CN113361685B - Knowledge tracking method and system based on learner knowledge state evolution expression - Google Patents

Knowledge tracking method and system based on learner knowledge state evolution expression Download PDF

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CN113361685B
CN113361685B CN202110572170.7A CN202110572170A CN113361685B CN 113361685 B CN113361685 B CN 113361685B CN 202110572170 A CN202110572170 A CN 202110572170A CN 113361685 B CN113361685 B CN 113361685B
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孙建文
刘三女牙
蒋路路
张凯
邹睿
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Central China Normal University
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Abstract

The invention provides a knowledge tracking method and a knowledge tracking system based on learner knowledge state evolution expression, wherein the method comprises the following steps: acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples; generating knowledge state representation of learners and building a knowledge tracking model; generating a predicted value of the future answer expression of the learner, wherein in the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner; generating an evolution item; the evolution item is incorporated into a loss function and optimized, the training goal of the knowledge tracking model is to generate accurate predicted values of future answer performances of the learner and accurately model the gradual change of the knowledge state, and the goal is characterized by defining the loss function.

Description

Knowledge tracking method and system based on learner knowledge state evolution expression
Technical Field
The invention belongs to the field of knowledge tracking, and particularly relates to a knowledge tracking method and system based on learner knowledge state evolution expression.
Background
Knowledge tracking is an important modeling method for learners, and is used for modeling a historical answer sequence of the learner, tracking the knowledge state of the learner and further predicting the future answer performance of the learner. Specifically, the knowledge state of the learner refers to the mastery degree of the learner on the knowledge point, and the mastery degree changes along with the answering situation. Generally speaking, in the process of adjacent answers, the knowledge state should be gradually transited and gradually evolves. How to restore the process of the gradual change of the knowledge state is a key problem of the knowledge tracking task.
The existing knowledge tracking model mainly comprises two types. The first type is a probabilistic knowledge tracking model, represented by classical Bayesian Knowledge Tracking (BKT), which uses state parameters with specific semantics to represent the knowledge state of a learner, and calculates the change of the knowledge state through the state parameters. The model has the advantages that the state parameter semantics are clear, and the interpretability is higher; the disadvantage is that there is no gradual change in the state of knowledge modeled. The second type is a Deep learning Knowledge tracking model, which is represented by classical Deep Knowledge Tracking (DKT), and uses a distributed vector or matrix generated by a Deep neural network to represent the Knowledge state of a learner, and the change of the Knowledge state is modeled by the change of the distributed vector or matrix at adjacent time steps. The model has the advantages of high prediction performance; the disadvantage is again that there is no gradual change in the state of knowledge modeled. The two models have good effects in practical application and are solid foundations of follow-up research. However, the common defects are that the process of gradual evolution of the knowledge state of the learner is difficult to model, and a real learning scene cannot be restored.
Disclosure of Invention
Aiming at the defects or the improvement requirements in the prior art, the invention provides a knowledge tracking method and a knowledge tracking system based on learner knowledge state evolution representation, which generate a learner knowledge state representation-state matrix by counting learner answer sequence data, and model the whole change of the learner knowledge state by calculating the difference value of the state matrix at adjacent time steps; further introducing an evolution weight for quantizing the influence magnitude of each state column in the state matrix in the overall change; further generating an evolution item for representing the accurate change of the knowledge state in the adjacent question answering process; and the evolution item is further incorporated into the loss function, the goal of restoring the gentle change process of the knowledge state is realized in the process of optimizing the loss function, and a real learning scene is modeled. The method can complete knowledge tracking tasks, defines the state matrix of the knowledge state of the learner represented by the state matrix, and can further predict the future answer performance of the learner through the state matrix.
In order to achieve the above object, the present invention provides a knowledge tracking method based on learner knowledge state evolution representation, which comprises the following steps:
s1, acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
s2, generating knowledge state representation of the learner, and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of the long-term and short-term memory neural network and the input of the full-connection neural network are cognitive data sets, and the output of the long-term and short-term memory neural network and the full-connection neural network is a state matrix;
s3, generating a predicted value of the future answer expression of the learner, wherein in the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner;
s4, generating an evolution item, and combining the evolution weight and the overall change of the knowledge state into the evolution item so as to represent the accurate change of the knowledge state of the learner in the adjacent answers;
and S5, incorporating the evolution item into a loss function and optimizing, wherein the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
As a further improvement of the present invention, the cognitive data set described in step S1 includes a plurality of time series, and a time series includes a plurality of time step data, and the plurality of time step data represent the answer condition of a learner at a plurality of knowledge points; a time step data is the answer of a learner at a knowledge point.
