An adaptive learning recommendation method based on behavior stability and knowledge dependency graph
By constructing a dynamic knowledge dependency graph and propagating the risk of forgetting, this method solves the problems of single forgetting models and insufficient utilization of knowledge structures in existing technologies, achieving high precision and robustness in personalized learning, and enabling dynamic adjustment of the forgetting rate and identification of sudden changes in learning state.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHWEST JIAOTONG UNIV
- Filing Date
- 2026-05-12
- Publication Date
- 2026-07-31
AI Technical Summary
Existing knowledge tracking and personalized learning recommendation technologies suffer from fixed and simplistic forgetting models, insufficient utilization of knowledge structures, lack of stability in learning behavior, lack of quantification and propagation of learning risks, and poor robustness in recommendation scheduling. These limitations make it difficult to achieve the organic integration of dynamic knowledge structure modeling, adaptive forgetting based on behavior, risk propagation, and structural anomaly detection.
An adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs constructs a dynamic knowledge dependency graph by acquiring student interaction sequence data, dynamically adjusts the forgetting rate, propagates the risk of forgetting, detects structural anomalies, and integrates multi-dimensional risks for exercise recommendation.
It enables more accurate, stable, and interpretable personalized learning services, improves the accuracy and robustness of learning assessment, can dynamically adjust forgetting models, identify sudden changes in learning states, and propagate learning risks.
Smart Images
Figure CN122491925A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of personalized learning and teaching technology, and in particular to an adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs. Background Technology
[0002] With the rapid development of online education and intelligent learning systems, accurately modeling learners' knowledge mastery status and achieving personalized exercise recommendations and learning path planning have become key research directions in the field of artificial intelligence education. Models such as Deep Knowledge Tracing (DKT) can predict the probability of learners mastering knowledge points by modeling their historical answer sequences, providing support for personalized learning. However, most existing knowledge tracing and learning recommendation technologies have the following shortcomings: Forgetting modeling is too simplistic and lacks an adaptive mechanism for individual behavior. Traditional methods often use exponential forgetting models with fixed parameters, failing to consider individual differences such as learner behavior stability, answer fluctuations, and time interval changes. The forgetting rate cannot be dynamically adjusted according to the learning state, resulting in insufficient accuracy in mastery and forgetting risk estimation.
[0003] The structural dependencies between knowledge points are not fully utilized. Most knowledge tracing models treat knowledge points as independent entities, ignoring the prerequisite, supporting, and coupling relationships between them. This makes it impossible to realize the propagation and deduction of forgetting risk and mastery status in the knowledge structure, and it is difficult to explain the causes of learning weaknesses.
[0004] Learning status assessment is often simplistic and lacks stability and anomaly detection. Existing technologies typically rely solely on correct answer rates or predicted mastery levels as evaluation criteria, failing to quantify learner behavior stability, prediction error fluctuations, and response time fluctuations. Furthermore, they do not detect abnormal drifts in knowledge structure and mastery status, making it difficult to identify abrupt changes and structural anomalies in learning status.
[0005] Recommendation decisions lack multi-dimensional risk fusion. Traditional exercise recommendations are mostly based on mastery or similarity for scheduling, without uniformly modeling and fusing the risks of forgetting, structural anomalies, and behavioral stability. This results in insufficient robustness of the recommendation strategy, making it difficult to provide stable and reliable learning scheduling under complex learning behaviors.
[0006] Therefore, existing technologies cannot simultaneously achieve the organic integration of dynamic knowledge structure modeling, behavioral adaptive forgetting, risk propagation, and structural anomaly detection, and cannot meet the needs of high-precision, high-robustness, and interpretable personalized learning assessment and intelligent exercise recommendation. Summary of the Invention
[0007] To address the problems in existing knowledge tracking and personalized learning recommendation systems, such as fixed and simplistic forgetting models, insufficient utilization of knowledge structures, lack of learning behavior stability, lack of quantification and propagation of learning risks, and poor robustness of recommendation scheduling, this invention proposes an adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs. By leveraging behavioral stability, dynamic knowledge dependency graphs, and the propagation of forgetting risks, this method aims to achieve more accurate, stable, interpretable, and personalized learning services that better align with real-world cognitive patterns.
