An adaptive grouping-based graph convolutional neural network question recommendation method

Abstract

The application discloses a kind of based on adaptive grouping's graph convolutional neural network test question recommendation method, first introduce a grouping level attention module in graph convolutional neural network, so that network itself can be adaptively grouped to student node and test question node, so that different grouping corresponds to different levels, then carry out graph convolution operation in each group again, so that the information possibly interfering model learning transmitted from other grouping is isolated as far as possible;Residual connection is introduced in graph convolution operation simultaneously, to increase the depth of network as far as possible.A large number of experiments on disclosed data set Junyi-Math, AICFE-Math show that the method is effective, and is superior to the benchmark method in relevant indicators such as recall rate Recall.

Description

TECHNICAL FIELD

[0001] The application relates to a self-adaptive grouping-based graph convolutional neural network test question recommendation method and belongs to the fields of recommendation methods, graph neural networks and machine learning. BACKGROUND

[0002] With the development of the Internet, recommendation systems are increasingly needed by people. Collaborative filtering (CF) as a relatively early appearing recommendation method includes two categories of statistical-based (including user-based collaborative filtering (UserCF) and item-based collaborative filtering (ItemCF)) and model parameter-based. In the model parameter-based collaborative filtering method, there are relatively classic matrix factorization (MF) and various methods based on deep learning appearing later. The main learning purpose of these methods is to learn a vector representation for each user and item through the historical interaction data of the user.

[0003] There are also some methods that fully exploit the graph information existing in the recommendation field to make recommendations. Some early work mainly uses random walk methods to exploit indirect preferences to make recommendations. Some subsequent methods explore the user-item interaction bipartite graph to enrich the interaction between users and items and exploit some other collaborative relationships, such as the relationships between users and users and between items and items. HOP-Rec uses random walk random sampling positive samples to enrich the training data. WalkRanker and CSE use random walk methods to explore high-order relationships between users and users and between items and items. These methods all depend on the training samples collected by random walk, so the recommendation effect of the model is more dependent on the quality of the collected training samples.

[0004] Recently, collaborative filtering methods based on graph convolutional neural networks (GCNs) have achieved relatively good results, mainly due to the ability of GCNs to extract useful information from graph data structures. The main learning method of GCNs is the transmission and aggregation of messages between neighboring nodes in the graph. NGCF believes that this information from higher-order neighbors helps to obtain better collaborative signals. However, GCNs in the recommendation domain also suffer from oversmoothing, because graph convolution is essentially a special type of graph Laplacian smoothing operation, so general GCNs can only stack a few layers. Recent works have attempted to alleviate this problem. LR-GCN simplifies graph convolution by removing some non-linear operations and adds a form of residual connection to mitigate the oversmoothing issue. LightGCN is also a simplified version of GCN, removing some non-linear activation functions and feature transformation operations. Although LightGCN's primary purpose is not to alleviate the oversmoothing problem, it does partially mitigate it.

[0005] Currently, there is relatively little work applying graph neural networks to student test question recommendation scenarios. In student test question recommendation scenarios, students have varying learning levels, and the difficulty of the test questions also varies. Therefore, the student test question interaction graph has a hierarchical structure of information. However, general graph neural network recommendation methods, such as NGCF, LR-GCN, and LightGCN, only perform graph convolution operations on a single interaction graph without utilizing any hierarchical structural information.