As a further improvement of the present invention, the input of the long-short term memory neural network described in step S2 is the acquired cognitive data set, and the output is the low-level feature representation of the knowledge state-distributed vector; the input of the fully-connected neural network is a distributed vector, the output is a high-level feature representation-state matrix of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner; the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge state of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
Figure BDA0003082954360000021
wherein, ks t The state matrix generated at the t-th time step, i belongs to {1, 2, … … n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state line represents the knowledge state of the learner on the knowledge point i, and the i-th state line comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively: p is a radical of i (L t ) The element (0, 1) is an initial learning parameter and represents the probability value of the knowledge point i learned before the learner answers; p is a radical of i (T t ) E (0, 1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical of formula i (G t ) E (0, 1) is a guess parameter and represents a guess probability value when the learner does not learn the knowledge point i; p is a radical of i (S t ) E (0, 1) is a fault parameter and represents the probability value of the fault answering of the learner at the learned knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l is a radical of an alcohol t Initial learning parameters representing all n knowledge points; t is t A learning ability parameter representing n knowledge points; g t Guess parameters representing n knowledge points; s t Fault parameters representing n knowledge points.
As a further improvement of the present invention, in step S3, the state matrix is input into a Bayesian knowledge tracking algorithm to calculate a predicted value of the learner ' S future question answering performance, and the probability vector p (C) of the learner ' S correct prediction of the learner ' S answer at the current time step t is calculated for the t +1 th future time step t+1 ) The expression of (c) is:
p(C t+1 )＝L t *(1-S t )+(1-L t )*G t
wherein the probability vector p (C) t+1 ) The ith dimension in (b) is the probability value of the learner to correctly answer the knowledge point i at the t +1 th time step in the future, and the probability vector p (C) t+1 ) Performing dot product operation with the knowledge point vector answered at the t +1 th time step to calculate the probability value of correct answer at the next time step of the learner, and predicting that the learner will correctly answer when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
As a further improvement of the present invention, in step S4, an evolutionary term is calculated to represent the exact change of the knowledge state of the learner in the adjacent answer, specifically: generating evolution weights by using the established knowledge tracking model, quantizing the action of each state column in the state matrix in the overall change, combining the evolution weights and the overall change of the knowledge state into evolution items, and generating the evolution item e at the current time step t t The expression of (c) is:
Figure BDA0003082954360000031
wherein w t ＝(w 1 ，w 2 ，w 3 ，w 4 )∈(0，1) 4 Is the evolution weight, Δ ks t The overall change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight.
As a further improvement of the present invention, the step of defining the loss function in step S5 includes: calculating cross entropy between a true value and a predicted value of future answer expression, and incorporating an evolution item to obtain a loss function of the knowledge tracking model, and finding a global minimum value or a local minimum value by optimizing the loss function to realize a training target of the knowledge tracking model, and further minimizing the loss function by using a random gradient descent method commonly used in the field to ensure that the knowledge tracking model reaches an optimal state, wherein the loss function of a time sequence in the knowledge tracking model is as follows:
Figure BDA0003082954360000032
wherein f (-) is a cross entropy function,
Figure BDA0003082954360000033
a predicted value of the learner's future answer performance t+1 Is the actual value of the learner's future answer performance, e t Is an evolution term representing the accurate change of the knowledge state, E belongs to N * Is the total number of questions answered by the learner sequence, N * Is a natural number set.
The invention also provides a knowledge tracking system based on learner knowledge state evolution expression, which comprises:
the statistical cognitive data module is used for acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
the knowledge state representation module generates knowledge state representation of learners and builds a knowledge tracking model on the basis of a long-short term memory neural network, a full-connection neural network and a Bayesian knowledge tracking algorithm;
the prediction module is used for generating a predicted value of the future answer expression of the learner and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output of the Bayesian knowledge tracking algorithm is the predicted value of the future answer expression of the learner;
the evolution module is used for generating evolution items and calculating the difference value of the state matrixes in the adjacent sequences so as to represent the integral change of the knowledge state of the learner in the adjacent answers;
and the optimization module is used for incorporating the evolution item into the loss function and optimizing the evolution item, the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
As a further improvement of the present invention, the cognitive data set in the statistical cognitive data module includes a plurality of time series, one time series includes a plurality of time step data, and the plurality of time step data represent the answering situation of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
As a further improvement of the invention, the input of the long-short term memory neural network in the knowledge state representation module is the acquired cognitive data set, and the output is the low-level feature representation-distributed vector of the knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is a high-level feature representation of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner.
