Learning style recognition method and system based on state evolution and attractor analysis

Abstract

The application provides a learning style recognition method and system based on state evolution and attractor analysis, and belongs to the fields of machine learning and educational data mining. The method comprises the following steps: obtaining a behavior log of a learner, mapping a behavior type to a multi-channel learning state component, and aggregating the multi-channel learning state component into a learning state vector sequence; estimating a discrete state transition model containing a state transition matrix and a bias vector based on the sequence; calculating a spectral radius of the state transition matrix and performing a stabilization process, solving an attractor through a fixed point condition, and taking the attractor as a stable mode representation of the learner; clustering all attractors of the learners as representation vectors to obtain dynamic learning style prototypes and assign a style category to each learner. The application changes learning style recognition from static label prediction to dynamic modeling of long-term stable modes of learner behavior states, effectively depicts dynamic evolution characteristics of learning styles, and provides interpretable technical support for online education personalized recommendation and learning warning.

Description

Technical Field

[0001] This invention belongs to the field of machine learning and educational data mining technology, and particularly relates to a learning style recognition method and system based on state evolution and attractor analysis. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid popularization of online education platforms and learning management systems, learners continuously generate a large amount of time-stamped behavioral data on these platforms, including various types of interaction records such as resource access, forum interaction, quiz answering, and announcement viewing. How to identify learners' learning styles from this behavioral data is a core technical challenge faced by personalized education recommendation and learning early warning systems.

[0004] Currently, mainstream methods in the field of learning style recognition primarily treat learning style as a static category label or preference score to be predicted. One type of method relies on questionnaire scales, such as those based on Felder-Silverman or VARK models, to infer the learner's learning style type from the questionnaire items completed by the learner. Another type of method extracts statistical features from learning behavior, such as resource access frequency, learning duration, and answer accuracy, and then inputs them into classifiers such as support vector machines, random forests, and XGBoost to complete the recognition. These methods are computationally efficient and can achieve certain results when there is sufficient data. However, their common characteristic is that they treat learning style as a fixed label that does not change over time for prediction. The input used is either a one-time questionnaire result or a summary statistic of behavioral data throughout the entire learning cycle, essentially ignoring the dynamic evolution of learner behavior as the course progresses.

[0005] To incorporate the temporal dimension of learning behavior, recent studies have begun to employ sequence modeling methods to characterize learner states. Approaches based on recurrent neural networks, hidden Markov models, state-space models, and knowledge tracing models can dynamically estimate learners' latent states using their behavioral sequences over time. While these methods acknowledge the temporal evolution of learner states, their modeling objectives primarily focus on estimating knowledge mastery or predicting learning performance. They do not concern themselves with whether learner behavioral states will converge to a stable pattern over long-term evolution, nor do they define such a long-term stable pattern as a representation of learning style.

[0006] In addition, some studies use clustering methods to profile or group learners, typically clustering statistical measures or stage-specific characteristics of learning behavior directly. The limitation is that the clustered objects are static summaries of the behavioral characteristics themselves, rather than depicting the dynamic structure of how behaviors influence and drive each other over time. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, this invention provides a learning style identification method and system based on state evolution and attractor analysis. It aims to solve the technical problems in the prior art that treats learning style as a static label and ignores its dynamic evolution process, and lacks characterization and modeling of the long-term stable pattern of learner's behavioral state, thereby realizing the automatic identification and interpretable representation of learner's dynamic learning style.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a learning style recognition method based on state evolution and attractor analysis; Learning-based style recognition methods based on state evolution and attractor analysis include: Obtain learners' behavior logs from online learning platforms, map the behavior types in the behavior logs to multi-channel learning state components, and aggregate them into a learning state vector sequence for each learner according to the real time window; Based on the learned state vector sequence, a discrete state transition model describing the evolution relationship between states at adjacent time points is estimated. The state transition model includes a state transition matrix and a bias vector. The spectral radius of the state transition matrix is ​​calculated and stabilized to ensure that the spectral radius of the stabilized state transition matrix does not exceed a preset stability threshold. Based on the stabilized state transition matrix and bias vector, the attractor of the learning state evolution system is solved by the fixed-point condition, whereby the state at the next time step is equal to the state at the current time step. Cluster all learners’ attractors as representation vectors to obtain dynamic learning style prototypes, and assign a corresponding style category to each learner.

[0009] As a further technical solution, the multi-channel learning state component includes at least four channels: resource usage state, interaction state, evaluation and participation state, and course follow-up state. The multi-channel learning state components are aggregated into a learning state vector sequence for each learner according to the real time window. Specifically, the behavior counts of each channel within the time window are subjected to logarithmic compression transformation and normalized according to the current learner's own trajectory range, so that the state components fall into a unified normalized value range.

[0010] As a further technical solution, the discrete state transition model is as follows:

[0011] in, for OK The state transition matrix of the column, for 3D bias vector; state transition matrix The Line 1 Column elements represent the first The state component is related to the first state component. The influence of the changing trend of each state component in the next time window, bias vector This represents a basic driving item that does not depend on the current state.