[0006] As in Figure 1 In the student-question interaction graph, s1 and s2 represent the student IDs of two students with different learning levels. q1 to q4 represent the question IDs appropriate for s1's learning level, and p1 to p4 represent the question IDs appropriate for s2's learning level. If a student has completed a question, there is an edge connecting them. Since not all questions a student has completed are appropriate for their learning level—sometimes they may be too easy, and sometimes too difficult—for example, s1 might be able to complete question p1, which is not well-suited to their learning level. Figure 1 In the graph convolution operation, the two nodes are connected by a dashed line (if the test question matches the student's learning level, they are connected by a solid line). s2 will answer test question q4, which is not well-matched to its learning level. In the graph convolution operation, connecting p1 and s1 may introduce interfering information to the learning represented by node s1, and connecting q4 and s2 may introduce interfering information to the learning represented by node s2. Summary of the Invention

[0007] Based on the above analysis, this invention proposes a graph convolutional neural network-based test question recommendation method with adaptive grouping. This method attempts to group students and test questions of similar levels into the same group (i.e.,...). Figure 1 For example, the approach involves grouping nodes q1 to q4 and s1 into one group, and p1 to p4 and s2 into another group. Then, graph convolution operations are performed within each group to minimize interference from other grouping levels. To achieve this, we designed a group-level attention module to adaptively adjust the group a node belongs to. Graph convolution operations are then performed within the same group to further isolate interference from other groups and improve learning performance. We also introduce a residual connection operation within the graph convolution operation to maximize model depth. The key features of this method are the design of a group-level attention module and the introduction of a residual connection operation within the graph convolution operation. The flowchart of this method is shown below. Figure 2 It includes the following main steps:

[0008] (1) Constructing a student-question interaction graph. The approach to constructing interaction graphs is essentially the same in the recommendation domain. In the student-question recommendation domain, we can utilize students' historical question-answering data to construct a student-question interaction graph. The nodes in the interaction graph are student nodes and question nodes. If a student has answered a question, there is an edge connecting the two nodes; if a student has not answered a question, there is no edge connecting the two nodes. Thus, we can obtain the student-question interaction graph from the students' historical question-answering data and input it as a dataset into a graph convolutional neural network for training, validating, and testing the model.

[0009] (2) Construct and train the graph convolutional neural network model. The graph convolutional neural network model based on adaptive grouping in this invention is constructed. A simplified diagram of the overall model structure is shown below. Figure 3 The student-question interaction graph obtained in step (1) is input into the constructed model for training. After training, the vector representations of students and questions are obtained.

[0010] The model building process mainly involves the following steps:

[0011] a. Initialize model parameters to obtain the model's embedding layer, corresponding to... Figure 3 The 0th layer of the graph convolution. In the student test question recommendation scenario, the embedding layer is a parameter matrix consisting of M+N d-dimensional vectors, where M is the number of students, N is the number of test questions, d is the dimension of the vectors, and the elements of the matrix are the learnable model parameters.

[0012] b. A grouping-level attention module is introduced to generate the weight coefficients of students and test items belonging to each group. Here, we specially design a grouping-level attention module. After the d-dimensional student or test item embedding vector is input into the attention module, a K-dimensional vector can be obtained, where K is a model hyperparameter that can be adjusted, representing the total number of groups. The sum of the elements of the K-dimensional vector is equal to 1, representing a discrete probability distribution, where the value of the kth element represents the probability that the input student or test item belongs to the kth group, that is, the model adopts a soft grouping, and the probability that the student or test item belongs to a certain group is adjusted through model training, rather than hard division of the group to which the student or test item belongs.

[0013] c. Grouping graph convolution operation and residual connection. In order to realize the graph convolution operation within each group by using the weight coefficients of students and test items belonging to each group obtained in the previous step, we modify the standard graph convolution formula in this step. Taking the graph convolution formula of the student node embedding vector as an example, the standard graph convolution formula is where N u represents the set of test items that interact with student u, |N u | represents the size of the set; N i represents the set of students that interact with test item i, |N i | represents the size of the set; is a symmetric normalization term that can avoid the increase of vector values with the increase of the number of graph convolution layers. and represent the embedding vectors of student u and test item i after the l+1th and lth graph convolution operations, respectively. We introduce the weight coefficients g i of test item nodes belonging to each group into the standard graph convolution formula, and obtain the formula for graph convolution operation within each group for student nodes where, represents the vector representation of student u belonging to the kth group after the l+1th graph convolution operation; g i,k represents the weight size of test item i belonging to the kth group (i.e., the value of the kth element in g i ). Taking student u as an example, if g i,k = 1, it means that the adjacent node i of u also belongs to the kth group, and normal graph convolution operation can be performed; if g i,k = 0, it means that the adjacent node i of u does not belong to the kth group and is discarded. In this way, graph convolution operation within each group can be realized). The process of obtaining the formula for graph convolution operation within each group for test item nodes is similar to that for student nodes, and the formula is where, G represents the vector representation of question i belonging to the k-th group after the (l+1)th graph convolution operation. u,k This represents the weight of student u belonging to the k-th group; other symbols have the same meaning as above.

