Art learning path optimization system with cross-domain collaborative recommendation and knowledge graph iteration

Abstract

The application relates to the technical field of knowledge graph and discloses an art learning path optimization system for cross-field collaborative recommendation and knowledge graph iteration, which comprises the following steps: firstly, collecting art behavior sequences, device running state sequences and teaching texts, and uniformly mapping the sequences into a dimensionless observation matrix; secondly, extracting a link change rate and a brush stroke movement complexity based on the observation matrix, calculating a disturbance uncertainty and converting the disturbance uncertainty into an evidence attenuation factor; subsequently, constructing a cross-disciplinary knowledge graph, calculating initial edge weights, and iteratively updating learner mastery and edge weights by using the evidence attenuation factor and attribution probability; then, obtaining a candidate skill comprehensive utility by combining cross-field guide weights and prerequisite support gains; finally, obtaining an optimal learning path by using the evidence attenuation factor to adjust an inertia weight of a particle swarm optimization algorithm based on the utility as a basis benefit, and distributing learning time and a feedback reinforcement coefficient.

Description

Technical Field

[0001] This invention relates to the field of knowledge graph technology, and more specifically, to an art learning path optimization system that combines cross-domain collaborative recommendation and knowledge graph iteration. Background Technology

[0002] The planning of art learning paths relies heavily on the precise analysis of the high-frequency, continuous action details (such as brush pressure and angle changes) generated during the learner's painting process. With the deepening of digital teaching, in special application scenarios such as strong electromagnetic interference, space exploration, or isolation restoration, it is often necessary to deploy optical modules with radiation-resistant microcontrollers to complete the data interaction between the front end and the back end.

[0003] However, existing recommended solutions have significant limitations when dealing with such special environments. On the one hand, traditional art teaching assessment models typically assume that the data transmission channel is ideal and transparent, failing to consider the fluctuations in the optical module link state caused by the penetration of high-energy particles in space or sudden electromagnetic interference, as well as the residual fluctuations during the recovery period. When a short-term disturbance occurs in the link, the data receiver may experience a surge in bit errors or timestamp jitter. On the other hand, because the painting action itself has a strong temporal locality, the aforementioned link fluctuations are easily confused with real painting errors such as unstable force control and hesitant brushstrokes.

[0004] Existing knowledge graph and path planning algorithms, upon receiving such disturbed action evidence, directly record it as a learner's skill deficiency. Consequently, during interdisciplinary recommendation and algorithm optimization, they incorrectly guide the learning path towards low-level basic control training. This evaluation contamination caused by device-specific perturbations not only reduces the suitability of recommended content but also severely impacts the learner's actual skill improvement progress. Summary of the Invention

[0005] This invention provides an art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration, which solves the technical problems mentioned in the background.

[0006] This invention provides an art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration. It is applied to a learning station that includes a pressure-sensitive digital easel, a posture eye-tracking collector, a radiation-resistant light module, and a processing server, and is configured to execute: Within the set acquisition session, the sequence of artistic behaviors generated by the digital easel and the acquisition device, the sequence of running status generated by the light module, and the teaching text containing skill nodes and prerequisite relationships are acquired and mapped into a dimensionless observation matrix. Based on the observation matrix, the link change rate and pen stroke motion complexity are extracted, the disturbance uncertainty characterizing the resistance to radiation disturbance is calculated, and it is converted into an evidence attenuation factor. Based on cross-domain semantic relevance and co-occurrence characteristics, a cross-domain knowledge graph containing the skill nodes is constructed from the teaching text, and the initial edge weights are calculated. Using the evidence decay factor and the skill attribution probability output by the preset model, the learner's skill mastery and the initial edge weights are iteratively updated to obtain the updated edge weights; A candidate skill set is constructed by the target skill node and the prior relationship, and the comprehensive utility of the candidate skills is calculated by using the matching degree of the set in each field and the skill mastery degree. The comprehensive utility is used as the base benefit, and the optimal learning path is obtained by adjusting the inertia weight of the particle swarm algorithm in combination with the evidence decay factor. The cross-domain knowledge graph is updated by allocating time proportions according to the optimal learning path and generating feedback reinforcement coefficients in conjunction with evidence decay factors.

[0007] The beneficial effects of this invention are as follows: By uniformly mapping multi-source heterogeneous data collection into dimensionless parameters and dynamically extracting disturbance uncertainties to generate evidence attenuation factors, this invention can smoothly correct fitness shifts in the knowledge graph iteration and particle swarm optimization process without directly discarding the original drawing behavior data. This invention effectively avoids the phenomenon of misjudging device errors as learner skill deficiencies due to hardware link fluctuations, thus improving the accuracy of interdisciplinary knowledge recommendation and the rationality of learning path generation. Attached Figure Description

[0008] Figure 1 This is a flowchart of the art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration of the present invention. Detailed Implementation

[0009] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0010] like Figure 1 As shown, the art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration is applied to a learning station that includes a pressure-sensitive digital easel, a posture eye tracker, an anti-radiation light module, and a processing server, and is configured to execute: Within the set acquisition session, the sequence of artistic behaviors generated by the digital easel and the acquisition device, the sequence of running status generated by the light module, and the teaching text containing skill nodes and prerequisite relationships are acquired and mapped into a dimensionless observation matrix. Based on the observation matrix, the link change rate and pen stroke motion complexity are extracted, the disturbance uncertainty characterizing the resistance to radiation disturbance is calculated, and it is converted into an evidence attenuation factor. Based on cross-domain semantic relevance and co-occurrence characteristics, a cross-domain knowledge graph containing the skill nodes is constructed from the teaching text, and the initial edge weights are calculated. Using the evidence decay factor and the skill attribution probability output by the preset model, the learner's skill mastery and the initial edge weights are iteratively updated to obtain the updated edge weights; A candidate skill set is constructed by the target skill node and the prior relationship, and the comprehensive utility of the candidate skills is calculated by using the matching degree of the set in each field and the skill mastery degree. The comprehensive utility is used as the base benefit, and the optimal learning path is obtained by adjusting the inertia weight of the particle swarm algorithm in combination with the evidence decay factor. The cross-domain knowledge graph is updated by allocating time proportions according to the optimal learning path and generating feedback reinforcement coefficients in conjunction with evidence decay factors.