[0008] This application discloses an adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs, including the following steps: S1. Obtain and preprocess the students' interaction sequence data; S2. Input the preprocessed interactive sequence data into the mastery calculation model and output the mastery prediction value of each knowledge point. S3. Construct a prediction error sequence and volatility index based on the mastery prediction value and interaction sequence data, and calculate the comprehensive behavioral stability index; S4. Based on the comprehensive behavioral stability index, dynamically adjust the forgetting rate hyperparameter to calculate the adaptive forgetting rate of students for knowledge points and the forgetting rate of exercises. S5. Construct a knowledge dependency graph and dynamically update the initial edge weight matrix between knowledge points as the residual time progresses; S6. Based on the mastery prediction value and the adaptive forgetting rate, the forgetting risk of each knowledge point is obtained, and the forgetting risk is propagated using the knowledge dependency graph to obtain the mastery degree coupled with the structure after propagation. S7. Construct a candidate pool and integrate the forgetting risk, structural anomaly index, and behavioral stability index to calculate the comprehensive risk of the exercises; S8. Sort all exercises in the candidate pool according to their overall risk, and recommend the exercise with the lowest overall risk.
[0009] Preferably, the interactive sequence data includes questions, knowledge points, answer results, answer timestamps, and answer times; The preprocessing includes deduplication, handling of abnormal times, handling of missing data, and normalization.
[0010] Preferably, step S3 includes the following steps: Extract the predicted mastery level:
[0011] in, For the first Mastery prediction vector for each interaction For the first The knowledge points involved in this interaction; Calculate the residual of a single interaction:
[0012] in, For the first The results of the questions involved in this interaction; The error fluctuation index is:
[0013] The time fluctuation indicator is:
[0014] in, For length is Sliding window, For the most recent The sequence of answer intervals; The overall behavioral stability index is as follows:
[0015] in, The weighting coefficient for the error fluctuation index. This represents the weighting coefficient for the time fluctuation index.
[0016] Preferably, step S4 includes the following steps: The hyperparameter of the regulated forgetting rate is:
[0017] in, Let be the initial forgetting rate hyperparameter. To control the intensity coefficient; Students' knowledge points The adaptive forgetting rate is:
[0018] in, This is the time interval between answering questions; The forgetting rate of the exercises is:
[0019] in, For the first Each exercise contains a set of knowledge points.
[0020] Preferably, step S5 includes the following steps: Construct a directed weighted graph:
[0021] in, Represents a set of knowledge points. express The set of edges at time, Represents the edge weight matrix. express Key points of time Knowledge points Priority / support strength; Calculation knowledge points In the sliding window Intra-aggregate residuals:
[0022] in, For the first The knowledge points involved in this interaction Representing knowledge points Indicator functions, It is a positive number; Calculation knowledge points With knowledge points Based on the correlation, the initial edge weight matrix is obtained:
[0023] in, For knowledge points The aggregation residual, For knowledge points The aggregation residual.
[0024] Preferably, step S6 includes the following steps: Define the risk of forgetting:
[0025] in, , This represents the total number of knowledge points. Update the risk of forgetting based on adaptive forgetting rate:
[0026] in, This represents element-wise multiplication. ; Construct a propagation matrix, the elements of which are:
[0027] in, Representing knowledge points Weighted in-degree, express Key points of time Knowledge points Priority / support strength; Define the propagation operator:
[0028] in, It is the identity matrix. , Represents the edge weight matrix Perform normalization; The risks after transmission are:
[0029] in, This indicates that the line is truncated to [0,1]. For the propagation intensity coefficient, ; The risk of forgetting each exercise is:
[0030] The structural coupling mastery is obtained as follows:
[0031] in, For the first The average risk of forgetting the knowledge points covered in each exercise.
[0032] Preferably, the candidate pool described in S7 is as follows:
[0033] in, Students For the The weight of each exercise, Students For the Exercise #1 The degree of mastery of the coupling of individual knowledge points .
[0034] Preferably, the structural anomaly index in S7 includes: Compute node state drift:
[0035] Calculation graph structure drift:
[0036] in, It is the Frobenius norm; The structural anomaly index is:
[0037] No. The structural anomaly index of each exercise is:
[0038] in, These are the weighting coefficients for node state drift. The weighting coefficients are used to account for the drift of the graph structure.