[0014] Residual connections, first introduced in the computer vision model ResNet, can increase model depth and alleviate the vanishing gradient problem in deep learning. We introduce residual connections into graph models, from... Figure 3 As can be seen, residual connections are a type of skip connection, where the results from the lower layers of the model bypass the intermediate layers and serve as input to higher layers. The following example, using a student node, explains the residual connection operation introduced in this model through formulas. All neighboring nodes i of student u... As input to the graph convolution operation, we obtain All adjacent points i of student u As input to the graph convolution operation, we obtain (The residual connections used in this model involve inputting the graph convolution results from previous layers into the graph convolution operations of subsequent layers.) Following this pattern, the graph convolution results for student u at layer L and group k can be obtained. All neighboring nodes i of student u... As input to the graph convolution operation, we can obtain The formula is expressed as Similarly, we can obtain the vector representation of question i at the Lth level and the kth group.

[0015] d. Combining the graph convolution results of each layer. Similar to the operation in LightGCN, we combine the graph convolution results of each layer as the final embedding vectors for optimizing the model loss function for both the student and the test question, and the coefficients of each layer are set to a fixed 1 / (1+L). At the grouped graph convolution, we combine the graph convolution results of different groups within the same graph convolution layer as the graph convolution result of that layer, as expressed in the following formula:

[0016]

[0017]

[0018] e. Use the Bayesian Personalized Ranking loss (BPR loss) function to train the model. The BPR loss function is a common pairwise learning approach. We use the BPR loss function to optimize the model, training it to minimize the BPR loss function. Minimizing the BPR loss function involves continuously adjusting the parameter values ​​in the student and question embedding vectors using the BP (Error Back Propagation) algorithm to achieve the effect of first-order neighbors (with...).Figure 1 For example, if s1 and q1 are directly connected by an edge, then these two nodes are first-order neighbors; if q1 and p1 are connected through node s1, then these two nodes are second-order neighbors; and so on, we can understand what other orders of neighbors mean. Generally, neighbors of second order or higher are called higher-order neighbors. For students and questions, the probability that a student can answer a question is greater than the probability that the student can answer a question from a higher-order neighbor connected to that student. After the model is trained, we can sort the questions based on the probabilities calculated from the vectors between the question nodes and a student node, filter out questions the student has already answered, and select the top few questions as recommendations for that student.

[0019] (3) Calculate the correlation between vectors. After the model is trained, use the vector representation obtained in step (2) to calculate the correlation between the student vector and the test question vector (the correlation used in this invention is the inner product between the two vectors).

[0020] (4) Obtain the recommendation results. After obtaining the N relevance values ​​between a student and N test questions using step (3), sort them from high to low according to the relevance value, filter out the test questions that the student has already done, and select the top n test questions to recommend to the student, thus completing the entire recommendation process.

[0021] This method utilizes grouping to extract hierarchical structural information about student learning levels and question difficulty in the student-question interaction graph. By designing a group-level attention module and modifying the standard graph convolution formula, graph convolution operations are performed within each group. A form of residual connection operation is also introduced to appropriately increase the model depth. Through these improvements, this method achieves better recommendation performance. Extensive experiments on public datasets Junyi-Math and AICFE-Math demonstrate its effectiveness, outperforming benchmark methods such as MF, NeuMF, GCMC, NGCF, and LightGCN in terms of recall and NDCG. Attached Figure Description

[0022] Figure 1 Example diagram of interactive test questions for students.