[0011] The cross-domain collaborative recommendation and knowledge graph iteration art learning path optimization system provided in this embodiment is applied to a learning station that includes a pressure-sensitive digital easel, a posture eye tracker, an anti-radiation light module, and a processing server. The processing server includes, but is not limited to, enterprise-level servers, cloud computing clusters, and industrial control computers, responsible for executing core algorithm calculations, model inference, and data storage. The pressure-sensitive digital easel is used to collect data on the learner's pen stroke coordinates, pen pressure, and stylus tilt angle during the drawing process. The sampling period is configurable from 1 millisecond to 1 second, with a default sampling period of 10 milliseconds. The posture and eye-tracking collector is used to collect data on the learner's gaze trajectory and human posture trajectory during the drawing process. The sampling period is synchronized with the pressure-sensitive digital easel, with a default sampling period of 33 milliseconds. The radiation-resistant light module is used to realize full-duplex data interaction between the acquisition terminal and the processing server. It has anti-electromagnetic interference and anti-space radiation capabilities and can operate stably in scenarios with strong electromagnetic interference, space exploration, or isolation and restoration. The sampling period is synchronized with the pressure-sensitive digital easel, with a default sampling period of 10 milliseconds. The acquisition parameters include power supply voltage, transmit and receive power, bit error count, bias current, and module temperature.

[0012] All acquisition terminals and processing servers within the system use the NTP network time protocol for clock synchronization. The main clock source is the built-in clock module of the processing server, and the synchronization error is controlled within 10% of the sampling period. For multi-source data with different sampling frequencies, the system uses linear interpolation to achieve resampling alignment. Using the sampling time of the pressure-sensitive digital easel as the reference time axis, the data acquired by the attitude eye tracker and the radiation-resistant light module are interpolated and mapped onto the reference time axis to ensure that the timestamps of all acquired data are strictly aligned. The system algorithm execution is divided into terminal side and server side. The terminal side is responsible for raw data acquisition, clock synchronization, data preprocessing, and data uploading, while the server side is responsible for text embedding processing, model inference, core algorithm calculation, path generation, and resource allocation instruction issuance.

[0013] The system is configured to perform the following steps: Within the defined acquisition session, the system acquires art behavior sequences generated by the digital easel and acquisition device, operational status sequences generated by the optical module, and instructional text containing skill nodes and prerequisite relationships. The acquisition session is a pre-configured continuous acquisition time interval with a unique start and end time. The session duration is configurable from 5 minutes to 120 minutes, with a default duration of 30 minutes. The art behavior sequence includes data aligned to the reference timeline, with synchronized timestamps, including brushstroke 2D coordinates, brushstroke normal pressure, stylus spatial tilt angle, gaze trajectory, and human posture trajectory. Each data item corresponds to an independent data channel. The operational status sequence includes data aligned to the reference timeline, with synchronized timestamps, including radiation-resistant optical module power supply voltage, transmit / receive power, bit error count, bias current, and module temperature, perfectly aligned with the reference timeline of the art behavior sequence. The teaching texts include skill node definitions for art and interdisciplinary courses, prerequisite relationships between skills, course description texts, and interdisciplinary explanatory texts. Each skill node has a unique identifier and corresponding standardized text description content. Interdisciplinary fields include, but are not limited to, aesthetic theory, color theory, human anatomy, perspective, and digital media technology.

[0014] Using the difference between the start and end times of the acquisition session as a benchmark, the current sequence acquisition time is converted into dimensionless time, calculated using the following formula:

[0015] Where t is the acquisition time on the reference time axis with physical time dimensions. To set the start time of the data collection session, To set the end time of the data collection session, The converted dimensionless time, with a value range of [0,1], is used to remove the influence of the physical time scale on subsequent calculations and to achieve data standardization and alignment for acquisition sessions of different durations.

[0016] For each independent data channel in the art behavior sequence and operational state sequence, an empirical cumulative distribution function (ECD) based on the current acquisition session data is constructed. An independent data channel refers to the time series corresponding to each single type of acquired data, and each channel corresponds to an independent ECD. The ECD is constructed based on all continuous raw data from the same channel for the same learner within the current acquisition session. For any raw data value within a channel, the function output is the proportion of samples in that channel that are less than or equal to that raw data value to the total number of samples, with a value range of [0,1]. For extremely short acquisition sessions with a sample size of less than 100, linear interpolation is used to smooth the ECD to avoid step-like jumps.

[0017] Substituting the continuous raw data from each independent data channel into the corresponding empirical cumulative distribution function for transformation, a dimensionless continuous observation sequence is generated. The calculation formula is as follows:

[0018] Where u is the learner's unique identifier, and c is the unique identifier of the independent data channel. This refers to continuous raw data with physical units within channel c. Let c be the empirical cumulative distribution function corresponding to channel c. It is a dimensionless continuous observation sequence after mapping, with a value range of [0,1], to achieve standardization and unification of multi-source acquisition data with different dimensions and value ranges.

[0019] Text embedding and normalization are performed on the teaching text to generate dimensionless discrete text feature vectors. The text embedding process uses a pre-trained natural language processing model, including but not limited to BERT and RoBERTa. The model input consists of skill descriptions and prerequisite relationship descriptions from the teaching text. The model output is a fixed-dimensional real-number vector, with the vector dimension configurable from 128 to 1024 dimensions, and a default dimension of 256 dimensions. L2 normalization is performed on the model output vector, converting it into a dimensionless discrete text feature vector in unit vector form. Each dimension of the vector takes values ​​in the range [-1, 1], and the vector magnitude is 1.

[0020] A dimensionless observation matrix is ​​generated by concatenating a dimensionless continuous observation sequence with a dimensionless discrete text feature vector. First, the dimensionless discrete text feature vector is broadcast along the time dimension, creating a sequence with the same time step length as the dimensionless continuous observation sequence, ensuring complete matching of the time and feature dimensions of the two sequences. Then, the feature dimension concatenation operation is performed, calculated using the following formula:

[0021] in, These are the dimensionless components of brushstroke coordinates, pressure, and tilt angle data in an art performance sequence after distribution mapping. These are the dimensionless components corresponding to the line-of-sight trajectory data. These are the dimensionless components corresponding to human posture trajectory data. For the dimensionless state parameters of the optical module corresponding to the operating state sequence, This is the dimensionless discrete text feature sequence corresponding to the course description text broadcast along the time dimension. Let m be the dimensionless discrete text feature sequence corresponding to the interdisciplinary explanatory text broadcast along the time dimension, where m is the feature dimension index after vector concatenation. The generated dimensionless observation matrix consists of each row corresponding to the full observation data at a reference time axis acquisition time, and each column corresponding to an independent observation feature dimension.

[0022] For the operational status sequence of the corresponding optical module in the dimensionless continuous observation sequence, the first norm of the first derivative is calculated according to the dimensionless time to obtain the link change rate. For the dimensionless time series with discrete sampling, the central difference method is used to approximate the calculation of the first derivative, and the forward and backward difference methods are used for the boundary sampling points. The calculation formula is as follows:

[0023] in, Dimensionless time The corresponding dimensionless state parameters of the optical module, Let be the first derivative of the dimensionless state parameter of the optical module with respect to dimensionless time, representing the instantaneous rate of change of the operating state of the optical module. This is a norm operation for vectors, which involves summing the absolute values ​​of all elements of the derivative vector. The calculated link change rate is a non-negative dimensionless scalar. The larger the value, the more severe the fluctuation of the optical link's state and the higher the degree of influence from irradiation or electromagnetic interference.

