Learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis

Abstract

The learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis disclosed in the application comprises: obtaining learner information; modeling a learner portrait according to the learner information to obtain a learner feature vector; constructing a knowledge point feature vector according to a knowledge graph; inputting the learner feature vector and the knowledge point feature vector into a neural collaborative filtering network to obtain a set of explicit and implicit weak knowledge points of the learner for the knowledge points that should be mastered; inputting the set of explicit and implicit weak knowledge points into a cognitive level diagnosis model, sorting, combining and disassembling the knowledge points by the cognitive level diagnosis model, and outputting a final personalized learning path recommendation list. The learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis can better adapt to the cognitive level and learning characteristics of the learner and improve the real-time performance and robustness.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent education, and particularly relates to a learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis. BACKGROUND

[0002] With the rapid development of education informatization, teaching resources are increasingly abundant, and teaching environments are gradually improving. However, the massive amount of teaching resources brings problems such as resource overload and selection difficulty to learners, and cannot meet the personalized teaching needs of learners, which easily leads to learning confusion and other phenomena. Therefore, in the research of personalized learning path generation, various methods have been proposed. Traditional methods include rule-based, clustering-based, and recommendation system-based methods. With the continuous development of deep learning technology, deep learning-based personalized learning path generation methods have also received widespread attention. Neural collaborative filtering algorithm is a commonly used recommendation algorithm and has been widely used in personalized recommendation field. Neural collaborative filtering algorithm uses neural network for embedding learning of learners and items, so as to well handle the problems of data sparsity and cold start. In the field of personalized learning path generation, researchers have also begun to try to apply neural collaborative filtering algorithm to the learning path generation task. For example, neural collaborative filtering algorithm is used to predict the knowledge point mastery level and learning interest of learners, so as to generate personalized learning path.

[0003] In addition, cognitive diagnosis technology is also widely used in personalized learning path generation. Cognitive diagnosis technology aims to diagnose and evaluate the cognitive level of learners, so as to help learners find their own learning difficulties and weak links, and provide corresponding teaching suggestions and support. Cognitive diagnosis technology combined with neural collaborative filtering algorithm can better recommend knowledge points and learning resources suitable for the cognitive level and learning interest of learners, so as to realize personalized learning path generation.

[0004] Finally, subject knowledge point modeling and learning path generation are also important directions of personalized learning path generation research. Subject knowledge point modeling can decompose and organize subject knowledge points to form a knowledge point system, providing a basis for learning path generation. Learning path generation needs to consider the correlation, difficulty and sequence of subject knowledge points and other factors. In recent years, researchers have also begun to explore the application of deep learning technology in subject knowledge point modeling and learning path generation, using deep learning technology for knowledge representation and learning path generation. For example, a deep neural network is used for embedding learning of subject knowledge points to form knowledge representation, and then a generative model is used to generate a learning path. In addition, some researchers also use knowledge graph technology to model subject knowledge points, so as to provide more accurate and comprehensive support for personalized learning path generation.

[0005] However, there are still many challenges in the current personalized learning path generation algorithm based on neural collaborative filtering and cognitive level diagnosis. First, the existing algorithm lacks fine analysis of the cognitive level of learners, resulting in a lack of personalization in the generated learning path; second, the real-time and robustness of the algorithm need to be further improved to cope with complex learning scenarios. Finally, single neural collaborative filtering or cognitive level diagnosis cannot track and analyze learners in real time, and cannot comprehensively analyze the current learning state of learners. SUMMARY

[0006] The purpose of the present application is to provide a learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis, which can better adapt to the cognitive level and learning characteristics of learners and achieve real-time and robustness improvement.

[0007] The technical solution adopted by the present application is: a learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis, comprising the following steps:

[0008] Step 1, obtaining learner information, including basic information, learning process and learning results;

[0009] Step 2, modeling the learner portrait according to the learner information obtained in step 1 to obtain a learner feature vector;

[0010] Step 3, constructing a knowledge point feature vector according to a knowledge graph;

[0011] Step 4, inputting the learner feature vector obtained in step 2 and the knowledge point feature vector obtained in step 3 into a neural collaborative filtering network to obtain a set of explicit and implicit weak knowledge points for the learner to master;

[0012] Step 5, inputting the set of explicit and implicit weak knowledge points obtained in step 4 into a cognitive level diagnosis model, sorting, combining and disassembling the knowledge points by the cognitive level diagnosis model, and outputting a final personalized learning path recommendation list.