[0023] Figure 2 This is a flowchart for using a graph neural network to recommend test items.

[0024] Figure 3 This is a simplified diagram of the model structure.

[0025] Figure 4 This is an example diagram of the interaction matrix.

[0026] Figure 5 A record of a student's history homework completion behavior.

[0027] Figure 6 The top 5 test questions recommended for a student by the graph neural network model of the method. DETAILED DESCRIPTION

[0028] The specific embodiments of the present application are described in further detail below in combination with mathematical formulas, experimental results and drawings.

[0029] (1) Constructing a student test interaction graph

[0030] The user-item interaction matrix (in the student test recommendation scenario, the user is a student and the item is a test), M and N represent the number of users and items in the data set, respectively, and r u,i is the element in the u-th row and i-th column, which represents that the user u and the item i have interacted if the value is non-zero, and that they have not interacted if the value is zero. Figure 1 The student test interaction graph shown in FIG. 1 can be represented by an interaction matrix of 2 rows and 8 columns, as shown in FIG. 2. Figure 4 Student s1 has done test q1, so the element value in the corresponding position is 1, and student s1 has not done test p1, so the element value in the corresponding position is 0. Similarly, the meaning of the element values in other positions can be known. The user-item interaction graph can be obtained from the user-item interaction matrix wherein represents the user node and the item node, and ε represents the edge between the nodes. If a user and an item have interacted, there is an edge between them. Figure 4 The interaction graph corresponding to the interaction matrix of FIG. 3 is shown in FIG. 4. Figure 1 Student s1 has done test q1, so there is an edge between the two nodes, and student s1 has not done test p1, so there is no edge between the two nodes. Similarly, the relationship between other nodes and nodes can be known. The user-item interaction graph can be input into the graph convolutional neural network to train, validate and test the model.

[0031] (2) Constructing and training a graph convolutional neural network model

[0032] a. Initialize the model parameters to obtain the embedding layer of the model

[0033] Similar to many previous works, in the embedding layer, the following formula is used: and represent the vector representation of the 0th layer of student u and test i, respectively, which is obtained by the Xavier initialization method, wherein d is a hyperparameter, representing the dimension of the embedding vector. The larger d is, the more parameters the model can learn, and the higher the complexity of the model, which requires a larger training set to train. The embedding vectors of all students and tests in the data set can form a learnable parameter matrix where M represents the number of students, and N represents the number of test questions.

[0034] b. Introducing a grouping-level attention module

[0035] Generally, we believe that in the interaction graph, the students and test questions directly connected can better depict each other, and the students and test questions directly connected are the first-order neighbors of the nodes in the interaction graph. In the graph convolutional neural network, the information of the first-order neighbors can be obtained through one layer of graph convolution operation. Therefore, in the grouping-level attention module, we take the initial, i.e., the 0th layer of vector representation and the 1st layer of vector representation obtained after one layer of graph convolution as the input, and after passing through a multilayer perceptron (MLP) and a softmax function, the weight coefficients of the students and test questions belonging to each group are obtained. The formula of one layer of graph convolution is as follows:

[0036]

[0037]

[0038] N u represents the set of test questions that interact with the student u, and |N u represents the size of the set; N i represents the set of students that interact with the test question i, and |N i represents the size of the set; is a symmetric normalization term, which can avoid the increase of the value of the vector with the increase of the number of graph convolution layers. and respectively represent the vector representation of the student u and the test question i after one layer of graph convolution.