[0012] As a further technical solution, the spectral radius of the state transition matrix is ​​calculated and stabilized to ensure that the spectral radius of the stabilized state transition matrix does not exceed a preset stability threshold, including: Calculate the spectral radius of the state transition matrix:

[0013] in, denoted as the spectral radius of the state transition matrix; This represents the k-th eigenvalue of the state transition matrix. When the spectral radius does not exceed the preset stability threshold, it indicates that the learner's state evolution system is stable; when the spectral radius exceeds the preset stability threshold, the matrix is ​​scaled proportionally so that the spectral radius of the scaled matrix is ​​exactly equal to the preset stability threshold.

[0014] in, This is the state transition matrix after stabilization. This is a preset stability threshold.

[0015] As a further technical solution, based on the stabilized state transition matrix and bias vector, the attractor of the learned state evolution system is solved by fixing-point conditions, including: Substitute the stabilized state transition matrix into the fixed-point condition, whereby the state at the next time step is equal to the state at the current time step:

[0016] in, For attractors; This is the state transition matrix after stabilization. for Bias vector; The fixed-point conditions are rearranged into a system of linear equations with the difference between the identity matrix and the stabilized state transition matrix as the coefficient matrix and the bias vector as the right-hand side:

[0017] in, Let be the coefficient matrix of the equation. It is a d-order identity matrix; Solving the linear equations using the Morpenrose pseudoinverse of the coefficient matrix yields the attractor vector:

[0018] in, Represents the Morpenrose pseudoinverse of a matrix; When the coefficient matrix is ​​invertible, the pseudo-inverse solution degenerates into the ordinary inverse matrix solution, and the resulting attractor is a unique analytical solution. When the coefficient matrix is ​​ill-conditioned or rank deficient, the pseudo-inverse solution provides a robust solution with the minimum norm in the least squares sense, so as to suppress the amplification effect of data noise on the attractor solution results.

[0019] As a further technical solution, all learners' attractors are used as representation vectors for clustering, including: The attractor vectors are standardized column-wise so that the attractor components of each state channel have zero mean and unit variance; The K-means clustering algorithm is used to divide learners into a predetermined number of style clusters, and the mean of the attractor vectors within the cluster is used as the attractor center of the style prototype. Explanatory style tags are automatically generated based on the relative strength of each style prototype center in each state channel.

[0020] As a further technical solution, the method also includes: using learners' actual academic results as external criterion, statistically analyzing the distribution of academic results under each dynamic style category, using the Cramer correlation coefficient to measure the correlation strength between style categories and academic results, and performing external validity verification on the dynamic learning style prototype.

[0021] A second aspect of the present invention provides a learning style recognition system based on state evolution and attractor analysis.

[0022] A learning style recognition system based on state evolution and attractor analysis includes: The learning state sequence construction module is configured to: obtain the behavior logs of learners in the online learning platform, map the behavior types in the behavior logs into multi-channel learning state components, and aggregate them into a learning state vector sequence for each learner according to the real time window; The state transition model estimation module is configured to: estimate a discrete state transition model describing the evolution relationship between states at adjacent time points based on the learned state vector sequence, wherein the state transition model includes a state transition matrix and a bias vector; The stability diagnosis and processing module is configured to: calculate the spectral radius of the state transition matrix and perform stabilization processing so that the spectral radius of the stabilized state transition matrix does not exceed a preset stability threshold. The attractor solving module is configured to: solve the attractor of the learned state evolution system based on the stabilized state transition matrix and bias vector through fixed-point conditions, wherein the fixed-point conditions are that the state at the next time step is equal to the state at the current time step; The dynamic style clustering module is configured to cluster all learners' attractors as representation vectors to obtain dynamic learning style prototypes, and assign a corresponding style category to each learner.

[0023] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the learning style recognition method based on state evolution and attractor analysis as described in the first aspect of the present invention.

[0024] A fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the learning style recognition method based on state evolution and attractor analysis as described in the first aspect of the present invention.

[0025] The above one or more technical solutions have the following beneficial effects: (1) This invention defines learning style as a stable attraction pattern in the evolutionary system of learner behavioral states, rather than traditional static category labels or questionnaire scores. Attractors reflect the stable destination that learners' behavioral states tend to reach in the long-term evolution, and their components can be directly explained by specific behavioral dimensions such as resource use, interactive participation, and evaluation input. Specifically, state channel mapping transforms the original log into a modelable state sequence, each element of the state transition matrix represents an interpretable inter-state influence coefficient, attractors reflect long-term stable states, and style centers automatically generate semantic labels. This gives the style recognition results a clear dynamic meaning and a traceable formation path.

[0026] (2) A dual-layer diagnostic mechanism of spectral radius stabilization and coefficient matrix condition number is introduced, which only performs minimal scaling on the divergence transition matrix to preserve the original state coupling structure to the greatest extent. For solving ill-conditioned problems, the Morpenrose pseudo-inverse is uniformly used to calculate the fixed-point attractor, avoiding the amplification of noise error by ordinary inversion. The stabilization marker, condition number, and prediction residual are recorded simultaneously as reliability labels to automatically select high-quality learner attractor samples. This overcomes the defects of model divergence, attractor unsolvability, or result distortion caused by finite-duration behavioral sequences, and makes the quantitative representation of long-term steady-state behavioral patterns numerically stable and verifiable.