[0013] The present application is characterized in that,

[0014] The basic information in step 1 includes the learner's number, age, gender and education; the learning process includes the learner's subject field, learning style, learning cost and learning time; the learning results include the learner's learning history, learning effect, learning progress and learning goal.

[0015] Step 2 specifically comprises the following steps:

[0016] Step 2.1, modeling the learner portrait according to the learner information obtained in step 1 as shown in formula (1):

[0017]

[0018] In formula (1), the components included in the basic information a are: ID, Age, Sex, and Edu; the components included in the learning result y are: Rec, Res, Pro, and Tar; the learning process b is composed of the eigenvalues λ1, λ2 of the two-dimensional matrix composed of the sub-matrix learning feature b1 and learning cost b2, and satisfies:

[0019]

[0020] In formula (2), the components included in the learning feature b1 are: Are and Sty; the components included in the learning cost b2 are: Exp and Tim;

[0021] Step 2.2, after modeling the learner portrait, the learners are classified by clustering, and the basic vector corresponding to each ID is taken as the center vector to obtain the cluster vector of its sub-cluster in turn, and then the learners are taken back to the learner cluster and assigned a cluster attribute, and the original basic portrait is expanded to a learner feature vector, and the private attribute of the learner is not replaced, so the learner feature vector is represented as:

[0022]

[0023] In formula (3), ID i is the learner feature vector; a' is the cluster vectorized basic information a, N Age is the cluster vector obtained by taking Age as the cluster center vector in the learner set library Stu, N Edu is the cluster vector obtained by taking Edu as the cluster center vector in the learner set library Stu; b' is the cluster vectorized learning process b, is the cluster vector obtained by taking the learning feature b1 as the cluster center vector in the learner set library Stu, is the cluster vector obtained by taking the learning cost b2 as the cluster center vector in the learner set library Stu; y' is the cluster vectorized learning result y, N Rec is the cluster vector obtained by taking the learning history Rec as the cluster center vector in the learner set library Stu, N Pro is the cluster vector obtained by taking the learning progress Pro as the cluster center vector in the learner set library Stu.

[0024] Step 4 specifically includes the following steps:

[0025] Step 4.1, the learner feature vector obtained in step 2 and the knowledge point feature vector obtained in step 3 are subjected to linear projection and nonlinear projection respectively, the feature distance between the learner feature and the knowledge point feature is represented as:

[0026]

[0027] In formula (4), U i , V j respectively represent two feature vectors, represents the dot product between the two feature vectors, and respectively represent the norms of and ; the value range of the final cosine distance is between [-1, 1], the closer to 1 indicates that the distance between the two feature vectors is closer, that is, the similarity is higher, and they can be fused, otherwise the lower the more unable to be fused;

[0028] Step 4.2, the learner linear projection and the knowledge point linear projection obtained in step 4.1 are combined to generate a learner-knowledge point static interaction matrix y ij , as shown in formula (5):

[0029]

[0030] In formula (5), U ik is the mastery of the i-th learner to the k-th knowledge point, P jk is the examination of the j-th question to the k-th knowledge point, and the individualized parameter of the learner to the specific target knowledge point;

[0031] Step 4.3, the learner nonlinear projection and the knowledge point nonlinear projection obtained in step 4.1 are combined to generate a learner-knowledge point dynamic interaction matrix R ij , as shown in formula (6):

[0032]

[0033] In formula (6), n is the number of learners, β x，i represents the feature vector of the learner i, d ij represents the difficulty value of the knowledge point j, c ij represents the cost value of the learner i on the knowledge point j; σ represents the sigmoid function, and w1 and w2 are weight parameters;

[0034] Step 4.4, the learner-knowledge point static interaction matrix obtained in step 4.2 is dimensionally analyzed to obtain an explicit weak knowledge point set, and for the explicit weak knowledge point set, only the first q learner clusters need to be filtered out. The knowledge points mastered by the learner are the explicit weak knowledge points of the learner, as shown in equation (7):