[0039] Then, taking the 0th layer and the 1st layer of student and test question vectors as the input, the final weight coefficients can be obtained, and the formula is as follows:

[0040]

[0041]

[0042] g u and g i are both K-dimensional vectors, and K is the total number of groups, where the kth dimension of g u represents the probability of the student u belonging to the kth group, and the kth dimension of g i represents the probability of the test question i belonging to the kth group. Such probability-based values are mainly obtained through the softmax function. The formula definition of the softmax function is as follows:

[0043]

[0044] where exp is the exponential operation, the dimension of vector x is K, and the value of the i-th dimension of vector x is x i After the softmax function, we get From the definition of the softmax function, we can get That is, the sum of the values of each element of the new vector obtained after a vector passes through the softmax function is 1, that is, it can represent a discrete probability distribution. For example, g u , the sum of the K elements in g u is 1, the value of the first dimension is used to represent the probability that student u belongs to the first group, the value of the second dimension is used to represent the probability that student u belongs to the second group, and so on, so we can know the meaning of other dimensions. That is, this model adopts a soft grouping, that is, through model training to adaptively adjust the probability that a student or a test belongs to a certain group, rather than rigidly dividing which group a student or a test belongs to.

[0045] where MLP is a three-layer neural network, and how to get g u For example, the network structure of MLP is described in detail as follows.

[0046]

[0047] is the weight coefficient of the first layer of MLP; is the bias of the first layer of MLP; d is the dimension of the vector; LeakyReLU is the activation function; g u1 is the output of the first layer of MLP.

[0048] g u2 = LeakyReLU(W2g u1 +b2)

[0049] is the weight coefficient of the second layer of MLP; is the bias of the second layer of MLP; g u2 is the output of the second layer of MLP.

[0050] g u = softmax(W3g u2 +b3)

[0051] is the weight coefficient of the third layer of MLP; is the bias of the third layer of MLP; K is the total number of groups.

[0052] c. Group convolution operation and residual connection are performed

[0053] From the second layer, the group convolution operation and the residual connection operation are introduced, and the formula of the graph convolution operation of the second layer and the kth group is as follows:

[0054]

[0055]

[0056] and respectively represent the vector representation of the kth group after the second graph convolution of the student u and the test item i; g u,k and g i,k respectively represent the weight size of the kth group of the student u and the test item i (i.e., the value of the kth dimension in g u and g i ). Taking the test item i as an example, if g u,k = 1, it means that the adjacent point u of i also belongs to the kth group, and the normal graph convolution operation can be performed; if g u,k = 0, it means that the adjacent point u of i does not belong to the kth group and is discarded. In this way, the graph convolution operation within the group is realized.

[0057] As the input of the graph convolution operation, the As the input of the graph convolution operation, the (the graph convolution result of the previous layer is also input into the graph convolution operation of the subsequent layer, which is the residual connection used in the present model).

[0058] Similarly, the graph convolution result of the Lth layer and the kth group of the student u can be obtained. As the input of the graph convolution operation, the The formula is as follows:

[0059]

[0060] Similarly, the vector representation of the Lth layer and the kth group of the test item i can be obtained:

[0061]

[0062] d. Combining the graph convolution results of each layer

[0063] Similarly to the operation in LightGCN, the graph convolution results of each layer are combined, and the coefficients of each layer are set to be fixed 1 / (1+L). In the group convolution, the convolution results of different groups in the same layer are combined as the convolution result of the layer, and the formula is as follows: ​​​

[0064]

[0065]

[0066] e. Training of the model using BPR loss function

[0067] The model adopts a pair-wise learning manner, in which a positive sample needs to be equipped with a negative sample. In the test question recommendation task, if a student has done a test question, the two constitute a positive sample, and if a student has not done a test question, the two constitute a negative sample, a positive sample and a negative sample constitute an input sample. That is, we need to constitute a triple (u, i + ,i - ), u and i + have interacted, constituting a positive sample, and u and i - have not interacted, constituting a negative sample. The loss function is the BPR loss function, which is expressed as follows:

[0068]

[0069] wherein, and are the inner products of the corresponding student and test question vectors, which are expressed as follows:

[0070]

[0071]

[0072] wherein, S = {(u, i + ,i - ) | (u, i + ) ∈ V + , (u, i - ) ∈ V -} represents the training set; V + represents the positive sample set in the training sample; V - represents the negative sample set in the training sample; λ is a regularization coefficient; and || Θ || 2 is an L2 regularization term.