[0027] (3) This invention uses attractor vectors representing long-term steady-state behavior as clustering objects to mine the essential style features of learners after evolutionary convergence. The optimal style category can be adaptively determined based on the silhouette coefficient, generating data-driven interpretable style prototypes without manual annotation. At the same time, the Cramer correlation coefficient is introduced to complete the external verification of academic results, quantify the objective correlation between style and learning output, and prove that the clustering results have practical educational significance. The entire solution does not require manual annotation costs, and the recognition results can be directly used for personalized resource recommendation and academic risk stratification intervention, adapting to most unlabeled real online education platform scenarios.

[0028] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0029] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0030] Figure 1 This is a flowchart of the method in the first embodiment.

[0031] Figure 2 This is a schematic diagram of the learning state trajectory and attractor solution for the first embodiment.

[0032] Figure 3 This is a distribution diagram of the attractor centers for the dynamic learning style prototype of the first embodiment.

[0033] Figure 4 This is a verification diagram showing the correlation between dynamic style and academic results in the first embodiment.

[0034] Figure 5 This is a system structure diagram of the second embodiment. Detailed Implementation

[0035] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0036] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0037] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0038] This invention no longer treats learning styles as static labels to be classified, but defines them as stable attraction patterns formed by learners' behavioral states over time. Specifically, firstly, time-stamped behavioral logs from the learning platform are mapped to multi-channel learning state components according to behavior type, and then aggregated into a learning state vector sequence for each learner according to a real-time window. Next, a discrete state transition model describing the evolution of each learner's state over time is estimated. Then, spectral radius stabilization and condition number diagnosis ensure the stability of the evolutionary system and well-posed attractor solutions. Subsequently, the fixed-point attractor of the system is solved as a stable pattern representation of the learner's long-term behavioral states. Finally, the learner group is clustered in the attractor representation space to obtain dynamic learning style prototypes, and the discovered styles are externally validated using real academic results. This method is fully implementable on real learning behavior logs, providing dynamic and interpretable learning style recognition technology support for personalized education recommendations and learning early warning.

[0039] Example 1 This embodiment discloses a learning style recognition method based on state evolution and attractor analysis; like Figure 1 As shown, the learning style recognition method based on state evolution and attractor analysis includes: Step S1: Obtain learners' behavior logs from the online learning platform, map the behavior types in the behavior logs into multi-channel learning state components, and aggregate them into a learning state vector sequence for each learner according to the real time window.

[0040] In a learning style recognition system, learners' raw data consists of time-stamped behavior logs generated by online learning platforms or learning management systems. Each behavior record includes at least the learner identifier, time stamp, identifier of the interacted resource or object, and an intensity count of the interaction. Assume the learning platform has a total of... The learner, the first A learner's original behavior log consists of several interaction records with time stamps.

[0041] To group numerous behavior or resource types into a finite number of learning state components with clear semantics, this embodiment establishes a mapping from behavior types to state channels. These state channels include at least four components: resource usage state, interaction state, evaluation and participation state, and course follow-up state. They can be further expanded to include more granular state components such as exploration level, reading level, task goal level, interaction level, cognitive engagement level, time engagement level, and attention stability level.

[0042] In one implementation, four learning state channels are defined: resource usage state, interaction state, evaluation and participation state, and course follow-up state. Specifically, behaviors such as resource browsing, content page access, and link navigation are mapped to the resource usage state; behaviors such as forum posting, collaboration, and wiki editing are mapped to the interaction state; behaviors such as quizzes and questionnaires are mapped to the evaluation and participation state; and behaviors such as directory navigation and periodic follow-up are mapped to the course follow-up state. Let the number of state channels be 1. In the four-channel implementation equal .

[0043] After determining the status channels, the behavior logs are aggregated according to a unified real-time window. Based on the time identifier, each learner's behavior is divided into time windows of fixed duration; in one implementation, a week is used as one time window. For those falling into the [specific category]... For all behaviors within a time window, the interaction intensity count is accumulated according to their respective state channels to obtain the original count for each channel within that time window. Since behavior counts typically exhibit a long-tailed distribution, a logarithmic compression transformation is applied to the original count for each channel:

[0044] in, For the first Within the first time window The original interaction count of each state channel, This is the compressed count. Subsequently, to eliminate differences in absolute activity levels among different learners and make state components comparable across learners, each channel is normalized according to its value range within the current learner's own trajectory:

[0045] in, These are the normalized state components; For learners in the The minimum value across all time windows for each channel; For learners in the The maximum value across all time windows for each channel.

[0046] After the above processing, the first Each learner receives a sequence of learning state vectors arranged in order of time windows:

[0047] in, For the first The number of effective time windows for each learner. To ensure the reliability of subsequent state transition model estimation, subsequent dynamic modeling is only performed on learners whose effective time windows are no less than a preset minimum number of steps. In one implementation, this minimum number of steps is set to 5. After this step, the discrete and heterogeneous behavioral logs are transformed into a multi-channel learning state sequence that is ordered in time and regular in dimensions, providing standardized input for state evolution modeling.