[0035]

[0036] In equation (7), is the proportion of knowledge points mastered by all learners in the cluster, b i is y ij is the weighted average value of the ith row;

[0037] Step 4.5, the learner-knowledge point dynamic interaction matrix obtained in step 4.3 is dimensionally analyzed to obtain an implicit weak knowledge point set, as shown in equation (8):

[0038]

[0039] In equation (8), represents the target space, θ k represents the knowledge iteration parameter, p(Z i，j |b i，j , R i , R j , σ R , θ k ) represents the probability that the performance of learner i on knowledge point j is predicted to be weak, σ R represents the learner's historical learning behavior data.

[0040] Step 5 is as follows:

[0041] Step 5.1, input the explicit weak knowledge point set X ij obtained in step 4.4 and the implicit weak knowledge point set Z ij obtained in step 4.5 into the cognitive diagnosis model, and the fuzzy cognitive diagnosis of the learner under the current learning state is represented as:

[0042]

[0043] In equation (9), ρ represents the proportion parameter between the common characteristics and the learning independent attribute mastery mode;

[0044] Step 5.2, track and update the parameters of the dynamic learning process of the learner, i.e., update and self-repair Z ij , and the objective function satisfies equation (10):

[0045]

[0046] In formula (10), λ1 and λ2 are regularization parameters; the learner feature matrix β1 and the knowledge point feature matrix β2 are updated by using a stochastic gradient descent method;

[0047] Step 5.3, recommending the knowledge points finally meeting the cognitive level condition range of the learner, and the generated recommendation list is the personalized learning path of the learner.

[0048] The beneficial effects of the present application are:

[0049] 1. The present application more comprehensively considers the static personalized parameters of the learner and the dynamic learning process data, so that the personalized learning path recommendation for the target learner is more accurate.

[0050] 2. The present application better captures the interaction information between the learner and the knowledge point, so that the personalized path recommendation is more accurate.

[0051] 3. The present application considers the different preferences among learners, more comprehensively and accurately acquires the learner preference features, and improves the prediction accuracy.

[0052] 4. The present application uses the historical record information of the learner, and can be trained offline when training the model. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is a structural schematic diagram of the learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis of the present application;

[0054] Figure 2 is an experimental effect diagram of the learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis of the present application. DETAILED DESCRIPTION

[0055] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0056] Embodiment 1

[0057] The present application provides a learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis, comprising:

[0058] Obtaining the basic information of the learner, including the number, age, gender, education, and other basic information of the learner.

[0059] Obtaining the learning process feature attribute of the learner, including the subject field, learning style, learning cost, learning time, and other information of the learner.

[0060] Obtaining the learning history record result of the learner, including the learning history, learning effect, learning progress, learning goal, and other information of the learner.

[0061] According to the basic attributes of the learners, the learner portrait modeling is performed to obtain the basic feature vector of the learners; the modeling is performed from three aspects, which are basic information, learning process and learning result, and the formula definition is:

[0062]

[0063] The components contained in the basic information α correspond to learner number, age, gender and education in sequence; the components contained in the learning result γ correspond to learning history, learning effect, learning progress and learning target in sequence. The learning process β is composed of the characteristic values λ1 and λ2 of the two-dimensional matrix composed of the learning characteristics β1 and the learning cost β2, and satisfies:

[0064]

[0065] The components contained in the learning characteristics β1 correspond to subject field and learning style in sequence; the components contained in the learning cost β2 correspond to learning cost and learning time in sequence.

[0066] After the learner portrait modeling is performed, the learners are classified by using clustering, and the basic vector of each ID is taken as the center vector to obtain the cluster vector of the sub-cluster. For example, the cluster vector obtained in the learner set library Stu by taking the age Age as the clustering center vector can be represented as:

[0067]

[0068] By repeating the above steps, the learners are taken back to the learner cluster in sequence, and are given the clustering attribute, and the original basic portrait is expanded to the learner feature vector, and the private attribute of the learner is not replaced. Therefore, the learner feature vector can be represented as:

[0069]