[0039] Preferably, the comprehensive risks of the calculation exercises described in S7 include: Construct risk feature vector:
[0040] No. The overall risk corresponding to each exercise is:
[0041] In the formula:
[0042] in, , , To hide the number of units, Indicates that the first layer is fully connected from To hide representation The bias vector, Indicates a fully connected second layer from Ultimately, the overall risk The bias vector.
[0043] This application also discloses an implementation of an adaptive learning recommendation system based on behavioral stability and knowledge dependency graphs, used to implement the adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs. The system includes: The data acquisition and preprocessing module is used to acquire historical interaction sequence data and clean and standardize the data. The mastery calculation module is used to calculate the predicted mastery of students' knowledge points through the mastery calculation model. The behavioral stability analysis module is used to construct the prediction error sequence, calculate the error fluctuation index and the time fluctuation index, and obtain the comprehensive behavioral stability index. The forgetting rate calculation module is used to calculate the adaptive forgetting rate of students for knowledge points and the forgetting rate of exercises; The knowledge dependency graph construction and dynamic update module is used to construct a directed weighted knowledge dependency graph and dynamically update the edge weights over time. The forgetting risk propagation module is used to calculate the forgetting risk and use the knowledge dependency graph to propagate the forgetting risk from previous knowledge points to subsequent knowledge points, so as to obtain the risk and structural coupling mastery degree after propagation; The structural anomaly detection module is used to measure node state drift and graph structure drift, and to calculate the structural anomaly index of knowledge points and exercises. The comprehensive risk calculation module is used to construct risk feature vectors and calculate the comprehensive risk of exercises through neural networks; The exercise recommendation module is used to rank and recommend candidate exercises based on comprehensive risk. The feedback update module is used to feed back students' new answer behaviors after completing the recommended exercises to the data collection and preprocessing module, forming a closed-loop update.
[0044] The beneficial effects of this invention are: (1) This invention introduces behavioral stability analysis, integrates the fluctuation of prediction error and the fluctuation of answer time interval into a behavioral stability index, and dynamically adjusts the forgetting rate based on the index, so that the forgetting model can adapt to individual behavioral characteristics. The more unstable the behavior, the faster the forgetting, thus improving the fitting accuracy of the mastery decay process.
[0045] (2) This invention automatically constructs and dynamically updates the knowledge dependency graph based on the residual correlation of knowledge points, thereby realizing the quantitative mining and structural modeling of the prior support strength between knowledge points and avoiding complete reliance on static expert annotation.
[0046] (3) This invention uses the forgetting risk propagation mechanism along the knowledge dependency graph to enable the forgetting risk of previous knowledge points to be passed on to subsequent ones, thus identifying chain learning risks.
[0047] (4) This invention constructs a structural anomaly index to perceive the drift of knowledge point mastery and graph structure in real time, thereby realizing the detection of sudden changes in learning state.
[0048] (5) This invention integrates forgetting risk, structural anomaly index and behavioral stability index and outputs comprehensive risk probability to drive exercise recommendation, forming a complete closed loop of data collection, state assessment, risk calculation, exercise scheduling and feedback update, so that the recommendation strategy has structural perception and risk perception capabilities, significantly improving the accuracy, robustness and interpretability of personalized learning assessment. Attached Figure Description
[0049] Figure 1 This is a flowchart of an adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to an embodiment of the present invention. Detailed Implementation
[0050] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided with reference to the accompanying drawings and embodiments.
[0051] This application discloses an adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs, the process of which is as follows: Figure 1 As shown, it includes the following steps S1-S8.
[0052] S1. Obtain and preprocess the students' interaction sequence data.
[0053] Specifically, the academic set is The total number of knowledge points is The knowledge points are set as follows .
[0054] student The interaction sequence (which is a record of interactions at the knowledge point level) is sorted by time as follows:
[0055] in, For the first The questions involved in this interaction, For the first The knowledge points involved in this interaction For students No. The answer results involved in this interaction (0 / 1, 0 indicates a correct answer, and 1 indicates a wrong answer). For students No. The timestamps of the answers involved in each interaction. For students No. The time required to respond to each interaction.
[0056] The time interval for answering questions is:
[0057] Preprocessing is performed to clean and standardize the interactive data generated by the learning platform, including at least: Remove duplicates and delete duplicate interaction records.