[0048] Step S2: Based on the learned state vector sequence, estimate a discrete state transition model that describes the evolution relationship between states at adjacent time points. The state transition model includes a state transition matrix and a bias vector.

[0049] For each learner that meets the minimum step requirement, a discrete state transition model describing the evolution of the state over time is estimated based on their learned state sequence. In one implementation, a first-order linear state transition model of the following form is used to describe the evolutionary relationship between states in adjacent time windows:

[0050] in, for OK The state transition matrix of the column, for dimensional bias vector, where This represents the number of state channels, i.e., the dimension of the learned state vector. State transition matrix. The Line 1 Column elements represent the first The state component is related to the first state component. The influence of the changing trend of each state component in the next time window, bias vector This represents the fundamental driving term that is independent of the current state. The model uses an explicit mathematical structure to characterize the coupling relationship between the learning state components and their mutual influence and driving over time.

[0051] To robustly estimate the state transition matrix from a finite-length sequence With bias vector Organize adjacent state pairs in the learner sequence into input and output samples: As input, with For the corresponding output, the bias term is incorporated into the parameter matrix to construct an augmented input. Regularized least-squares estimation of the parameters is used, with the objective of minimizing the sum of the squared error of the one-step prediction and the parameter regularization term:

[0052] in, This is a regularization coefficient used to suppress overfitting and improve numerical conditions when the sequence is short. Represented by the state transition matrix With bias vector Composed of columns OK Column augmented parameter matrix, Let Frobenius norm be the Frobenius norm of the matrix, which is the square root of the sum of the squares of all the elements of the matrix. The solution can be obtained by taking the pseudo-inverse of the augmented normal equation to obtain a closed-form solution.

[0053] Given the finite length of real learner sequences, regularized estimation can provide robust solutions when sequences are short. In one implementation, the estimation exhibits good well-posedness when the number of time windows is significantly larger than the state dimension.

[0054] To evaluate the fitting ability of the estimated transition model to the learner's state sequence, two metrics are calculated: one-step prediction residual and multi-step rolling prediction residual. The one-step prediction residual is the root mean square error of predicting the next state from the true current state, calculated by... Obtain the predicted value at each time step, and then calculate the root mean square error between it and the actual value:

[0055] in, To predict residuals in one step, The total number of effective time windows for learners. Here is the state transition matrix. This is the bias vector.

[0056] The multi-step rolling prediction residual is the root mean square error between the actual trajectory and the model prediction value after repeatedly using the model prediction value as the input for the next step to recursively generate the entire trajectory, starting from the beginning of the sequence.

[0057] make ,according to The entire predicted trajectory is generated recursively and then compared with the actual trajectory:

[0058] in, For multi-step rolling prediction of residuals, The model generates the predicted state vector for the t-th time window recursively, starting from the initial state. Multi-step rolling residuals impose stricter requirements on the model's dynamic extrapolation capability and can be used to quantify the reliability of the transferred model. When the values ​​of the one-step prediction residual and the multi-step rolling prediction residual are close, it indicates that the model has not shown significant error divergence during multi-step extrapolation.

[0059] Step S3: Calculate the spectral radius of the state transition matrix and perform stabilization processing to ensure that the spectral radius of the stabilized state transition matrix does not exceed a preset stabilization threshold.

[0060] Since the state transition matrix A obtained directly from a finite-length sequence may not satisfy the stability condition (i.e., it may have eigenvalues ​​with a magnitude greater than one), leading to divergence in the state evolution system and the absence of a long-term stable attractor, this embodiment introduces a stability criterion based on spectral radius and stabilization processing.

[0061] First, calculate the spectral radius of the state transition matrix A, which is the maximum value of the magnitudes of all its eigenvalues:

[0062] in, denoted as the spectral radius of the state transition matrix; Let be the k-th eigenvalue of the state transition matrix A. When the spectral radius does not exceed a preset stability threshold, the learner's state evolution system is considered stable and requires no further action. When the spectral radius exceeds this threshold, the matrix is ​​scaled proportionally so that the spectral radius of the scaled matrix is ​​exactly equal to the threshold.

[0063] in, This is the state transition matrix after stabilization. The stabilization threshold is set to a value close to and less than 1. This stabilization process preserves the relative coupling structure between state components while ensuring the convergence of the evolving system. Whether stabilization is triggered is recorded as a diagnostic marker for the learner. Unlike implicitly forcing convergence, by using the spectral radius as an explicit criterion, minimal stabilization is performed only when the system diverges, making the stabilization process itself a reportable and auditable diagnostic step.

[0064] To further evaluate the well-posedness of the subsequent attractor solution, the condition number of the coefficient matrix (obtained by subtracting the stabilized transition matrix from the identity matrix) is calculated. ,in It is a d-order identity matrix. This is the state transition matrix after stabilization (details explained in the following steps). An excessively large condition number indicates that the coefficient matrix is ​​close to singular, making the attractor solution sensitive to noise and with low reliability; a small condition number indicates that the attractor solution is well-stressed. This condition number is recorded as a quantitative diagnostic indicator of attractor reliability.

[0065] Step S4: Based on the stabilized state transition matrix and bias vector, solve for the attractor of the learning state evolution system through fixed-point conditions, whereby the state at the next time step is equal to the state at the current time step.