[0024] The autocorrelation function of the link change rate is calculated, and the optical link disturbance hysteresis length is obtained based on the ratio of the first-order moment integral to the zero-order moment integral of the absolute value of the autocorrelation function. The autocorrelation function is calculated using an unbiased estimation method. For discrete sampling sequences, the trapezoidal numerical integration method is used to calculate the integral term. The calculation formula is as follows:

[0025] Where 'a' is a dimensionless lag time variable, with a value range of [0,1]. Link change rate The corresponding unbiased autocorrelation function is used to characterize the degree of autocorrelation in the rate of change of the link under different lag times. Let be the absolute value of the autocorrelation function, the numerator be the integral of the first moment of the absolute value of the autocorrelation function over the interval [0,1], and the denominator be the integral of the zero moment of the absolute value of the autocorrelation function over the interval [0,1]. The calculated optical link disturbance hysteresis length is a dimensionless scalar with a value range of (0,1], representing the time span during which the optical link disturbance affects subsequent data acquisition. When the integral value in the denominator is less than 1e-6, ... The default value of 0.1 is used to avoid errors caused by dividing by zero.

[0026] The art performance sequence is divided into single-stroke intervals, and the stroke center time is determined. A single-stroke interval refers to the continuous time interval from the start of contact between the stylus and the pressure-sensitive digital easel to the end of contact. The stylus contact threshold is a stroke pressure greater than or equal to 5% of the full-scale pressure value, and the contact release threshold is a stroke pressure less than 5% of the full-scale pressure value. Short-duration interruptions lasting less than 50 milliseconds are merged into consecutive stroke intervals to avoid over-segmentation. Each single-stroke interval corresponds to a unique stroke identifier, and the stroke center time is the arithmetic mean of the start and end dimensionless times of the single-stroke interval, denoted as […]. s is the unique identifier for a single stroke.

[0027] The temporal lag effect value is obtained by integrating the link change rate with an exponential decay kernel constructed based on the optical link disturbance lag length. The exponential decay kernel is used to quantify the influence weight of link disturbances at different times on the current stroke; the closer the link disturbance is to the center of the stroke, the higher its weight. For discrete sampling sequences, the trapezoidal numerical integration method is used to calculate the integral term, with the integration step size consistent with the sampling step size of the reference time axis. The calculation formula is as follows:

[0028] in, Let be the dimensionless time variable for integration, with a value range of [0,1]. Dimensionless time The corresponding link change rate, For the constructed exponentially decaying kernel, when At this time, the kernel function value is set to 0 to achieve integral truncation and improve computational efficiency. The calculated time lag effect value is a non-negative dimensionless scalar with a value range of [0, max(L(τ))]. The larger the value, the higher the degree of influence of optical link disturbance on the current pen stroke interval.

[0029] Within a single stroke interval, the complexity of the stroke motion is obtained by integrating the sum of the second-norm of the dimensionless coordinates, the absolute value of the first-norm of the dimensionless pressure, and the second-norm of the first-norm of the dimensionless tilt angle, and dividing by the interval length. For discrete sampling sequences, the first and second derivatives are calculated using the central difference method, and the integral term is calculated using the trapezoidal numerical integration method. The calculation formula is as follows:

[0030] in, Let represent the stroke motion complexity corresponding to a single stroke 's'. 's' is a non-negative, dimensionless scalar used to quantify the degree of fluctuation in a learner's penmanship within a single stroke range. A larger value indicates a more drastic change in penmanship. The dimensionless time interval length corresponding to a single stroke s is equal to , Let s be the dimensionless time at the start of a single stroke. Let s be the dimensionless time at the end of a single stroke. Let s be the dimensionless coordinate vector corresponding to a single brush stroke. Let be the second derivative of the dimensionless coordinates with respect to dimensionless time. For vector 2 norm operations, This represents the dimensionless pressure sequence corresponding to a single brush stroke s. Let the first derivative of the dimensionless pressure with respect to the dimensionless time be . Let be the dimensionless tilt vector corresponding to a single brush stroke s. It is the first derivative of the dimensionless tilt angle with respect to dimensionless time.

[0031] The disturbance uncertainty is obtained by multiplying the complexity of the brushstroke motion by the value of the time lag effect, dividing by one, and adding the sum of the two values. The formula is as follows:

[0032] in, Let be the disturbance uncertainty corresponding to a single stroke s, a dimensionless scalar with a value range of [0,1). It quantifies the probability that the motion fluctuation of the current stroke is caused by optical link disturbance. A larger value indicates higher uncertainty in the current stroke data due to disturbance, and lower data reliability. When... and When both are 0, Use 0 to avoid division by zero errors.

[0033] Dividing the disturbance uncertainty by one and performing a nonlinear mapping with its own value generates the evidence attenuation factor, calculated as follows:

[0034] in, Let be the evidence attenuation factor corresponding to a single stroke 's'. It is a dimensionless scalar with a value range of [0, 0.5). It is used to attenuate and correct the evaluation evidence corresponding to perturbed stroke data. A larger value indicates a higher degree of evidence attenuation, and a lower weight in subsequent skill mastery updates and graph iterations. The numerical boundary of the evidence attenuation factor corresponds to the perturbation misjudgment as follows: when... When the value is greater than or equal to 0.3, it is determined that the current pen stroke data is affected by a strong disturbance, and the corresponding evidence undergoes a high degree of attenuation; when When the value is less than 0.1, it is determined that the current pen stroke data is basically unaffected by disturbances, and the corresponding evidence is basically not subject to attenuation.

[0035] This process extracts graph-structured association facts containing starting skill nodes and target skill nodes from teaching texts. The parsing of these association facts employs a pre-trained relation extraction model, including but not limited to a BERT+ classifier architecture. The model input consists of paragraphs from the teaching text, and the output is a triple containing the starting skill node, the target skill node, and the association type. Association types include prerequisite relationships, cross-domain collaborative relationships, and progressive learning relationships, each with a unique identifier. Starting skill nodes represent prerequisite skills that must be mastered beforehand, while target skill nodes represent subsequent skills that can be learned based on those prerequisite skills. All parsed triples are manually verified and then stored in a standardized graph-structured association fact base.

[0036] The cosine similarity between the text feature vectors corresponding to the starting skill node and the target skill node is calculated as the cross-domain semantic relevance. The calculation formula is as follows:

[0037] in, Let be the dimensionless discrete text feature vector corresponding to the starting skill node 'a'. Let b be the dimensionless discrete text feature vector corresponding to the target skill node b. The cosine similarity between two vectors ranges from -1 to 1. After translation normalization, the cross-domain semantic relevance ranges from 0 to 1, with higher values ​​indicating a stronger semantic connection between the two skill nodes. The translation normalization formula is as follows:

[0038] in, The final cross-domain semantic correlation degree is a dimensionless scalar with a value range of [0,1].

