy as the goal, the establishment of the course module.

The key to designing the course module is to determine the teaching content of each module. The determination of the content of each module should be based on the teaching objectives of the course to be achieved through the refinement and strengthening of the teaching objectives to determine the course needs to be mastered by the students of the basic capabilities, and then around the objectives of each module to determine the content of the teaching, the number of hours of teaching, teaching recommendations and implementation conditions.

The specific arrangement of the content of each module should be based on a real task. Multiple real tasks can constitute a large practical training project, the cognitive process involved in the project, the quality of the foundation, the cultivation of the ability to a thematic arrangement of the way integrated into a module through the development of the project training, to improve the hands-on ability of the students and the ability to innovate. Table 2 exhibits the modularized teaching content of electronic information engineering courses.

Modularized teaching of electronic information engineering courses is implemented using the digital learning platform designed above. In this paper, the learning flat belt is equipped with a course knowledge map and a graph convolutional network recommendation algorithm, which can realize the recommendation of the student’s learning path at the same time, greatly mobilize the students’ enthusiasm for learning, and improve the students’ interest in learning. It has a positive effect on the cultivation of students’ analytical and problem-solving abilities, and is of great help in improving the hands-on abilities of students majoring in electronic information engineering.

In addition, the teaching mode also integrates “case task-driven” through the classic case study to put forward the teaching task, students in the teacher’s guidance, the teaching task to analyze, discuss, independent exploration and collaborative learning, and finally complete the teaching task.In the implementation of each module, the content of the course module consists of several teaching cases and teaching tasks, which requires teachers to ensure that the cases and tasks are feasible, easy to operate and interesting when choosing cases and designing tasks so as to integrate the knowledge and skills that should be grasped by students into the cases and tasks.