[0066] After obtaining the stabilized state transition model, the stable attractor of the state evolution system is further solved. The attractor refers to the stable state point that the learner's state approaches after long-term iterative evolution; once the learner's state reaches this point, the system will no longer drive it to continue changing, thus this point represents the long-term evolutionary destination of the learner's behavioral state. From a dynamic perspective, the attractor is the fixed point of the state evolution mapping, defined as: after substituting the current state into the evolution model, the state obtained at the next moment is equal to the current state.

[0067] Based on this, setting the next time window state equal to the current time window state yields the attractor. The fixed point conditions that must be met are:

[0068] The above equation represents the attractor The state remains unchanged after one state transition. To solve for this unknown vector, we will use... By moving the terms to the same side of the equation and combining like terms, that is, by subtracting the state transition terms from both sides of the equation, the fixed-point conditions can be rearranged as about The system of linear equations:

[0069] in, Let be the coefficient matrix of the equation. Let be the d-order identity matrix. This coefficient matrix characterizes the net change operator of the state during a single transition, and the bias vector b on the right-hand side of the equation is the fundamental term driving the state away from the origin. The solution to this system of linear equations is the attractor we are looking for.

[0070] The solvability of the above linear equation system depends on whether the coefficient matrix is ​​invertible. This has been ensured in step S3 by stabilizing the spectral radius. All eigenvalues ​​of the matrix have a magnitude strictly less than 1, and all eigenvalues ​​of the coefficient matrix are non-zero. Therefore, in the ideal case, the coefficient matrix is ​​invertible, and the attractor exists and is unique. It can be directly obtained by inverting the coefficient matrix.

[0071] However, when When eigenvalues ​​close to one exist, the coefficient matrix, while not singular, has a large condition number. Direct inversion amplifies noise in the state sequence estimation, leading to numerical instability in the attractor solution. To obtain a robust solution in this case, the Morpenrose pseudoinverse of the coefficient matrix is ​​further used for the solution:

[0072] in, This represents the Morpenrose pseudoinverse of the matrix.

[0073] In this embodiment, the pseudo-inverse solution serves a dual purpose. When the coefficient matrix is ​​invertible, the pseudo-inverse degenerates into a regular inverse, and the resulting solution is consistent with the unique solution. When the coefficient matrix is ​​ill-conditioned or rank-deficient, the pseudo-inverse provides a robust solution with the minimum norm in the least squares sense, thus avoiding numerical divergence under ill-conditioned conditions caused by direct inversion. The condition number of the coefficient matrix calculated in step S3 is used to quantify the well-posedness of the solution; a smaller condition number indicates a more reliable attractor solution.

[0074] To verify the requirements Indeed, this is a stable attraction point for the state evolution system. Further examination is needed to determine the convergence behavior of the state sequence when repeatedly applying the state transition model starting from any initial state. From the stabilization condition, it can be seen that any initial state... After multiple transitions, the difference between the state transition matrix and the attractor decays exponentially with respect to the state transition matrix:

[0075] because The spectral radius is strictly less than 1, and its power tends to zero as the number of iterations increases. Therefore, regardless of the initial state, the state sequence converges to the same attractor. This is mathematically guaranteed The rationale for a stable attraction pattern. For example... Figure 2 As shown, the learner's learning state starts from the initial state and evolves step by step along the state transition model, eventually converging to a stable attractor. The background arrows in the figure indicate the direction of evolution of each point in the state space, which intuitively reflects the attraction of the attractor to the surrounding state.

[0076] Furthermore, to ensure that the attractor components have an interpretable range consistent with the learned state components, the obtained attractor components are truncated to the normalized range of the state components. The physical meaning of this truncation is that since the learned state components are defined within the normalized range, the attractor, as a long-term stable state, should also fall within the same interpretable range. Truncation eliminates out-of-bounds values ​​that may arise from linear extrapolation, allowing each attractor component to be directly interpreted according to the meaning of its respective state channel. The resulting attractor... As a representation of the learner's long-term stable behavioral pattern, the value of this indicator in each state channel describes the learner's long-term tendency towards stability in resource use, interaction, assessment participation, and course follow-up.

[0077] Finally, by combining the one-step prediction residual and the multi-step rolling prediction residual in step S2, and the spectral radius and coefficient matrix condition number in step S3, the reliability of the attractor sought by each learner is evaluated as a whole.

[0078] For each learner, if their one-step residual or multi-step residual Exceeding a preset threshold, or triggering spectral radius stabilization and coefficient matrix... If the number of conditions exceeds the preset upper limit, the learner is judged to have low attractor reliability and is marked or removed from the cluster to ensure the discovery quality of dynamic learning style prototypes; otherwise, it is included in the normal cluster.

[0079] Step S5: Cluster all learners’ attractors as representation vectors to obtain dynamic learning style prototypes, and assign a corresponding style category to each learner.