[0070] The ID i is the learner feature vector; the α' is the basic information α of the cluster vectorization, the N Age is the cluster vector obtained in the learner set library Stu by taking the age Age as the clustering center vector, the N Edu is the cluster vector obtained in the learner set library Stu by taking the education Edu as the clustering center vector; the β' is the learning process β of the cluster vectorization, the N is the cluster vector obtained in the learner set library Stu by taking the learning characteristics β1 as the clustering center vector, is the cluster vector obtained in the learner set library Stu by taking the learning cost β2 as the clustering center vector; the γ' is the learning result γ of the cluster vectorization, and the N RecN is a cluster vector obtained in the learner set library Stu with the learning history Rec as a clustering center vector. Pro N is a cluster vector obtained in the learner set library Stu with the learning progress Pro as a clustering center vector.

[0071] The learners in the learner set are taken back to the learner cluster, and a new learner cluster with multiple vector clustering centers is recalculated until the cluster center remains unchanged. In this way, both the vector set of the basic attributes of each learner is established, and the purpose of classifying, merging, and normalizing learners according to different attributes to form a common attribute library is achieved. In this process, each feature value is scaled, and all feature values are merged into a unified range, so that each learner feature satisfies:

[0072]

[0073] where x is the original feature value, and x satisfies: x e {a T , b T , g T}, x' is the scaled value, min(x) is the minimum value of the feature value, and max(x) is the maximum value of the feature value. In this way, the dimensional and proportional differences between feature values can be eliminated, thereby making different features more comparable.

[0074] According to the knowledge graph, knowledge point feature vectors of knowledge points are obtained from different dimensions such as difficulty levels of knowledge points;

[0075] The learner basic feature vector and the knowledge point basic feature vector are input into the neural collaborative filtering network to obtain the explicit and implicit weak knowledge point set of the learner for the knowledge point to be mastered. After obtaining the feature vector interaction matrix of the learner and the knowledge point, the matrix decomposition method is used to decompose it into row vectors representing different mastery of the same learner for analysis, and column vectors representing the mastery of different learners under the same knowledge point. Here, combined with learner clustering, the row vector is selected, and taking max(x) as an example, the knowledge points mastered by it are first normalized, and the cosine distance between different learners is further calculated to group the dynamic learning behavior data of the learners. The distance between them can be represented as:

[0076]

[0077] where, and are two vectors, represents the dot product of and , and represent and the norm (i.e. the length of the vector). In actual computation, the vectors and are represented as n-dimensional vectors, where n is the dimension of the vectors, and then the product sum of their respective elements are computed sequentially. The final cosine distance ranges between [-1, 1], the closer to 1 indicates the two vectors are more similar, the closer to -1 indicates the two vectors are more dissimilar, and the value of 0 indicates the two vectors are orthogonal.

[0078] The learner linear projection and the knowledge point linear projection are interactively combined to generate a learner-knowledge point static interaction matrix y ij :

[0079]

[0080] where U ik is the mastery of the ith learner on the kth knowledge point, P jk is the examination of the jth question on the kth knowledge point, and the individualized parameter of the learner on the specific target knowledge point;

[0081] The learner nonlinear projection and the knowledge point nonlinear projection are interactively combined to generate a learner-knowledge point dynamic interaction matrix R ij :

[0082]

[0083] where n is the number of learners, β x，i represents the feature vector of the learner i, d ij represents the difficulty value of the knowledge point j, c ij represents the cost value of the learner i on the knowledge point j; σ represents the sigmoid function, and w1 and w2 are weight parameters;

[0084] Therefore, for the explicit weak knowledge point set, only the first q knowledge points are filtered out, where the proportion of the knowledge points mastered by the learner is less than the proportion of the knowledge points mastered by all learners, which satisfies the formula as follows:

[0085]

[0086] where, is the proportion of the knowledge point mastered by all learners in the cluster class, b i is the weighted average value of the ith row of y ij .

[0087] By adding the personalized static parameters of learners in the probability matrix decomposition, the low-dimensional latent factor feature matrix is further decomposed to depict the performance of learners and test items in the low-dimensional space. Therefore, the set of implicit weak knowledge points Z ij can be expressed as:

[0088]

[0089] wherein, represents the target space, θ k represents the knowledge iteration parameter, p(Z i，j |b i，j , R i , R j , σ R , θ k ) represents the probability that the performance of learner i on knowledge point j is predicted to be weak, σ R represents the historical learning behavior data of the learner.