[0039] In the parsed graph structure association facts, the joint probability of the co-occurrence of the starting and target skill nodes is calculated and divided by the natural logarithm of the product of their respective independent probabilities. This logarithmic value is then normalized to serve as the co-occurrence feature. The sample space for probability statistics is the entire graph structure association fact database. For zero-probability events, a smoothing method of adding 1 is used to avoid the problem of meaningless logarithmic operations. The formula for calculating point mutual information is:

[0040] Where *a* is the starting skill node, *b* is the target skill node, *r* is the association type between the two nodes, *P(a,b,r)* is the joint probability of the starting skill node *a*, the target skill node *b*, and the association *r* appearing in the full association fact base, *P(a)* is the independent probability of the starting skill node *a* appearing in the full association fact base, *P(b)* is the independent probability of the target skill node *b* appearing in the full association fact base, *P(r)* is the independent probability of the association *r* appearing in the full association fact base, and *PMI(a,b,r)* is the calculated point mutual information value. Min-max normalization is performed on all *PMI* values ​​in the full association fact base to obtain the dimensionless co-occurrence feature, calculated using the following formula:

[0041] in, The minimum PMI value in the full relational fact base. The maximum value of the PMI in the full relational fact base. This is the final dimensionless co-occurrence feature, with values ​​ranging from [0,1]. A larger value indicates a higher degree of co-occurrence between the two nodes under this association. hour, Use 0.5 to avoid the error of dividing by zero.

[0042] The comprehensive relevance is calculated by combining cross-domain semantic relevance with co-occurrence features, and the formula is as follows:

[0043] in, The comprehensive correlation degree is the relationship between the starting skill node a and the target skill node b, with the relationship r. It is a dimensionless scalar with a value range of [0,2]. It combines semantic-level correlation and statistical-level co-occurrence correlation to fully quantify the correlation strength between the two skill nodes.

[0044] For all target skill nodes pointed to by the initial skill node, calculate the natural exponent of the comprehensive correlation degree and perform probability normalization on the node correlation dimension to generate initial edge weights. To avoid exponential underflow, numerical stabilization processing is performed on the comprehensive correlation degree, and the calculation formula is as follows:

[0045] in, Let be the set of all target nodes of the starting skill node 'a' under the association relationship 'r', and let b' be the traversed nodes within the set. This represents the maximum comprehensive correlation degree of all target nodes corresponding to the starting skill node a under the correlation relationship r. In the 0th iteration, the initial edge weight of the starting skill node a pointing to the target skill node b with the association relationship r is a dimensionless scalar with a value range of (0,1). The sum of the initial edge weights of all outgoing edges under the same starting node and the same association relationship is 1, which is used to characterize the association weight between the two skill nodes in the initial state without learner behavior data.

[0046] A pre-defined brushstroke skill evaluation model was constructed to output the skill attribution probability and performance score corresponding to a single brushstroke. The model employs a temporal classification and regression architecture using CNN+BiLSTM+fully connected layers. The model input is a dimensionless observation matrix fragment corresponding to a single brushstroke interval, with the input dimension being brushstroke length × feature dimension. The model output includes two branches: a classification branch outputs the attribution probability of each skill node corresponding to the brushstroke, and a regression branch outputs the performance score of each skill node corresponding to the brushstroke. The model training dataset contains over 100,000 annotated art brushstroke samples, with annotations including the skill node label and skill performance score corresponding to the brushstroke. The annotations were completed by teachers with over 5 years of art teaching experience. The model training uses a multi-task loss function: the classification branch uses the cross-entropy loss function, and the regression branch uses the mean squared error loss function. The total loss is the weighted sum of the losses from the two branches, with weights of 0.6 and 0.4, respectively. The optimizer used in model training is AdamW, with a learning rate of 1e-4, a batch size of 32, and 50 training epochs. An early stopping mechanism is employed to avoid overfitting. During the model inference phase, zero-padding or truncation is performed on the input brushstroke observation matrix fragments to unify them into a fixed length. The attribution probability of the inference output is normalized by softmax and takes a value range of [0,1]. The sum of the attribution probabilities of all skill nodes corresponding to the same brushstroke is 1. The performance score is mapped by sigmoid and takes a value range of [0,1]. The higher the value, the better the learner's mastery of the corresponding skill in that brushstroke.

[0047] The effective confidence score obtained by subtracting the evidence attenuation factor is multiplied by the corresponding skill attribution probability and performance score output by the preset evaluation model for the current stroke segment, and then weighted and accumulated according to the skill attribution probability to obtain the cumulative observation feature value of a single skill. The calculation formula is as follows:

[0048] Where n is the iteration index of the graph, u is the unique identifier of the learner, and k is the unique identifier of the skill node. Let s be the set of all pen stroke fragments for learner u in the current acquisition session, and let s be the pen stroke identifier within the set. Let be the skill attribution probability of the skill node k corresponding to the brush stroke s. Let be the effective confidence level corresponding to stroke s, and be a dimensionless scalar with a value range of (0.5, 1]. The performance score for the skill node k corresponding to brush stroke s is given. Let be the cumulative observed feature value of learner u corresponding to skill node k in the nth iteration. It is a dimensionless scalar used to quantify the learner's overall performance on the corresponding skill within the current session. When less than 1e-6, Use 0 to avoid division by zero errors.

[0049] The skill mastery scores from learners' historical records are extracted, subjected to a log-odds transformation, and then accumulated by summing the observed feature values ​​and subtracting the system-preset group average baseline value. This is followed by a forward logistic mapping to generate the updated skill mastery score. Skill mastery quantifies a learner's proficiency in a corresponding skill node, with a value ranging from (0,1), where higher values ​​indicate better mastery. The log-odds transformation is converted to the inverse function of the logistic function, transforming the mastery score in the (0,1) interval into a real-number value for linear summation. The logistic mapping then transforms the real-number result back into a mastery score value in the (0,1) interval. The updated skill mastery score calculation formula is as follows:

[0050] in, This represents the historical skill mastery degree of learner u corresponding to skill node k in the nth iteration. The smoothing minimum constant, used to prevent mathematical boundary overflow, is set to 1e-6. Let be the logarithmic probability transformation function, defined as , The system's pre-defined average baseline value for skill node k in the nth iteration is the group average, while is the arithmetic mean of the cumulative observed feature values ​​of all learners for that skill, updated monthly. For the positive logical stith mapping function, it is defined as follows: , Let be the skill mastery level updated in the (n+1)th iteration. It is a dimensionless scalar with a value range of (0, 1). For cases where the value exceeds the range [-10, 10] after logarithmic probability transformation, numerical clamping is performed to prevent saturation of the logistic function.