[0073] Experiments are conducted on two public datasets Junyi-Math, AICFE-Math, and the specific information of the two datasets is shown in Table 1. According to the general preprocessing method, students and test questions with less interaction are filtered out to ensure that students and test questions interact at least 5 times. For each dataset, leave-one-out method is used for division, that is, the last question of each student is used as the test set, the second last question is used as the validation set, and the rest is used as the training set. The model is trained on the training set, the model hyperparameters are selected on the validation set, and finally the test set is used to measure the final performance of the model. Recall and normalized discounted cumulative gain (NDCG) are used to measure the performance of the model.

[0074] Table 1: Related information of the dataset

[0075] Dataset Number of students Number of test questions Number of wrong question behaviors Junyi-Math 8,394 700 118,540 AICFE-Math 1,075 863 22,990

[0076] In the selection of model parameters, the dimensions of student and test question vectors are fixed at 64, the Adam gradient optimizer is used, the default learning rate is 0.001, the default batch size is 1024, the L2 regularization coefficient is 0.0001, the number of graph convolution layers is selected from {3, 4, 5, 6, 7}, the number of groups is selected from {2, 3, 4}, and the early stopping strategy and LigthGCN are consistent.

[0077] To verify the effectiveness of the model, experiments are compared with the following benchmark models:

[0078] MF is a matrix factorization method optimized using BPR loss function. From the perspective of deep learning, MF is a shallow deep learning model.

[0079] NeuMF is a multi-hidden-layer MF that uses MLP instead of vector inner product calculation, and can be combined with MF.

[0080] GCMC uses one layer of graph convolution to obtain the direct connection between nodes.

[0081] NGCF combines collaborative filtering and graph convolution, and uses graph convolution to obtain the characteristics of high-order neighbors to improve the recommendation effect.

[0082] LightGCN is a simplified version of NGCF that removes feature transformation and activation functions, making graph convolution more suitable for recommendation tasks and achieving good results.

[0083] The experimental comparison results of the model and other models are shown in Table 2, and all the reported results are experimental results on the test set. It can be seen that compared with other benchmark models, the model achieves the best results on two public data sets.

[0084] Table 2: Final experimental comparison results of each model

[0085]

[0086] After the model training converges, the e u and e i are the final vector representations of the students and the test questions.

[0087] (3) Calculate the correlation between vectors

[0088] Using the final vector representations of the students and the test questions e u and e i obtained in step (2), calculate the inner product between the student vector and the test question vector.

[0089] (4) Get the recommended results

[0090] Finally, after obtaining the N correlation values between a certain student and N test questions in step (3), sorting them from high to low, filtering out the test questions that the student has already done, and selecting the top n test questions to recommend to the student, the entire recommendation process is completed. Figure 5 is the test question record of a certain student, Figure 6 are the top 5 test questions recommended to the student by the method, and it can be seen that the knowledge points involved in the recommended test questions and the knowledge points of the test questions in the historical behavior record are basically consistent, which directly shows that the recommendation of the method is effective.