[0090] The explicit and implicit weak knowledge point sets are input into the cognitive diagnosis model, and the learners are sorted according to their mastery of knowledge points by matrix decomposition, similarity matching, etc. Thus, the fuzzy cognitive diagnosis of learners under the improved model framework can be expressed as:

[0091]

[0092] wherein, ρ ∈ [0, 1] represents the proportion parameter between the common characteristics and the mastery mode of the independent attributes of the learner, the greater the value of ρ, the greater the influence of the prediction score on the cognitive diagnosis model, and the smaller the value of ρ, the greater the influence of the prediction score on the common characteristics. In the application process of the model, the value of ρ should be selected according to the actual data and test conditions.

[0093] Since X ij is a static parameter, it remains almost unchanged in a learning session interaction record, therefore, only the dynamic parameter estimation part, i.e. Z ij needs to be updated and repaired. The final objective function is:

[0094]

[0095] wherein λ1 and λ2 are regularization parameters. By using the stochastic gradient descent method, the learner feature matrix β1 and the knowledge point feature matrix β2 can be updated. Specifically, for each (i, j), the following update formula can be used:

[0096]

[0097]

[0098] wherein α is the learning rate, represents the error. Through continuous iteration, the optimal learner feature matrix β1 and the knowledge point feature matrix β2 can be updated, so as to obtain the interaction matrix R between the learner and the knowledge point ij , and then update the implicit weak knowledge point set Z ij .

[0099] Finally, the generated knowledge point set is unidirectionally and qualitatively output according to a certain coefficient relationship, that is, the personalized learning path of the learner.

[0100] In the above manner, the learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis provided by the present application combines the neural collaborative filtering network and the cognitive diagnosis technology, analyzes the personalized static parameters and dynamic learning behavior data of the learner, finds the explicit and implicit weak knowledge point set of the learner, analyzes and diagnoses the learner, and generates the optimized learning path according to the personalized needs and historical learning state of the learner. Figure 2 As shown in the figure, the X-axis represents the explicit weak knowledge point set of the learner, the Y-axis represents the implicit weak knowledge point set of the learner, and the Z-axis represents the learning effect of the learner. The empirical results show that the method significantly improves the learning effect and satisfaction of the learner, and compared with only using the neural collaborative filtering algorithm or the cognitive level diagnosis strategy, the effect is obviously improved.

[0101] Embodiment 2

[0102] The learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis provided by the present application is shown in the figure. Figure 1 When operating, the method is specifically as follows:

[0103] Step 1: respectively analyze the historical record information of the learner and the knowledge point relationship information of the knowledge graph to obtain the historical record information of the learner and the knowledge point relationship information;

[0104] Step 2: according to the learner information and the knowledge graph, construct the learner feature vector and the knowledge point feature vector;

[0105] Step 3: the constructed learner feature vector and knowledge point feature vector are respectively subjected to linear projection and nonlinear projection, and the adjacent related node information is fused;

[0106] Step 4.1: the learner linear projection and the knowledge point linear projection are interactively combined to generate a learner-knowledge point static interaction matrix;

[0107] Step 4.2: the learner nonlinear projection and the knowledge point nonlinear projection are interactively combined to generate a learner-knowledge point dynamic interaction matrix;

[0108] Step 5: The explicit weak knowledge point set is obtained by further dimension reduction analysis from the learner-knowledge point static interaction matrix in step 4.1;

[0109] Step 6: The implicit weak knowledge point set is obtained by further dimension reduction analysis from the learner-knowledge point dynamic interaction matrix in step 4.2;

[0110] Step 7: The explicit and implicit weak knowledge point sets in step 5 and step 6 are input into the cognitive level diagnosis model;

[0111] Step 8: The knowledge points are sorted, combined, and decomposed by the cognitive level diagnosis model, and the final personalized learning path recommendation list is output.