[0051] Based on the residuals of effective confidence level, skill attribution probability, performance score, and historical mastery of the target skill node, the multidimensional weighted aggregation result is calculated as the edge weight update increment. The calculation formula is as follows:

[0052] Where 'a' is the starting skill node, 'b' is the target skill node, and 'r' is the relationship type. Let be the probability of belonging to the starting skill node a corresponding to the brush stroke s. Let s be the probability of belonging to the target skill node b corresponding to the brush stroke s. To represent the residual term between the score and the historical mastery of the target skill node, it is used to quantify the deviation between the learner's actual performance and historical mastery of the target skill. To sum all the stroke fragments from all learners, In the nth iteration, the update increment of the edge weight from the starting node a to the target node b under the association r is a dimensionless scalar. When the residual term is positive, the update increment is positive, and the corresponding edge weight will increase; conversely, the edge weight will decrease. When the sum of the denominators is less than 1e-6... Use 0 to avoid division by zero errors.

[0053] Multiply the initial edge weight by the natural exponent of the edge weight update increment, then sum and normalize again within the outgoing edge set of the starting skill node to generate the updated edge weight. The calculation formula is as follows:

[0054] in, Let be the edge weight from the starting node a to the target node b under the association r in the nth iteration. The updated edge weight in the (n+1)th iteration is a dimensionless scalar with a value range of (0,1). The sum of the updated edge weights of all outgoing edges under the same starting node and the same association is 1. This realizes the dynamic iteration of the knowledge graph edge weights based on the learner's actual learning behavior, so that the association weights of the graph match the learner's learning patterns.

[0055] The set of target skill nodes, along with the set of prerequisite nodes obtained from the prior knowledge structure analysis and the set of cross-domain bridging nodes, are merged to form a unified candidate skill set. The target skill node is the final art skill node that the learner pre-determines and expects to master. The set of prerequisite nodes obtained from the prior knowledge structure analysis is the set of all prerequisite skill nodes obtained by traversing backwards along the prerequisite relationships from the target skill node, including direct and indirect prerequisite nodes. The set of cross-domain bridging nodes is the set of the top 10 skill nodes with the highest relevance to the target skill node within a preset cross-domain, ranked by cross-domain semantic relevance. The formula for calculating the candidate skill set is:

[0056] in, The target skill nodes set for learner u This refers to the set of prerequisite nodes corresponding to the target skill node. The set of cross-domain bridging nodes for the target skill node within the preset cross-domain set D. The unified candidate skill set generated after merging contains all relevant skill nodes required to learn the target skill.

[0057] The learner's user domain feature vector is calculated to represent their learning preferences and basic skill levels across various learning domains. Each dimension of the user domain feature vector corresponds to a predefined cross-domain, with the dimension value being the weighted average of the learner's skill mastery across all learned skill nodes within that domain, and the weight representing the proportion of learning time spent on the corresponding skill node. The user domain feature vector is then L2 normalized to a unit vector, calculated using the following formula:

[0058] Where d is the unique identifier of the preset intersection domain. Let d be the set of all learned skill nodes of learner u in domain d. The cumulative learning time of learner u at skill node k. Let be the user domain feature vector components of learner u in domain d. All domain components are combined to form the complete user domain feature vector, which is then L2 normalized to a unit vector with a magnitude of 1. For new users without historical learning data, the average of all dimensions of the user domain feature vector is taken to initialize the cold start scenario.

[0059] The cosine similarity between the learner's user domain feature vector and the embedding vectors of each candidate skill node is calculated and then normalized by translation as the single-domain graph matching degree. The embedding vectors of candidate skill nodes are generated using the TransR knowledge graph embedding algorithm. The algorithm input is triplet data from a cross-domain knowledge graph. Uniform negative sampling is used, and the pairwise ranking loss function is employed. The training epochs are set to 100, and the learning rate is 1e-3. Each skill node corresponds to a unique embedding vector within each preset cross-domain, and these embedding vectors are L2 normalized to become unit vectors. The formula for calculating the single-domain graph matching degree is:

[0060] Where k is the candidate skill node identifier, and d is the unique identifier of the learning domain. Let be the user domain feature vector of learner u in domain d. Let be the embedding vector of candidate skill node k in domain d. Let be the cosine similarity between two vectors, with values ​​ranging from [-1, 1]. After translation and normalization, is the single-domain graph matching degree, a dimensionless scalar with a value range of [0,1]. The larger the value, the higher the degree of matching between the learner and the candidate skill node in the corresponding domain.

[0061] The average single-domain graph matching degree of all skill nodes in the candidate skill set within the preset cross-domain is calculated, and then normalized by the natural index to generate cross-domain guiding weights. The calculation formula is as follows:

[0062] in, For learner u, the set of candidate skills Let D be the number of nodes in the candidate skill set, and D be the preset cross-domain set. Let be the arithmetic mean of the single-domain graph matching degree of learner u for all candidate skill nodes in domain d. Let be the cross-domain guidance weight for learner u in domain d. It is a dimensionless scalar with a value range of (0,1). The sum of the cross-domain guidance weights of all domains is 1. It is used to quantify the guidance weight of different domains in candidate skill recommendation. The higher the matching degree of a domain, the higher its guidance weight.

[0063] Extract the update weights of the prerequisite nodes associated with the current candidate skill, multiply them by the skill mastery of the corresponding prerequisite node, sum them, and add one to obtain the prerequisite support gain coefficient. The calculation formula is as follows:

[0064] in, Let be the set of all direct prerequisite nodes corresponding to candidate skill node k, where 'a' is the identifier of the prerequisite node in the set. Let the update weight of the prior node 'a' pointing to the candidate skill node 'k' under the prior relationship be defined. This represents the learner u's skill mastery of the prerequisite node a. Let be the prerequisite support gain coefficient corresponding to candidate skill node k. It is a dimensionless scalar with a value range of [1, +∞). The higher the mastery of the prerequisite node and the higher the prerequisite association weight, the larger the prerequisite support gain coefficient. This indicates that the learner has a more solid prerequisite foundation for learning the candidate skill, and the higher the learning benefit. The addition of 1 in the formula is to prevent the prerequisite support gain coefficient from being 0 when the prerequisite node set is empty, ensuring that the basic gain is 1.

[0065] The sum of the products of the single-domain graph matching degree and the corresponding cross-domain guidance weight in each domain is multiplied by one, minus the skill improvement potential obtained from the current candidate skill mastery, and then multiplied by the prior support gain coefficient to obtain the comprehensive utility of the candidate skill. The calculation formula is as follows:

[0066] in, Let $k$ be the skill improvement space corresponding to candidate skill node $k$. $k$ is a dimensionless scalar with a value range of (0,1). The larger the value, the greater the potential improvement space for the learner in that skill. Let be the cross-domain weighted matching degree corresponding to candidate skill node k, which is a dimensionless scalar with a value range of [0,1]. Let $k$ be the overall utility of learner $u$ corresponding to candidate skill node $k$. $k$ is a non-negative dimensionless scalar. The larger the value, the higher the overall benefit of learning the skill and the higher the priority of recommendation.