As a further improvement of the present invention, in the evolution module, the difference value of the state matrix in the adjacent sequence is calculated to represent the overall change of the knowledge state of the learner in the adjacent answer, specifically: and generating evolution weights by using the established knowledge tracking model, quantifying the action of each state column in the state matrix in the overall change, and combining the evolution weights and the overall change of the knowledge state into an evolution item to express the accurate change of the knowledge state of the learner in the adjacent answers.
As a further improvement of the present invention, the step of defining the loss function in the optimization module comprises: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating into the evolution item to obtain the loss function of the knowledge tracking model, and optimizing the loss function to enable the loss function to find the global minimum or the local minimum so as to realize the training target of the knowledge tracking model, and further using a random gradient descent method commonly used in the field to minimize the loss function, so that the knowledge tracking model reaches the optimal state.
As a further improvement of the invention, the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
Figure BDA0003082954360000051
wherein ks is t The state matrix generated at the t-th time step, i belongs to {1, 2.. the., n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state row represents the knowledge state of the learner on the knowledge point i, and the knowledge state comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively as follows: p is a radical of i (L t ) E (0, 1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical of i (T t ) E (0, 1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical of formula i (G t ) The element (0, 1) is a guess parameter and represents a guess probability value when a learner does not learn the knowledge point i; p is a radical of i (S t ) E (0, 1) is a fault parameter and represents the probability value of the fault answering of the learner at the learned knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l is a radical of an alcohol t Initial learning parameters representing all n knowledge points; t is t A learning ability parameter representing n knowledge points; g t Guess parameters representing n knowledge points; s. the t Fault parameters representing n knowledge points.
As a further improvement of the invention, the probability vector p (c) of correct prediction of answer of the learner at the current time step t and the t +1 th future time step t+1 ) The expression of (a) is:
p(C t+1 )＝L t *(1-S t )+(1-L t )*G t
wherein the probability vector p (C) t+1 ) The ith dimension in (b) is the probability value of the learner to correctly answer the knowledge point i at the t +1 th time step in the future, and the probability vector p (C) t+1 ) Will perform dot product operation with the knowledge point vector of the t +1 time step to calculate the probability value of the learner's correct answer at the next time step, which is the probability valueIf the number is more than or equal to 0.95, the learner is predicted to answer correctly; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
As a further improvement of the invention, at the current time step t, the evolution term e t The expression of (a) is:
Figure BDA0003082954360000052
wherein, w t ＝(w 1 ，w 2 ，w 3 ，w 4 )∈(0，1) 4 Is the evolution weight, Δ ks t The overall change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight.
As a further improvement of the invention, in the knowledge tracking model, the loss function of a time series is as follows:
Figure BDA0003082954360000053
wherein f (-) is a cross entropy function,
Figure BDA0003082954360000061
for the learner's predicted value of future answer performance, a t+1 Is the actual value of the learner's future answer performance, e t Is an evolution term representing the accurate change of the knowledge state, E belongs to N * Is the total number of questions answered by the learner sequence, N * Is a natural number set.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein when the processor runs the computer program, the steps of the knowledge tracking method based on the learner knowledge state evolution representation are executed.
The present invention also provides a computer readable storage medium storing a computer program for causing a computer to perform the steps of the method for knowledge tracking based on an evolving representation of learner knowledge state as disclosed above.
Generally, compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a knowledge tracking method and a knowledge tracking system based on learner knowledge state evolution expression, wherein a state matrix generated by utilizing the memory characteristic of a long-short term memory network neural network when processing time sequence data inherits the characteristics hidden in a learner answer sequence, accords with the learning rule of the learner when answering questions, more accurately expresses the knowledge state of the learner in the answering process, and is more suitable for predicting the future answering performance of the learner.
The knowledge tracking method and the knowledge tracking system based on learner knowledge state evolution representation introduce the evolution item to specifically represent the accurate change of the knowledge state of a learner in the adjacent answering process, incorporate the evolution item into the loss function, reversely train the model to generate a more reasonable knowledge state of the learner, and finally achieve the aim of gradual change and gradual transition of the knowledge state of the learner. The method and the system solve the defects in the classical knowledge tracking model, restore the real learning process, are the key part for establishing the accurate knowledge tracking model, and can better assist the concrete teaching practice.
Drawings
FIG. 1 is a schematic diagram of a knowledge tracking method based on learner knowledge state evolution representation according to the present invention;
fig. 2 is a schematic structural diagram of an evolution item of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to fig. 1-2. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. The present invention will be described in further detail with reference to specific embodiments.