[0058] Handling abnormal timestamps: Delete or truncate abnormal timestamp values, such as those that are reversed or exceed a reasonable range.
[0059] Missing tags: Handling missing tags. For example, missing... The record is deleted or inserted.
[0060] Normalization: for , After performing logarithmic transformation and scaling, we obtain , .
[0061] S2. Input the preprocessed interaction sequence data into the mastery calculation model and output the mastery prediction value of each knowledge point.
[0062] In this embodiment, the mastery calculation model adopts the Deep Knowledge Tracing (DKT) model, which includes: Input layer:
[0063] in, As input to the model, Representing knowledge points One-hot encoding, Indicates the first Tags for each interactive response result Indicates the first Next and first Interval between interactions Normalized features after logarithmic transformation and scaling Indicates the first The response time for each interaction Normalized features after logarithmic transformation and scaling.
[0064] LSTM layer:
[0065] in, Indicates that LSTM is in the first... The hidden state vector of the step.
[0066] Fully connected layer:
[0067] in, For the first Predicted mastery of each interaction For the Sigmoid activation function, This is the weight matrix of the fully connected layer. This is the bias vector.
[0068] Output layer:
[0069] in, For the first Mastery prediction vector for each interaction Representing knowledge points The predicted value of mastery.
[0070] S3. Construct a prediction error sequence and volatility index based on the mastery prediction value and interaction sequence data, and calculate the comprehensive behavioral stability index.
[0071] S31. Construction of prediction error sequence.
[0072] From vector Take out the first one Knowledge points related to this interaction Predicted mastery values:
[0073] Calculate the single-interaction residual (prediction error):
[0074] The structure is of length. Sliding window:
[0075] The error fluctuation index is defined as follows:
[0076] S32. Calculate the fluctuation index of the time interval between answering questions.
[0077] Define the most recent Interval sequence of answers:
[0078] Calculate the time fluctuation index:
[0079] S33. Calculate the comprehensive behavioral stability index:
[0080] in, The weighting coefficient for the error fluctuation index. This represents the weighting coefficient for the time fluctuation index. For students The comprehensive behavioral stability index is a measure of behavior stability; the higher the value, the more unstable the behavior.
[0081] S4. Based on the comprehensive behavioral stability index, dynamically adjust the forgetting rate hyperparameter to calculate the adaptive forgetting rate of students for knowledge points and the forgetting rate of exercises.
[0082] The traditional formula for calculating the exponential forgetting rate is:
[0083] in, This is the forgetting rate hyperparameter.
[0084] This embodiment introduces a behavioral stability regulation mechanism, and the hyperparameter of the forgotten rate after regulation is:
[0085] in, This indicates that after incorporating behavioral stability regulation, at time... The forgetting rate hyperparameter, This represents the initial forgetting rate hyperparameter. This represents the control intensity coefficient, used for control. right The extent of the impact.
[0086] This allows us to obtain students' understanding of the knowledge points. The adaptive forgetting rate is:
[0087] When the behavioral fluctuations are greater The smaller the value, the faster the rate of forgetting.
[0088] The forgetting rate of the exercises is:
[0089] in, For the first Each exercise contains a set of knowledge points.
[0090] S5. Construct a knowledge dependency graph and dynamically update the initial edge weight matrix between knowledge points as the residual time progresses.
[0091] S51. Construct a directed weighted graph:
[0092] in, Represents a set of knowledge points. express The set of edges at time, Represents the edge weight matrix. express Key points of time Knowledge points Pre-repair / support strength.
[0093] The initial graph is provided directly from the course syllabus, expert annotations, or knowledge system, and the edges are trimmed first.
[0094] S52. Edge weight estimation based on knowledge point residual correlation.
[0095] residual The data is assigned to corresponding knowledge points, resulting in the residual time series for each knowledge point. All knowledge points involved for this student Aggregate the residuals of the interaction records to obtain the result in the sliding window. Intra-aggregate residuals:
[0096] in, Representing knowledge points The indicator function is used to determine the first... What knowledge points are included in this interaction? It is a very small positive number, used to avoid the value from exploding due to an excessively small denominator.