[0067] Calculate the cumulative sum of the skill improvement space of each node within the candidate skill set, round up to determine the number of dynamic search nodes for the particle swarm optimization algorithm, and determine the optimization iteration round based on the total number of elements in the set. The calculation formula is as follows:

[0068] in, This represents the number of dynamic search nodes in the particle swarm optimization algorithm, i.e., the maximum number of skill nodes contained in a single learning path. For floor operations, The particle swarm size in the particle swarm optimization algorithm is the number of candidate paths for parallel optimization, which is equal to the total number of elements in the candidate skill set. The maximum number of iterations for the particle swarm optimization algorithm is equal to the product of the total number of elements in the candidate skill set and the preset number of intersection domains, ensuring that the algorithm has enough iterations to achieve convergence.

[0069] Encoding and decoding rules for discrete skill paths are defined to achieve a bidirectional mapping between skill node sequences and particle position vectors. Sequential encoding is used, where the particle position vectors are integer sequences with a sequence length equal to the number of dynamically searched nodes. Each element in the sequence is a unique index of a skill node in the candidate skill set, with the index value ranging from 0 to 1. Duplicate index values ​​are not allowed in the sequence. The decoding method involves mapping the integer sequence of particle position vectors sequentially to the corresponding skill node sequence, which is a single candidate learning path. For elements in the sequence that are outside the index range, they are replaced with random valid indices from the candidate skill set; for duplicate elements in the sequence, they are replaced with valid indices that have not appeared, ensuring that the decoded path is a valid skill node sequence.

[0070] Particle initialization for the particle swarm optimization algorithm embeds hard constraints based on prerequisite rules. Each particle's initial position vector is generated using a topological sort based on prerequisite rules, ensuring that the positions of all prerequisite nodes in the initial path are earlier than their corresponding target skill nodes, thus avoiding initial paths that violate prerequisite logic. The particle's initial velocity vector is initialized as an all-zero vector, with the same dimension as the position vector, and each element's value range is... , Set as To avoid excessive speed causing search divergence.

[0071] The average value of the evidence decay factor for skill-related brushstrokes in the currently optimized single candidate path is calculated, and the inertia weight of the particle swarm algorithm is generated through an inverse proportional smoothing mapping. The calculation formula is as follows:

[0072] Where i is the unique identifier of a particle in the particle swarm. This represents a single candidate path corresponding to the i-th particle. This represents the number of skill nodes included in the candidate path. This represents the average evidence decay factor for all brushstrokes associated with skill node k in the candidate path. Let be the inertial weight corresponding to the i-th particle. is a dimensionless scalar with a value range of (0.5, 1]. The larger the average value of the evidence decay factor, the smaller the inertial weight, the lower the particle's dependence on historical paths during the optimization process, and the stronger its global exploration capability. Conversely, the smaller the average value of the evidence decay factor, the stronger its local development capability.

[0073] Based on the prerequisite relationships of a single candidate path, calculate the order penalty for path arrangement violations of prerequisite logic. For all skill node pairs with direct prerequisite relationships in the path, only violations of logic such as a prerequisite node appearing after the target node are penalized. The calculation formula is as follows:

[0074] Where P is a single candidate path sequence, and a and b are skill node pairs in the path that have a direct prerequisite relationship, where a is the direct prerequisite node of b. This is the index of the skill node's position in path P. The smaller the index value, the earlier the skill node appears in the path. This is a ReLU activation function that outputs x when x > 0 and 0 otherwise. It is used to penalize only logical violations where the preceding node appears after the target node. The constant for the smoothing minimum value is 1e-6. The minimum position index difference is set to 1 to ensure that the dimensions of the denominator are completely consistent with those of the numerator. The term is a pre-order penalty term, which is a dimensionless scalar with a value range of [0,1]. The larger the value, the higher the degree to which the path violates the pre-order logic, and the greater the penalty.

[0075] Calculate the normalized resource cost term for a single candidate path. The resource cost term is a weighted sum of the time cost, computing power cost, and teaching aid cost required to learn the corresponding skill. All cost terms are pre-normalized to the [0,1] interval, and the weighted sum is also normalized to the [0,1] interval, denoted as . , is a dimensionless scalar with a value range of [0,1]. A larger value indicates higher resource consumption for learning the skill. The formula for calculating the average resource cost of a single path is:

[0076] in, Let P be the average resource cost of a single candidate path P. It is a dimensionless scalar with a value range of [0,1].

[0077] Based on the cumulative comprehensive utility value of the candidate skills included in a single candidate path, after deducting the order penalty for path arrangement violating pre-requisite logic and the resource cost of mapping prediction, the comprehensive fitness of a single candidate path is obtained, calculated using the following formula:

[0078] in, This is the sum of the combined utility of all skill nodes in path P. Let be the normalized total utility of the path, and let be a dimensionless scalar with values ​​ranging from (0,1). This is a dimensionless prior order penalty term, with values ​​ranging from [0,1]. The average resource cost is a dimensionless term with a value range of [0,1]. All three terms have the same dimension, and addition and subtraction operations are legal and valid. F(P) is the overall fitness of a single candidate path P, which is a dimensionless scalar. The larger the value, the higher the overall quality of the path and the more it meets the requirements of the optimal learning path.

[0079] Within each optimization iteration, inertial weights are used to adjust the optimal approach step size between the individual and the global scale, performing dimensionally unified particle velocity and position updates. In the velocity update formula, the dimensions of all terms are completely unified to position index units / iteration step, and the position update formula introduces a unit iteration step size to ensure dimension matching. The calculation formula is as follows:

[0080]

[0081] Where g is the algebraic index of the particle swarm optimization algorithm. Let be the optimization velocity vector of the i-th particle in the g-th generation, with dimensions in position index units / iteration step. This is the optimization velocity vector updated in the (g+1)th generation. Let be the inertial weight corresponding to particle i, which is a dimensionless scalar. , The learning constant is a pre-set value of 2, and is a dimensionless scalar. , It is a random vector with values ​​in the range [0,1], and is a dimensionless scalar. This is the element-wise multiplication operation for vectors. Let be the optimization position vector of the i-th particle in the g-th generation, with the dimension in position index units, corresponding to the skill node arrangement sequence of a single candidate path. Let be the optimal position vector of the i-th particle corresponding to the highest fitness achieved in the iteration history, with the dimension being position index units. This represents the globally optimal position vector corresponding to the highest fitness achieved by the entire particle swarm throughout the iteration history, with the dimension being position index units. The unit iteration step size, with a value of 1, has the dimension of iteration step. This represents the particle position vector updated in generation g+1. After the velocity update, the velocity vector is clamped to ensure that the value of each element is within the specified range. Within the specified range; after the location update is complete, perform a validity check, correct duplicate and out-of-bounds indexes, and ensure that the decoded path conforms to the hard constraints of the pre-corrected rules.