[0112] Example 3

[0113] The present example provides a learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis, and the specific implementation process is as follows:

[0114] Step 1: First, analyze the learner information provided by the learner, which contains three dimensions of data, namely: basic information a, learning process β, and learning result γ. Traverse each component as Key and the remaining components as Value in turn, and store them in a Map to realize clustering of learners and divide learners of different attribute categories into a class. Among them, the clustering Map table with basic information as Key value is shown in Table 1:

[0115] Table 1 Clustering Map table of learner basic information

[0116]

[0117]

[0118] Step 2: Construct the learner-knowledge point interaction matrix, and the specific construction process is as follows:

[0119] Step 2.1: Based on the learner clustering Map table, each learner belongs to a different clustering cluster, so the center cluster vector feature value of each cluster is taken as a component of the learner feature vector, and the learner feature vector can be obtained.

[0120] Step 2.2: Each node in the knowledge graph represents a knowledge point, and the edge represents the association relationship between different knowledge points. Take this as an index, query the weight parameters of different knowledge points, and construct a knowledge point feature vector in this way. For each test question, it is necessary to represent the test question as a vector form. This can be done by averaging or concatenating the vectors of the knowledge points involved in the test question to obtain the representation of the test question.

[0121] Step 2.3: Based on the obtained learner feature vector and knowledge point feature vector, a learner-knowledge point interaction matrix is generated with neural collaborative filtering as support.

[0122] Step 3: Calculate the explicit weak knowledge point set of the learner

[0123] Step 3.1: Linearly project the learner feature vector and the knowledge point feature vector respectively, and input them into the neural collaborative filtering model as static parameters to further update the interaction matrix of the learner and the knowledge point, i.e. to obtain the static weak knowledge point set of the learner.

[0124] Step 3.2: Nonlinearly project the learner feature vector and the knowledge point feature vector respectively, and perform matrix decomposition on the updated interaction matrix to obtain the learner latent feature matrix and the knowledge point low-dimensional projection. With the learner historical data and the static component as parameters, input them into the neural collaborative filtering model, and the implicit weak knowledge point set can be expressed as the learner's underlying probability of insufficient mastery of this knowledge point under the above five-tuple.

[0125] Step 4: According to the explicit and implicit weak knowledge point sets obtained in step 3, update the learner target in step 1 in turn and perform re-Embedding arrangement, and input it into the cognitive diagnosis model to further determine whether the obtained knowledge point sequence meets the learning level of the learner. If it does not meet the requirements, it is marked as an unrecommended learning sequence for re-output in the next cycle.

[0126] Step 5: After filtering, noise reduction and filtering of the rearranged knowledge point learning sequence, the learning path is output.