FIG. 1 is a schematic diagram of a knowledge tracking method based on learner knowledge state evolution representation according to the present invention. As shown in fig. 1, the method comprises the steps of:
s1, acquiring a statistical cognitive data set of a plurality of learners for a plurality of knowledge point samples. The cognitive data set comprises a plurality of time sequences, wherein each time sequence comprises a plurality of time step data, and the plurality of time step data represent the answering conditions of a learner on a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
For example: the cognitive data set comprises S time series, S belongs to N * Number of different learners in the data set, N * Is a natural number set; a time sequence comprises a plurality of time step data, which is the answering condition of a learner on a plurality of knowledge points; a time step data x t ＝(q t ，a t ) Is a learner S belongs to [1, S ]]At a knowledge point i e [1, n ]]The answer situation of (1), wherein q t Is a vector representation of the current knowledge point to answer, a t Is the current answer result, a t 0 denotes a response error, a t 1 means correct response. t is an element of [1, E ∈]，E∈N * Is the total number of answer questions, N, of the learner * Is a natural number set, and n is the number of different knowledge points in the cognitive data set.
And S2, generating knowledge state representation of the learner and building a knowledge tracking model. In the established knowledge tracking model, the input of the long-term and short-term memory neural network and the fully-connected neural network is a cognitive data set, and the output is a state matrix;
the input of the long-short term memory neural network is an acquired cognitive data set, and the output is a low-level feature representation-distributed vector of a knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is a high-level feature representation of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner.
At the t time step, the time step data x t Input into long-short term memory neural network, output is low-level feature representation of knowledge state of learner s-distributed vector h t ∈(0，1) N Where N is the number of hidden nodes. h is t The knowledge state of the learner s at the current time step t is shown, and the summary shows the knowledge state of the learner for n knowledge points, each of which has no specific meaning. Vector h to be distributed t Input to the whole neural network, and output is the state matrix ks, which is a high-level feature representation of the knowledge state of the learner s t ＝|L t ，T t ，G t ，S t L, the ith state row (p) therein i (L t )，p i (T t )，p i (G t )，p i (S t ))∈(0，1) 4 Are the four state parameters of knowledge point i, representing the knowledge state of learner s with respect to knowledge point i. Status column L t Representing initial learning parameters of the learner s for all n knowledge points; t is a unit of t The learning ability parameter represents the learning ability of the learner s to the n knowledge points; g t Representing guess parameters of the learner s for the n knowledge points; s. the t Error parameters of the learner s for n knowledge points are represented. At the t-th time step, ks t The knowledge state of the learner for each knowledge point is represented, and the expression is as follows:
Figure BDA0003082954360000071
and S3, generating a predicted value of the future answer expression of the learner. In the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is a predicted value of the future answer expression of the learner.
At the t-th time step, the state matrix ks t Inputting the result into a Bayesian knowledge tracking algorithm, and calculating a prediction probability vector p (C) of a learner s with correct answer at the t +1 th time step in the future by using a prediction probability calculation formula in the algorithm t+1 ) The calculation formula is as follows:
p(C t+1 )＝L t *(1-S t )+(1-L t )*G t
wherein the probability vector p (C) t+1 ) The ith dimension in (1) is the probability value of the knowledge point i that the learner s correctly answers at the t +1 th time step in the future.
Further, a probability vector p (C) t+1 ) Knowledge point vector q that will answer with the t +1 time step t+1 Performing dot product operation to calculate the probability value of correct answer at the next time step of learner s, and if the probability value is greater than or equal to 0.95, predicting the answer result
Figure BDA0003082954360000081
When the probability value is less than 0.95, the predicted answer result
Figure BDA0003082954360000082
For example, learner s answers knowledge point j, p (C) at time step t +1 t+1 ) And q is t+1 The result of performing the dot product operation will be p j (C t+1 ) The probability value of the knowledge point j correctly answered by the learner s at the t +1 th time step in the future. When p is j (C t+1 ) Predicting that the learner s will answer correctly when the learner s is more than or equal to 0.95; when p is j (C t+1 ) < 0.95, the learner s are predicted to respond correctly and incorrectly.
And S4, generating an evolution item, and combining the evolution weight and the integral change of the knowledge state into the evolution item so as to represent the accurate change of the knowledge state of the learner in the adjacent answers.