[0080] After obtaining the attractor vectors of all learners that meet the criteria, this step performs unsupervised clustering of the learner group in the attractor representation space to discover dynamic learning style prototypes with discriminative significance. Unlike existing methods that directly cluster behavioral statistical features, the clustering object in this step is the attractor vector obtained by state evolution modeling and fixed-point solving for each learner. This vector describes the stable pattern that learners' behavioral states tend to approach over a long period of time, rather than a snapshot of behavior at a certain moment or stage. Therefore, the style prototypes obtained by clustering on this vector reflect the learners' stable behavioral tendencies over a long period of time.

[0081] Specifically, all learner attractor vectors that meet the reliability criteria are stacked row-wise to form an attractor representation matrix, where the number of rows represents the number of learners participating in the modeling, and the number of columns represents the number of state channels. Since the attractor components of different state channels may have scale differences in their numerical distribution, direct clustering would cause channels with larger value ranges to dominate the distance metric. Therefore, the attractor representation matrix is ​​first standardized column-wise to ensure that the attractor components of each state channel have zero mean and unit variance, guaranteeing that each channel has equal contribution weight in subsequent distance calculations.

[0082] In the standardized attractor representation space, a clustering algorithm is used to divide learners into a predetermined number of style clusters. In this embodiment, K-means clustering is used, which divides the standardized attractor vectors of N learners into... Divide the data into K clusters and minimize the sum of squares within each cluster.

[0083] in, The set of all clusters; For the k-th cluster, there is a set of indices containing several learners; Let be the center vector of the k-th cluster, and be the mean of all samples within that cluster.

[0084] By iteratively executing each... Assign the target value to the nearest cluster center; then update the center according to the cluster mean; until the center no longer changes. Take the minimum target value among multiple random initializations as the final result.

[0085] Using Euclidean distance as a similarity measure, the number of style clusters is set to 4. After clustering, for each style cluster, the mean of the attractor vectors of all learners in the cluster on each state channel is used as the attractor center of the prototype of the dynamic learning style. This center represents the long-term stable state that the learner group belonging to this style tends to.

[0086] To ensure the interpretability of the discovered style prototypes, their names are not pre-fixed. Instead, interpretive labels are automatically generated based on the relative strength of each style prototype's attractor center across different state channels: when a style prototype's attractor center is generally high across all channels, it is labeled as "High-Active Engagement Type"; when it is generally low across all channels, it is labeled as "Low-Active Steady-State Type"; and when it is significantly prominent in a specific channel, it is named according to the semantic meaning of that channel. For example, a style prototype prominent in the evaluation engagement channel is labeled as "Evaluation Engagement Prominent Type," and a style prototype prominent in the resource usage and interaction channel is labeled as "Interactive Resource Driven Type." This data-driven naming method avoids interference from prior assumptions in style definition, allowing the semantics of style prototypes to directly derive from the state distribution of attractors.

[0087] To assess the separability among the discovered style prototypes, silhouette coefficients of the clustering results are calculated. For the i-th sample, let... Let it be the average distance to other samples in the same cluster. The minimum of the average distances to all samples in the nearest heterogeneous cluster is the profile value of that sample. for:

[0088] The mean of all sample profile values ​​is the cluster profile coefficient.

[0089] in, This is the cluster silhouette coefficient. The silhouette coefficient comprehensively measures the degree to which each sample is closely related to samples in the same cluster and to the degree of separation from the nearest samples in different clusters. The value ranges from [-1, 1]. The larger the value, the higher the discriminative power of each style prototype in the attractor representation space and the clearer the cluster structure. This coefficient can be used as a basis for selecting the number of style clusters, that is, selecting the value that maximizes the silhouette coefficient from several candidate clusters, thereby determining the number of style prototypes with the best separability without manual annotation.

[0090] Furthermore, following the steps described above, each learner is assigned a dynamic learning style category, which is the style cluster to which their attractor vector belongs and its corresponding explanatory label, serving as the learner's dynamic learning style identification result. This result can be output to downstream applications such as personalized education recommendations, learning alerts, or teaching interventions. For newly joined learners, after accumulating behavioral logs over a sufficient time window, their attractor vector is calculated using the steps described above, and then this vector is assigned to the nearest style prototype center to obtain their dynamic learning style identification result.

[0091] In the absence of authoritative, manually labeled real-world data on learning style, this embodiment uses learners' actual academic results to externally validate the discovered dynamic attractor styles. The distribution of academic results under each dynamic style category is statistically analyzed, and the correlation strength between style categories and academic results is measured using a contingency table. In one implementation, the Cramer correlation coefficient is used as the correlation strength measure.

[0092] in, The chi-square statistic for the contingency table of style categories and academic results. The total number of samples, and These represent the number of rows and columns in the contingency table, respectively. The coefficients range from 0 to 1; larger values ​​indicate a stronger association between the dynamic style and academic outcomes. It should be noted that this validation step aims to provide external validity support for the attractor style discovered in unsupervised learning, helping to differentiate risk groups for different learning outcomes, rather than for precise prediction of academic performance.

[0093] Furthermore, to characterize the degree of difference between different dynamic learning styles, the distance between any two style prototype attractor centers can be calculated as an indicator of the difficulty of style transfer: the smaller the distance, the closer the two styles are in the state space and the lower the transfer difficulty; the larger the distance, the greater the difference and the higher the transfer difficulty. This indicator can serve as a reference for designing personalized teaching intervention paths.