Claims

1. A learning path recommendation method based on neural collaborative filtering and cognitive level diagnosis, characterized by, Comprise the following steps: Step 1, obtaining learner information, including basic information, learning process and learning result; wherein, the basic information includes the number, age, gender and education background of the learner; the learning process includes the subject field, learning style, learning cost and learning time of the learner; the learning result includes the learning history, learning effect, learning progress and learning goal of the learner; Step 2, modeling the learner portrait according to the learner information obtained in step 1 to obtain the learner feature vector; specifically comprising the following steps: Step 2.1, modeling the learner portrait according to the learner information obtained in step 1 as shown in formula (1): （1） In formula (1), basic information The components included are: number ,age ,gender and academic qualifications Learning outcomes The components included are: learning history Learning outcomes Learning progress and learning objectives Learning process Learning features from subarrays and learning expenses eigenvalues ​​of the constructed two-dimensional matrix The structure constitutes and satisfies: （2） In formula (2), the learning features include a subject field and a learning style ; and the learning overhead includes a learning cost and a learning time ; Step 2.2, after modeling the learner portrait, the learners are classified by clustering, and the basic vector corresponding to each ID is taken as the center vector to obtain the cluster vector of its sub-cluster, then the learners are taken back to the learner cluster and assigned with the clustering attribute, and the original basic portrait is expanded to the learner feature vector, and the private attribute of the learner is not replaced, so the learner feature vector is represented as: （3） In formula (3), is a learner feature vector; is a basic information of cluster vectorization , is a cluster vector obtained in a learner set library Stu with an age Age as a cluster center vector, is a cluster vector obtained in a learner set library Stu with an educational background as a cluster center vector; is a learning process of cluster vectorization , is a cluster vector obtained in a learner set library Stu with a learning feature as a cluster center vector, is a cluster vector obtained in a learner set library Stu with a learning cost as a cluster center vector; is a learning result of cluster vectorization , is a cluster vector obtained in a learner set library Stu with a learning history as a cluster center vector, is a cluster vector obtained in a learner set library Stu with a learning progress as a cluster center vector; Step 3, constructing a knowledge point feature vector according to a knowledge graph; Step 4, inputting the learner feature vector obtained in step 2 and the knowledge point feature vector obtained in step 3 into a neural collaborative filtering network to obtain the explicit and implicit weak knowledge point set of the learner for the knowledge point to be mastered; specifically comprising the following steps: Step 4.1, the learner feature vector obtained in step 2 and the knowledge point feature vector obtained in step 3 are subjected to linear projection and nonlinear projection respectively, the feature distance between the learner feature and the knowledge point feature is represented as: （4） In formula (4), respectively represent two feature vectors, represent the dot product between two feature vectors, and respectively represent and the norm of; the value range of the final cosine distance is between [-1, 1], the closer to 1 indicates that the distance between the two feature vectors is closer, that is, the similarity is higher, and the two can be fused; otherwise, the lower the distance, the less capable of being fused. Step 4.2, the learner linear projection and the knowledge point linear projection obtained in step 4.1 are interactively combined to generate a learner-knowledge point static interaction matrix y ij As shown in formula (5): （5） In formula (5), U ik the mastery of the first learner on the first knowledge point, i k the mastery of the first learner on the first knowledge point, P jk the mastery of the first learner on the first knowledge point, j the mastery of the first learner on the first knowledge point, k the mastery of the first learner on the first knowledge point, and the mastery of the first learner on the first knowledge point.​ Step 4.3, the learner nonlinear projection and the knowledge point nonlinear projection obtained in step 4.1 are combined interactively to generate a learner-knowledge point dynamic interaction matrix R ij As shown in formula (6): （6） In formula (6), n is the number of learners, β x,i is a feature vector of a learner i , d ij is a difficulty value of a knowledge point j , c ij is an expense value of a learner i on a knowledge point j ; σ is a function sigmoid , w 1 and w 2 are weight parameters; Step 4.

4. Dimension reduction analysis of the learner-knowledge point static interaction matrix obtained in step 4.2 to obtain the explicit weak knowledge point set. For the explicit weak knowledge point set, only the knowledge points mastered by the cluster class to which the first learner belongs need to be filtered out, i.e. the explicit weak knowledge point set of the learner, as shown in formula (7): q ​ （7） In formula (7), the proportion of the knowledge points mastered by all learners in the cluster, b i is y ij The first i weighted average value of the row; Step 4.5, the learner-knowledge point dynamic interaction matrix obtained in step 4.3 is dimensionally reduced and analyzed to obtain the implicit weak knowledge point set, as shown in formula (8): （8） In formula (8), represents a target space, θ k represents a knowledge iteration parameter, p (Z i,j |b i,j , R i , R j , σ R , θ k ) represents a learner i on a knowledge point j is predicted to be weak, σ R represents learner historical learning behavior data; Step 5, inputting the explicit and implicit weak knowledge point set obtained in step 4 into a cognitive level diagnosis model, sorting, combining and disassembling the knowledge points by the cognitive level diagnosis model, and outputting the final personalized learning path recommendation list; specifically comprising the following steps: Step 5.1, obtaining the explicit weak knowledge point set from the result of step 4.4 X ij obtaining the implicit weak knowledge point set from the result of step 4.5 Z ij The fuzzy cognitive diagnosis representation of the learner under the current learning state cognitive level input into the cognitive diagnosis model is: （9） In formula (9), ρ represents a proportional parameter between the common characteristics and the learner independent attribute mastery pattern; Step 5.2: Track and update parameters of the learner's dynamic learning process, that is, ... Z ij The objective function, which performs updates and self-repair, satisfies formula (10): （10） In formula (10), and is a regularization parameter; the learner feature matrix and the knowledge point feature matrix are updated using a stochastic gradient descent method Step 5.3, recommending the knowledge points that meet the cognitive level condition range of the learner, and the generated recommendation list is the personalized learning path of the learner.

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