[0097] If two knowledge points have a dependent / shared foundation, their "deviation" will move together, thus calculating the knowledge points. With knowledge points Based on the correlation, the initial edge weight matrix is obtained:
[0098] in, For knowledge points The aggregation residual, For knowledge points The aggregation residual.
[0099] The initial edge weight matrix represents whether knowledge points fluctuate together, that is, whether there is a dependency relationship between knowledge points.
[0100] S6. Based on the mastery prediction value and the adaptive forgetting rate, the forgetting risk of each knowledge point is obtained, and the forgetting risk is propagated using the knowledge dependency graph to obtain the mastery degree coupled with the structure after propagation.
[0101] If a prerequisite knowledge point is forgotten, it will not only affect itself, but also "drag down" the subsequent knowledge points that depend on it. Therefore, the risk must be passed from the prerequisite to the subsequent along the knowledge dependency graph.
[0102] First, define the risk of forgetting. The higher a student's mastery of a particular knowledge point, the higher the risk of forgetting that knowledge point. The lower the value, the better. The formal formula is:
[0103] in, .
[0104] Since the risk of forgetting increases with longer time, the risk of forgetting is updated over time based on an adaptive forgetting rate, using the following formula:
[0105] in, This represents element-wise multiplication. , It increases as it increases.
[0106] Constructing a propagation matrix (Diagonal matrix), the elements of the matrix are:
[0107] in, Representing knowledge points The weighted in-degree ("degree value" is used to measure how many edges a node is connected to), that is, the weighted in-degree of each node. (Knowledge Points) The "sum of incoming edge weights" (the sum of the weights of all edges pointing to it) means that for all knowledge points... The edge weights corresponding to the relevant knowledge points are summed. express Key points of time Knowledge points The prerequisite / support strength, i.e., the knowledge point Points of knowledge The weight of this directed edge.
[0108] Define the propagation operator:
[0109] in, It is the identity matrix. , , Represents the edge weight matrix Normalization. Equivalent to knowledge points. It is subject to a weighted average / weighted sum of all its prior risks, normalizing the impact from multiple prior knowledge points so that the intensity of the spread is not amplified unnecessarily due to "many prior / multiple sides".
[0110] The risk of forgetting subsequent knowledge points = the risk of forgetting them oneself + the additional risk of forgetting previous knowledge points. Therefore, propagating the risk of forgetting previous knowledge points to subsequent knowledge points yields the risk after propagation:
[0111] in, This indicates that the line is truncated to [0,1]. For the propagation intensity coefficient, .
[0112] The risk of forgetting each exercise is:
[0113] in, For the first The average risk of forgetting the knowledge points covered in each exercise.
[0114] At the same time, the degree of control over structural coupling can be obtained as follows:
[0115] S7. Construct a candidate pool and integrate the forgetting risk, structural anomaly index, and behavioral stability index to calculate the comprehensive risk of the exercises.
[0116] S71. Construct the candidate pool as follows:
[0117] in, Students For the The weight of each exercise, Students For the Exercise #1 The degree of mastery of the coupling of individual knowledge points .
[0118] S72, Structural anomaly detection.
[0119] Node state drift measures how much the mastery of a knowledge point changes between two adjacent time points. The formula is:
[0120] Graph structure drift measures which dependencies in a knowledge-dependent graph become stronger / weaker and how much the overall edge weights change. The formula is:
[0121] in, The Frobenius norm (the square root of the sum of the squared differences between the elements in the matrix) is equivalent to the "overall change in edge weights".
[0122] The final structural anomaly index is:
[0123] in, For node state drift The weighting coefficients, For the structure drift of the diagram The weighting coefficients.
[0124] No. The structural anomaly index of each exercise is:
[0125] S73, Comprehensive Risk Calculation.
[0126] This utilizes a two-layer feedforward neural network, one of which is a fully connected hidden layer (containing the ReLU activation function). (A hidden unit) integrates the three types of risk characteristics into the final risk probability.
[0127] First, construct the risk feature vector:
[0128] The final The overall risk corresponding to each exercise is:
[0129] In the formula:
[0130] in, , , To hide the number of units, Indicates that the first layer is fully connected from To hide representation The bias vector, Indicates a fully connected second layer from Ultimately, the overall risk The bias vector.