[0082] Perform iterative convergence checks and output the convergent path sequence with the highest overall fitness as the optimal learning path. Convergence conditions include: the number of iterations reaches the preset maximum number of iteration rounds. The global optimal fitness value shows no improvement after 20 consecutive iterations; the standard deviation of the particle swarm fitness is less than 1e-6. The algorithm terminates iteration when either of these conditions is met, and the optimal learning path output formula is:

[0083] in, Let be the optimal learning path for learner u, and let be the path sequence with the highest overall fitness in the entire particle swarm after iterative convergence, satisfying the prior logic constraints and maximizing the learning utility.

[0084] Extract the comprehensive utility ratio of candidate skills corresponding to each skill node in the optimal learning path, determine the time proportion, and the calculation formula is as follows:

[0085] in, Let be the time proportion corresponding to skill node k in the optimal learning path. It is a dimensionless scalar with a value range of (0,1). The sum of the time proportions of all skill nodes in the optimal learning path is 1. The higher the overall utility of a skill node, the higher its corresponding time proportion and the longer the learning time allocated to it.

[0086] The system receives the total available time configuration parameter, multiplies it by the time ratio, and converts it into the absolute learning time for the corresponding skill node. The calculation formula is as follows:

[0087] in, Configure parameters for the total available time received by the system, including physical time units, representing the total time the learner can use for this learning session. The absolute learning time corresponding to skill node k has the same physical time unit as the total available time, and is the actual learning time allocated to this skill node.

[0088] Multiply the time ratio by the skill improvement potential, and then multiply by the average evidence decay factor associated with the path, to calculate the dimensionless feedback reinforcement coefficient. The calculation formula is as follows:

[0089] in, Let be the feedback reinforcement coefficient corresponding to skill node k. It is a non-negative dimensionless scalar. The larger the value, the higher the degree of feedback reinforcement required for the skill node. Skill nodes with higher time ratios, greater skill improvement potential, and higher average evidence decay factors have higher feedback reinforcement coefficients.

[0090] Interactive training tasks are distributed to the learning terminal based on absolute learning time, and key review and correction resources are allocated based on a descending sequence of feedback reinforcement coefficients. Interactive training tasks are art training content matched to corresponding skill nodes, including but not limited to brushstroke exercises, copying exercises, and creative exercises. The duration of each task is consistent with the absolute learning time of the corresponding skill node, and the task arrangement order is completely consistent with the skill node order of the optimal learning path. Key review and correction resources include teacher-led review time, AI error correction analysis computing power, and error reproduction training resources, allocated in descending order of feedback reinforcement coefficient. Skill nodes with higher feedback reinforcement coefficients receive more resources and have higher priority for review and correction.

[0091] After the training task is completed, the updated skill mastery and edge weights are written back to the underlying cross-domain knowledge graph in a closed loop. Training task completion refers to the learner completing the interactive training tasks corresponding to all skill nodes in the optimal learning path. The system collects all art behavior sequences and running state sequences during this training process, completes a new round of skill mastery and edge weight update calculations, and writes the updated skill mastery and edge weights into the underlying cross-domain knowledge graph. This enables continuous iterative optimization of the knowledge graph, providing an updated graph foundation for the next learning path planning. The trigger condition for iterative updates is the completion of a single training task, and the iteration termination condition is that the change in edge weights in the knowledge graph for five consecutive rounds is less than 1e-3. At this point, the graph is considered converged, and iterative updates stop.

[0092] For cold start scenarios, the system performs the following initialization processes: For new users with no historical learning data, the initial mastery of all skill nodes is set to 0.5, and the average value of all dimensions of the user domain feature vector is taken; For new skill nodes corresponding to newly added teaching texts, the initial edge weights are generated by calculating the cross-domain semantic relevance and the default co-occurrence feature, with the default co-occurrence feature value set to 0.5.

[0093] In response to abnormal scenarios, the system performs the following fault tolerance measures: When data is missing in the art behavior sequence or running status sequence, linear interpolation is used to fill in the missing data, and segments with a missing duration of more than 1 second are directly discarded; when division by zero or numerical overflow occurs during algorithm calculation, a preset default value is used as a fallback to ensure that the calculation process is not interrupted; in strong disturbance scenarios, when the average evidence attenuation factor is greater than or equal to 0.3, the system automatically extends the collection session duration to increase the amount of effective data collected and ensure the accuracy of skill assessment.

[0094] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A cross-domain collaborative recommendation and knowledge graph iteration art learning path optimization system, applied to a learning station including a pressure-sensitive digital easel, a posture eye-tracking collector, a radiation-resistant light module, and a processing server, characterized in that... Configured for execution: Within the set acquisition session, the sequence of artistic behaviors generated by the digital easel and the acquisition device, the sequence of running status generated by the light module, and the teaching text containing skill nodes and prerequisite relationships are acquired and mapped into a dimensionless observation matrix. Based on the observation matrix, the link change rate and pen stroke motion complexity are extracted, the disturbance uncertainty characterizing the resistance to radiation disturbance is calculated, and it is converted into an evidence attenuation factor. Based on cross-domain semantic relevance and co-occurrence characteristics, a cross-domain knowledge graph containing the skill nodes is constructed from the teaching text, and the initial edge weights are calculated. Using the evidence decay factor and the skill attribution probability output by the preset model, the learner's skill mastery and the initial edge weights are iteratively updated to obtain the updated edge weights; A candidate skill set is constructed by the target skill node and the prior relationship, and the comprehensive utility of the candidate skills is calculated by using the matching degree of the set in each field and the skill mastery degree. The comprehensive utility is used as the base benefit, and the optimal learning path is obtained by adjusting the inertia weight of the particle swarm algorithm in combination with the evidence decay factor. The cross-domain knowledge graph is updated by allocating time proportions according to the optimal learning path and generating feedback reinforcement coefficients in conjunction with evidence decay factors.

2. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration as described in claim 1, characterized in that, Acquire the art behavior sequence generated by the digital easel and collector, the runtime state sequence generated by the light module, and the teaching text containing skill nodes and prerequisite relationships, and map them into a dimensionless observation matrix, including: Extract the time-stamped coordinates, pressure, tilt angle, and line-of-sight trajectory data from the art behavior sequence, as well as the voltage, optical power, and bit error count data from the running state sequence; Using the difference between the start and end times of the set acquisition session as a benchmark, the current sequence acquisition time is converted into dimensionless time; For each independent data channel in the art behavior sequence and the running state sequence, an empirical cumulative distribution function based on the current collection session data is constructed; The continuous raw data from each independent data channel are substituted into the corresponding empirical cumulative distribution function for transformation to generate a dimensionless continuous observation sequence. The teaching text is processed by text embedding and normalized to generate a dimensionless discrete text feature vector. The dimensionless continuous observation sequence is concatenated with the dimensionless discrete text feature vector to generate the dimensionless observation matrix.

3. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration as described in claim 2, characterized in that, The process of extracting the link change rate and pen stroke motion complexity based on the observation matrix, calculating the disturbance uncertainty characterizing the resistance to radiation disturbance, and converting it into an evidence attenuation factor includes: For the operating state sequence of the corresponding optical module in the dimensionless continuous observation sequence, the first norm of the first derivative is obtained according to the dimensionless time to obtain the link change rate; Calculate the autocorrelation function of the link change rate, and obtain the optical link disturbance hysteresis length based on the ratio of the first moment integral to the zero moment integral of the absolute value of the autocorrelation function. The art behavior sequence is divided into single brushstroke intervals and the brushstroke center time is determined. The link change rate and the exponential decay kernel constructed based on the optical link disturbance lag length are integrated to obtain the time lag effect value. Within the single stroke interval, the sum of the second derivative norm of the dimensionless coordinates, the absolute value of the first derivative of the dimensionless pressure, and the first derivative norm of the dimensionless tilt angle is integrated and divided by the interval length to obtain the stroke motion complexity. The disturbance uncertainty is obtained by multiplying the pen stroke motion complexity and the time lag effect value, dividing by one, and adding the sum of the two values. The evidence attenuation factor is generated by nonlinearly mapping the disturbance uncertainty to a sum of its own value.

4. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration as described in claim 1, characterized in that, The process of constructing a cross-domain knowledge graph containing the skill nodes from the teaching text and calculating initial edge weights based on cross-domain semantic relevance and co-occurrence features includes: The graph structure association facts containing the starting skill node and the target skill node are extracted from the teaching text; Calculate the cosine similarity between the text feature vectors corresponding to the starting skill node and the target skill node, and use it as the cross-domain semantic correlation. In the parsed graph structure association facts, the natural logarithm of the joint probability of the co-occurrence of the starting and target skill nodes is calculated and divided by the product of their respective independent probabilities, and is used as the co-occurrence feature. The cross-domain semantic correlation degree and the co-occurrence feature are superimposed to form the comprehensive correlation degree; For all target skill nodes pointed to by the starting skill node, calculate the natural index value of the comprehensive correlation degree and perform probability normalization on the node correlation dimension to generate the initial edge weight.

5. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration as described in claim 1, characterized in that, The step of iteratively updating the learner's skill mastery and the updated edge weights using the evidence decay factor and the skill attribution probability output by the preset model, and the initial edge weights, includes: The effective confidence level obtained by subtracting the evidence attenuation factor is multiplied by the corresponding skill attribution probability and performance score output by the preset evaluation model for the current pen stroke segment, and then weighted and accumulated according to the skill attribution probability to obtain the cumulative observation feature value of a single skill. The skill mastery of learners is extracted from their historical records, subjected to log-odds transformation, superimposed with the cumulative observed feature values, and subtracted from the system-preset group average baseline value. The updated skill mastery is then generated through positive logistic mapping. Based on the residual terms of the effective confidence level, skill attribution probability, performance score and historical mastery of the target skill node, the multidimensional weighted aggregation result is calculated as the edge weight update increment. The initial edge weight is multiplied by the natural exponent of the edge weight update increment, and then summed and normalized again within the outgoing edge set of the starting skill node to generate the updated edge weight.

6. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration as described in claim 5, characterized in that, The process of constructing a candidate skill set based on the target skill node and the prior relationship, and calculating the comprehensive utility of the candidate skills using the matching degree of this set in various fields and the skill mastery degree, includes: The cosine similarity between the learner's user domain feature vector and the embedding vector of each candidate skill node is calculated and then normalized by translation as the single-domain graph matching degree. The average value of the single-domain graph matching degree of all skill nodes in the candidate skill set within the preset cross domain is calculated, and cross-domain guiding weights are generated by natural index normalization. Extract the updated weight of the prerequisite node associated with the current candidate skill, multiply it by the skill mastery of the corresponding prerequisite node, sum them up and add one to obtain the prerequisite support gain coefficient. The sum of the products of the single-domain graph matching degree and the corresponding cross-domain guidance weight in each domain is multiplied by one minus the skill improvement space obtained by the skill mastery degree of the current candidate skill, and then multiplied by the prior support gain coefficient to obtain the comprehensive effect of the candidate skill.

7. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration as described in claim 6, characterized in that, The step of using the comprehensive utility as the base return, combined with the evidence decay factor to adjust the inertia weights of the particle swarm optimization algorithm, to find the optimal learning path includes: The set target skill node is merged with the set of prerequisite nodes parsed along the prerequisite structure to form a unified set of candidate skills; Calculate the cumulative sum of the skill improvement space of each node in the candidate skill set, round up to determine the number of dynamic search nodes for the particle swarm algorithm, and determine the optimization iteration round based on the total number of elements in the set; The average value of the evidence decay factor of the skill-related brushstrokes contained in the currently optimized single candidate path is calculated, and the inertial weight of the particle swarm algorithm is generated by inverse proportional smoothing mapping. Based on the cumulative value of the comprehensive utility of the candidate skills contained in a single candidate path, the order penalty for violating the prior logic of the path arrangement and the resource cost of the mapping prediction are deducted to obtain the comprehensive fitness of a single candidate path. Within the optimization iteration rounds, the inertial weights are used to adjust the optimal approach step size between the individual and the global model, and the path sequence that converges and has the highest overall fitness is output as the optimal learning path.

8. The art learning path optimization system based on cross-domain collaborative recommendation and knowledge graph iteration according to claim 7, characterized in that, The step of allocating time proportions according to the optimal learning path and generating feedback reinforcement coefficients in conjunction with evidence decay factors to update the cross-domain knowledge graph includes: Extract the comprehensive utility ratio of the candidate skills corresponding to each skill node in the optimal learning path, and determine the time ratio; Obtain the configuration parameter of the total available time received by the system, multiply it by the time ratio, and convert it into the absolute learning time of the corresponding skill node; Multiply the time ratio by the skill improvement space, and then multiply by the average value of the evidence decay factor associated with the path to calculate the dimensionless feedback reinforcement coefficient. Interactive training tasks are arranged on the learning terminal based on the absolute learning time, and key review and error correction resources are allocated based on the descending sequence of the feedback reinforcement coefficients. After the training task is completed, the updated skill mastery and the updated edge weights are written back to the underlying cross-domain knowledge graph in a closed loop.

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