Claims

1. An adaptive grouping-based graph convolutional neural network question recommendation method, comprising the following steps: (1) Using the student's historical test behavior data, a student test interaction graph is constructed and input into a graph convolutional neural network to train, validate and test the model; (2) Construct and train a graph convolutional neural network model a. Initialize the model parameters to obtain the embedding layer of the model; In the embedding layer, we use and denote the 0-th layer vector representation of student u and item i, respectively, which are initialized by Xavier initialization, where d is a hyperparameter representing the dimension of embedding vectors; the embedding vectors of all students and items in the dataset form a learnable parameter matrix where M denotes the number of students and N denotes the number of items. b. Realize adaptive grouping of student nodes and test nodes in the student test interaction graph through a grouping level attention module; In the grouping level attention module, the initial 0th layer vector representation and the 1st layer vector representation obtained after one layer of graph convolution are taken as input, and after passing through a multi-layer perception MLP and a softmax function, the weight coefficients of students and tests belonging to each group are obtained; The formula of one layer of graph convolution is as follows: N u a set of test questions that representative u has interacted with, |N u | represents the size of the set; i a set of students that test question i has interacted with, |N i | represents the size of the set; is a symmetric standardization term, which can avoid the increase of the value of the vector with the increase of the number of graph convolution layers; and respectively represent the vector representation of student u and test question i after one layer of graph convolution. Then the student and test vectors of the 0th layer and the 1st layer are taken as input to obtain the final weight coefficient, which is expressed as follows: where MLP is a three-layer neural network; g u and g i are K-dimensional vectors, K is the total number of groups, where the kthdimension of g u represents the probability that student u belongs to the kthgroup, and the kthdimension of g i represents the probability that item i belongs to the kthgroup; soft grouping is used, i.e., the probability that a student or an item belongs to a certain group is adjusted adaptively through model training, rather than hard division of which group a student or an item belongs to; c. Grouping graph convolution operation and residual connection, realize the graph convolution operation and residual connection operation in each group on the basis of adaptive grouping; From the 2nd layer, the grouping graph convolution operation and the residual connection operation are introduced, and the graph convolution operation formula of the 2nd layer and the kth group is as follows: and respectively represent the vector representation of student u and test item i after the second graph convolution, which belongs to the kth group; g u,k and g i,k respectively represent the weight size of student u and test item i belonging to the kth group, that is, g u and g i the value of the kth dimension; if g u,k = 1, it means that the adjacent point u of i also belongs to the kth group, and the normal graph convolution operation is performed; if g u,k = 0, it means that the adjacent point u of i does not belong to the kth group, and is discarded, thereby realizing the graph convolution operation within the group; all the adjacent points i of the student u As the input of the graph convolution operation, the following is obtained all the adjacent points i of the student u As the input of the graph convolution operation, the following is obtained ; that is, the graph convolution result of the previous layer is also input into the graph convolution operation of the subsequent layer, which is the residual connection used by the present model; the graph convolution result of the Lth layer and the kth group of the student u is obtained by repeatedly operating multiple times; all the adjacent points i of the student u As the input of the graph convolution operation, the following is obtained The formula is as follows: Similarly, the vector representation of the i-th test in the Lth layer and the kth group is obtained: d. Combine the graph convolution results of each layer; Similar to the operation in LightGCN, the graph convolution results of each layer are combined, and the coefficients of each layer are set to fixed 1 / (1+L). In the grouping convolution, the convolution results of different groups in the same layer are combined as the convolution result of the layer, which is expressed as follows: e. Use BPR loss function to train the model; The loss function used is BPR loss function, which is as follows: wherein and is the inner product of the respective student and test vectors, which is expressed by the formula: where S = {(u, i + ) , i - > , (u, i + ) ∈ V + , (u, i - ) ∈ V -} represents the training set; V + represents the positive sample set in the training example; V - represents the negative sample set in the training example; λ is a regularization coefficient; and ||Θ|| 2 is an L2 regularization term. After the model training is completed, the e u and e i are the final vector representations of the students and the test questions. (3) Calculate the correlation between vectors; The final vector representation e of the student and the test question obtained using step (2) u and e i The inner product between the student vector and the test question vector is calculated; (4) Obtain the recommendation result; Finally, after obtaining the N correlation values between a certain student and N tests in step (3), the tests are sorted from high to low according to the correlation, and after filtering out the tests that the student has done, the top n tests are recommended to the student, thereby completing the entire recommendation process.

Images