[0131] S8. All problems in the candidate pool are evaluated based on comprehensive risk. Sort, select the first Recommendations are made for exercises that minimize overall risk.
[0132] After the exercise recommendations are completed, students' new answer behaviors are entered into the data collection module again, forming a closed-loop update mechanism for exercise recommendations.
[0133] Another embodiment of this application discloses an implementation of an adaptive learning recommendation system based on behavioral stability and knowledge dependency graphs, used to implement the aforementioned adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs. The system includes: The data acquisition and preprocessing module is used to collect historical interaction sequence data and clean and standardize the data.
[0134] The mastery calculation module is used to calculate the predicted mastery level of students on knowledge points through a deep knowledge tracing model.
[0135] The behavioral stability analysis module is used to construct the prediction error sequence, calculate the error fluctuation index and the time fluctuation index, and obtain the comprehensive behavioral stability index.
[0136] The forgetting rate calculation module is used to calculate the adaptive forgetting rate of students for knowledge points and the forgetting rate of exercises.
[0137] The knowledge dependency graph construction and dynamic update module is used to construct a directed weighted knowledge dependency graph and dynamically update the edge weights over time.
[0138] The forgetting risk propagation module is used to calculate the forgetting risk and use the knowledge dependency graph to propagate the forgetting risk from previous knowledge points to subsequent knowledge points, so as to obtain the risk and structural coupling mastery degree after propagation.
[0139] Structural Anomaly Detection Module: Used to measure node state drift and graph structure drift, and calculate the structural anomaly index of knowledge points and exercises.
[0140] The comprehensive risk calculation module is used to construct risk feature vectors and calculate the comprehensive risk of exercises through neural networks.
[0141] The exercise recommendation module is used to rank and recommend candidate exercises based on comprehensive risk.
[0142] The feedback update module is used to feed back students' new answer behaviors after completing the recommended exercises to the data collection and preprocessing module, forming a closed-loop update.
[0143] Compared with existing knowledge tracking and personalized learning recommendation technologies, the embodiments of this application overcome the inherent defects of traditional technologies by adding key means such as learning behavior stability analysis, behavior adaptive dynamic forgetting modeling, dynamic knowledge dependency graph construction and updating, forgetting risk propagation along the knowledge dependency graph, structural anomaly detection, and multi-dimensional learning risk fusion assessment. These defects include fixed forgetting model parameters, independent modeling of knowledge points, single dimension of learning state assessment, lack of quantitative and propagation mechanism for learning risk, and lack of structure-driven and robustness guarantee for exercise recommendation.
[0144] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.
Claims
1. An adaptive learning recommendation method based on behavior stability and knowledge dependency graph, characterized in that, Includes the following steps: S1. Obtain and preprocess the students' interaction sequence data; S2. Input the preprocessed interactive sequence data into the mastery calculation model and output the mastery prediction value of each knowledge point. S3. Construct a prediction error sequence and volatility index based on the mastery prediction value and interaction sequence data, and calculate the comprehensive behavioral stability index; S4. Based on the comprehensive behavioral stability index, dynamically adjust the forgetting rate hyperparameter to calculate the adaptive forgetting rate of students for knowledge points and the forgetting rate of exercises. S5. Construct a knowledge dependency graph and dynamically update the initial edge weight matrix between knowledge points as the residual time progresses; S6. Based on the mastery prediction value and the adaptive forgetting rate, the forgetting risk of each knowledge point is obtained, and the forgetting risk is propagated using the knowledge dependency graph to obtain the mastery degree coupled with the structure after propagation. S7. Construct a candidate pool and integrate the forgetting risk, structural anomaly index, and behavioral stability index to calculate the comprehensive risk of the exercises; S8. Sort all exercises in the candidate pool according to their overall risk, and recommend the exercise with the lowest overall risk.
2. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graph as described in claim 1, characterized in that, The interactive sequence data includes the question, knowledge point, answer result, answer timestamp, and answer time; The preprocessing includes deduplication, handling of abnormal times, handling of missing data, and normalization.
3. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 2, characterized in that, S3 includes the following steps: Extract the predicted mastery level: in, For the first Mastery prediction vector for each interaction For the first The knowledge points involved in this interaction; Calculate the residual of a single interaction: in, For the first The results of the questions involved in this interaction; The error fluctuation index is: The time fluctuation indicator is: in, For length is Sliding window, For the most recent The sequence of answer intervals; The overall behavioral stability index is as follows: in, The weighting coefficient for the error fluctuation index. This represents the weighting coefficient for the time fluctuation index.
4. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 3, characterized in that, S4 includes the following steps: The hyperparameter of the regulated forgetting rate is: in, Let be the initial forgetting rate hyperparameter. To control the intensity coefficient; Students' knowledge points The adaptive forgetting rate is: in, This is the time interval between answering questions; The forgetting rate of the exercises is: in, For the first Each exercise contains a set of knowledge points.
5. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 4, characterized in that, S5 includes the following steps: Construct a directed weighted graph: in, Represents a set of knowledge points. express The set of edges at time, Represents the edge weight matrix. express Key points of time Knowledge points Priority / support strength; Calculation knowledge points In the sliding window Intra-aggregate residuals: in, For the first The knowledge points involved in this interaction Representing knowledge points Indicator functions, It is a positive number; Calculation knowledge points With knowledge points Based on the correlation, the initial edge weight matrix is obtained: in, For knowledge points The aggregation residual, For knowledge points The aggregation residual.
6. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 5, characterized in that, S6 includes the following steps: Define the risk of forgetting: in, , This represents the total number of knowledge points. Update the risk of forgetting based on adaptive forgetting rate: in, This represents element-wise multiplication. ; Construct a propagation matrix, the elements of which are: in, Representing knowledge points Weighted in-degree, express Key points of time Knowledge points Priority / support strength; Define the propagation operator: in, It is the identity matrix. , Represents the edge weight matrix Perform normalization; The risks after transmission are: in, This indicates that the line is truncated to [0,1]. For the propagation intensity coefficient, ; The risk of forgetting each exercise is: The structural coupling mastery is obtained as follows: in, For the first The average risk of forgetting the knowledge points covered in each exercise.
7. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 6, characterized in that, The candidate pool described in S7 is as follows: in, Students For the The weight of each exercise, Students For the Exercise #1 The degree of mastery of the coupling of individual knowledge points .
8. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 7, characterized in that, The structural anomaly index described in S7 includes: Compute node state drift: Calculation graph structure drift: in, It is the Frobenius norm; The structural anomaly index is: No. The structural anomaly index of each exercise is: in, These are the weighting coefficients for node state drift. The weighting coefficients are used to account for the drift of the graph structure.
9. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 8, characterized in that, The overall risks of the calculation exercises described in S7 include: Construct risk feature vector: No. The overall risk corresponding to each exercise is: In the formula: in, , , To hide the number of units, Indicates that the first layer is fully connected from To hide representation The bias vector, Indicates a fully connected second layer from Ultimately, the overall risk The bias vector.
10. The adaptive learning recommendation method based on behavioral stability and knowledge dependency graphs according to claim 8, characterized in that, An adaptive learning recommendation system based on behavioral stability and knowledge dependency graphs is used, the system comprising: The data acquisition and preprocessing module is used to acquire historical interaction sequence data and clean and standardize the data. The mastery calculation module is used to calculate the predicted mastery of students' knowledge points through the mastery calculation model. The behavioral stability analysis module is used to construct the prediction error sequence, calculate the error fluctuation index and the time fluctuation index, and obtain the comprehensive behavioral stability index. The forgetting rate calculation module is used to calculate the adaptive forgetting rate of students for knowledge points and the forgetting rate of exercises; The knowledge dependency graph construction and dynamic update module is used to construct a directed weighted knowledge dependency graph and dynamically update the edge weights over time. The forgetting risk propagation module is used to calculate the forgetting risk and use the knowledge dependency graph to propagate the forgetting risk from previous knowledge points to subsequent knowledge points, so as to obtain the risk and structural coupling mastery degree after propagation; The structural anomaly detection module is used to measure node state drift and graph structure drift, and to calculate the structural anomaly index of knowledge points and exercises. The comprehensive risk calculation module is used to construct risk feature vectors and calculate the comprehensive risk of exercises through neural networks; The exercise recommendation module is used to rank and recommend candidate exercises based on comprehensive risk. The feedback update module is used to feed back students' new answer behaviors after completing the recommended exercises to the data collection and preprocessing module, forming a closed-loop update.