[0094] To verify the feasibility and effectiveness of the method of this invention, the complete technology chain was implemented and run on a publicly available learning analytics dataset. This dataset contains learners' date-identified behavioral logs. Experiments were aggregated by week as the time window based on real dates. Dynamic modeling was completed for 25,724 learners, with an average trajectory step count of 24.04 steps and a minimum trajectory step count of 5 steps. The trajectory length is sufficient to support robust estimation of the individual-level state transition model. Key relevant metrics are shown in Table 1.

[0095] Table 1 Key performance indicators of OULAD real-time experiments

[0096] Experimental results show that only 1.6% of learners triggered spectral radius stabilization, and the state evolution systems of the vast majority of individuals could satisfy the stability condition after estimation from real logs. The median condition number of the coefficient matrix used to solve for the attractor was 2.526, which is within the well-posed range, indicating that the attractor solution is generally reliable at the population level. The mean root mean square error of one-step prediction was 0.2310, and the mean root mean square error of multi-step rolling prediction was 0.2536. The two values ​​are close, indicating that the model did not show significant error divergence during multi-step extrapolation.

[0097] Learners were clustered into four dynamic learning style prototypes in the attractor representation space: highly active and engaged, assessment-participatory, interaction-resource driven, and low-active and steady-state. The cluster silhouette coefficient was 0.2523, indicating a moderate degree of separation among the style prototypes. External validity was validated using real academic outcomes. The Cramér's V correlation coefficient between style categories and academic outcomes was 0.1055, indicating an observable association. The different styles showed variations in the distribution of pass / drop results, demonstrating the external validity of the identified styles.

[0098] Figure 3 The invention demonstrates the component distribution of the attractor centers of four dynamic learning style prototypes obtained on the experimental dataset using the method of this invention, reflecting the differentiated stable patterns of different styles in resource use, interaction, assessment participation, and course follow-up. Figure 4 The study shows the correlation distribution between various dynamic learning styles and actual academic outcomes. It can be seen that different styles have different proportions of outcomes such as pass, excellent, failure, and course dropout, which corroborates the observable association between the discovered attractor styles and academic performance.

[0099] Example 2 This embodiment discloses a learning style recognition system based on state evolution and attractor analysis; like Figure 5 As shown, the learning style recognition system based on state evolution and attractor analysis includes: The learning state sequence construction module is configured to: obtain the behavior logs of learners in the online learning platform, map the behavior types in the behavior logs into multi-channel learning state components, and aggregate them into a learning state vector sequence for each learner according to the real time window; The state transition model estimation module is configured to: estimate a discrete state transition model describing the evolution relationship between states at adjacent time points based on the learned state vector sequence, wherein the state transition model includes a state transition matrix and a bias vector; The stability diagnosis and processing module is configured to: calculate the spectral radius of the state transition matrix and perform stabilization processing so that the spectral radius of the stabilized state transition matrix does not exceed a preset stability threshold. The attractor solving module is configured to: solve the attractor of the learned state evolution system based on the stabilized state transition matrix and bias vector through fixed-point conditions, wherein the fixed-point conditions are that the state at the next time step is equal to the state at the current time step; The dynamic style clustering module is configured to cluster all learners' attractors as representation vectors to obtain dynamic learning style prototypes, and assign a corresponding style category to each learner.

[0100] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0101] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the learning style recognition method based on state evolution and attractor analysis as described in Example 1.

[0102] Example 4 The purpose of this embodiment is to provide an electronic device.

[0103] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the learning style recognition method based on state evolution and attractor analysis as described in Embodiment 1.

[0104] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0105] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0106] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A learning style recognition method based on state evolution and attractor analysis, characterized in that, include: Obtain learners' behavior logs from online learning platforms, map the behavior types in the behavior logs to multi-channel learning state components, and aggregate them into a learning state vector sequence for each learner according to the real time window; Based on the learned state vector sequence, a discrete state transition model describing the evolution relationship between states at adjacent time points is estimated. The state transition model includes a state transition matrix and a bias vector. Calculating and stabilizing the spectral radius of the state transition matrix to ensure that the spectral radius of the stabilized state transition matrix does not exceed a preset stability threshold includes: Calculate the spectral radius of the state transition matrix: in, denoted as the spectral radius of the state transition matrix; This represents the k-th eigenvalue of the state transition matrix. When the spectral radius does not exceed the preset stability threshold, it indicates that the learner's state evolution system is stable; when the spectral radius exceeds the preset stability threshold, the matrix is ​​scaled proportionally so that the spectral radius of the scaled matrix is ​​exactly equal to the preset stability threshold. in, This is the state transition matrix after stabilization. The preset stability threshold is used; Based on the stabilized state transition matrix and bias vector, the attractor of the learned state evolution system is solved through fixed-point conditions. Specifically, the stabilized state transition matrix is ​​substituted into the fixed-point conditions, whereby the state at the next time step is equal to the state at the current time step. in, For attractors; This is the state transition matrix after stabilization. for Bias vector; The fixed-point conditions are rearranged into a system of linear equations with the difference between the identity matrix and the stabilized state transition matrix as the coefficient matrix and the bias vector as the right-hand side: in, Let be the coefficient matrix of the equation. It is a d-order identity matrix; Solving the linear equations using the Morpenrose pseudoinverse of the coefficient matrix yields the attractor vector: in, Represents the Morpenrose pseudoinverse of a matrix; When the coefficient matrix is ​​invertible, the pseudo-inverse solution degenerates into the ordinary inverse matrix solution, and the resulting attractor is a unique analytical solution; when the coefficient matrix is ​​ill-conditioned or rank deficient, the pseudo-inverse solution gives a robust solution with the minimum norm in the least squares sense, so as to suppress the amplification effect of data noise on the attractor solution results. Cluster all learners’ attractors as representation vectors to obtain dynamic learning style prototypes, and assign a corresponding style category to each learner.

2. The learning style recognition method based on state evolution and attractor analysis as described in claim 1, characterized in that, The multi-channel learning state component includes at least four channels: resource usage state, interaction state, evaluation and participation state, and course follow-up state. The multi-channel learning state components are aggregated into a learning state vector sequence for each learner according to the real time window. Specifically, the behavior counts of each channel within the time window are subjected to logarithmic compression transformation and normalized according to the current learner's own trajectory range, so that the state components fall into a unified normalized value range.

3. The learning style recognition method based on state evolution and attractor analysis as described in claim 1, characterized in that, The discrete state transition model is as follows: in, for OK The state transition matrix of the column, for 3D bias vector; state transition matrix The Line 1 Column elements represent the first The state component is related to the first state component. The influence of the changing trend of each state component in the next time window, bias vector This represents a basic driving item that does not depend on the current state.

4. The learning style recognition method based on state evolution and attractor analysis as described in claim 1, characterized in that, Cluster all learners' attractors as representation vectors, including: The attractor vectors are standardized column-wise so that the attractor components of each state channel have zero mean and unit variance; The K-means clustering algorithm is used to divide learners into a predetermined number of style clusters, and the mean of the attractor vectors within the cluster is used as the attractor center of the style prototype. Explanatory style tags are automatically generated based on the relative strength of each style prototype center in each state channel.

5. The learning style recognition method based on state evolution and attractor analysis as described in claim 1, characterized in that, Also includes: Using learners' actual academic outcomes as external criterion, the distribution of academic outcomes under each dynamic style category is statistically analyzed. The Cramer correlation coefficient is used to measure the strength of the association between style category and academic outcome, thereby validating the external validity of the dynamic learning style prototype.

6. A learning style recognition system based on state evolution and attractor analysis, characterized in that, include: The learning state sequence construction module is configured to: obtain the behavior logs of learners in the online learning platform, map the behavior types in the behavior logs into multi-channel learning state components, and aggregate them into a learning state vector sequence for each learner according to the real time window; The state transition model estimation module is configured to: estimate a discrete state transition model describing the evolution relationship between states at adjacent time points based on the learned state vector sequence, wherein the state transition model includes a state transition matrix and a bias vector; The stability diagnosis and processing module is configured to: calculate the spectral radius of the state transition matrix and perform stabilization processing to ensure that the spectral radius of the stabilized state transition matrix does not exceed a preset stability threshold, including: Calculate the spectral radius of the state transition matrix: in, denoted as the spectral radius of the state transition matrix; This represents the k-th eigenvalue of the state transition matrix. When the spectral radius does not exceed the preset stability threshold, it indicates that the learner's state evolution system is stable; when the spectral radius exceeds the preset stability threshold, the matrix is ​​scaled proportionally so that the spectral radius of the scaled matrix is ​​exactly equal to the preset stability threshold. in, This is the state transition matrix after stabilization. The preset stability threshold is used; The attractor solving module is configured to: solve for the attractors of the learned state evolution system based on the stabilized state transition matrix and bias vector, using fixed-point conditions. Specifically, the stabilized state transition matrix is ​​substituted into the fixed-point conditions, where the state at the next time step is equal to the state at the current time step. in, For attractors; This is the state transition matrix after stabilization. for Bias vector; The fixed-point conditions are rearranged into a system of linear equations with the difference between the identity matrix and the stabilized state transition matrix as the coefficient matrix and the bias vector as the right-hand side: in, Let be the coefficient matrix of the equation. It is a d-order identity matrix; Solving the linear equations using the Morpenrose pseudoinverse of the coefficient matrix yields the attractor vector: in, Represents the Morpenrose pseudoinverse of a matrix; When the coefficient matrix is ​​invertible, the pseudo-inverse solution degenerates into the ordinary inverse matrix solution, and the resulting attractor is a unique analytical solution; when the coefficient matrix is ​​ill-conditioned or rank deficient, the pseudo-inverse solution gives a robust solution with the minimum norm in the least squares sense, so as to suppress the amplification effect of data noise on the attractor solution results. The dynamic style clustering module is configured to cluster all learners' attractors as representation vectors to obtain dynamic learning style prototypes, and assign a corresponding style category to each learner.

7. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the learning style recognition method based on state evolution and attractor analysis as described in any one of claims 1-5.

8. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the learning style recognition method based on state evolution and attractor analysis as described in any one of claims 1-5.

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