At the t-th time step, the overall change delta ks of the knowledge state between the t-th time step and the previous time step t-1 is calculated t The calculation formula is as follows:
Figure BDA0003082954360000083
then, the output evolution weight w of the full-connection neural network is utilized t ＝(w 1 ，w 2 ，w 3 ，w 4 )∈(0，1) 4 。w t And generating according to the characteristics of the learner data, wherein each dimension of weight represents the action of each state column in the whole knowledge state change process. Then, the evolution weight w t Global change from knowledge state Δ ks t Combining into evolution terms e t E (0, 1), and the calculation formula is as follows:
Figure BDA0003082954360000084
fig. 2 is a schematic diagram of an evolution term of an embodiment of the invention. The evolution item is used for representing the change of an accurate knowledge state in the process of answering questions adjacently, and each dimension weight represents the effect of each state column in the change of the overall knowledge state. The evolution item aims at modeling the accurate change of the knowledge state in the knowledge tracking model, and is specifically applied to the loss function of the knowledge tracking model to train the knowledge tracking model reversely, so that the knowledge state generated by the knowledge tracking model is more reasonable.
And S5, incorporating the evolution item into a loss function and optimizing, wherein the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
The model has two training targets, one is to generate accurate predicted value of learner's future answer performance, and the other is to accurately model the gentle change of knowledge state. Therefore, the loss function also comprises two parts, namely calculating the cross entropy between the real value and the predicted value of the future answer performance, and calculating the evolution item. The loss function is optimized using a commonly used stochastic gradient descent method such that it finds a global minimum or a local minimum, enabling two training objectives of the model. For the learner s, the total number of questions E belonging to N * The loss function is:
Figure BDA0003082954360000091
wherein f (-) is a cross entropy function,
Figure BDA0003082954360000092
predicted value of answer performance for learner s at t +1 th time step in future, a t+1 Is the true value of the learner s' answer performance at the t +1 th time step in the future, e t Is an evolution term representing the accurate change of the knowledge state, E belongs to N * Is the total number of answers of the learner sequence, N * Is a natural number set.
For all learners in the cognitive dataset, the loss function is:
Figure BDA0003082954360000093
wherein S is belonged to N * Number of different learners in the data set, N * Is a natural number set.
Table 1 shows the results of the knowledge tracking method of the present invention and the prior art method for predicting the future answer of the learner. As shown in table 1, experiments were performed on three cognitive datasets, ASSIST2009, ASSIST2015, Statics2011, respectively. The prior art method comprises a classic Bayesian knowledge tracking method and a depth knowledge tracking method, and the measurement index of the experimental result is Area Under Cut (AUC). As can be seen from the table, the prediction result of the technical scheme of the embodiment of the present invention is superior to that of the prior art.
Table 1 shows the results of the knowledge tracking method of the present invention and the prediction of learner's answer in the prior art method
Figure BDA0003082954360000094
In order to make the knowledge tracking method based on learner knowledge state evolution expression more clear, taking a learner as an example, the knowledge tracking method based on learner knowledge state evolution expression of the learner in a time sequence is introduced:
(1) the cognitive data set comprises a plurality of time sequences, and the answer sequence of each learner is a time sequence. If a learner answers 5 times in total (3 different knowledge points in total), the answer data is input once per time step, and the length of the time series is 5. In table 2, the practice data of the learner is shown, and the first line is the total number of the questions practiced by the learner, and 5 practice questions are made in total; the second line is the label of the knowledge point that the learner answered, such as the 1 st practice question that the first learner answered is about knowledge point 3, and the 2 nd practice question about knowledge point 1; the third line is the result of the learner's answer, 0 represents wrong answer, 1 represents correct answer, such as wrong answer when the first learner answers the 1 st question, wrong answer for the 2 nd question, etc.
TABLE 2 data Format
Figure BDA0003082954360000101
(2) At the 1 st time step, the input data is x 1 ＝(q 1 ，a 1 )＝(0，0，1，0) T Wherein q is 1 ＝(0，0，1) T Is a one-hot vector representation of the current knowledge point to answer, and represents the third knowledge point that the student answers. a is 1 And 0 is the current response result, and represents a response error.
(3) Long-short term memory neural network according to x in knowledge tracking model 1 Low-level feature representation of knowledge states-distributed vector h is generated 1 ∈(0.1，0.4，0.2，0.1) T Where it is assumed that the number of hidden nodes of the neural network is 4, and thus the vector dimension is 4.
(4) All neural network basis h in knowledge tracking model 1 The state matrix ks, an advanced feature representation of the knowledge state, is generated 1 ＝|L 1 ，T 1 ，G 1 ，S 1 L is as follows:
Figure BDA0003082954360000102
where the first line is the learner's knowledge state for knowledge point 1, the second line is the learner's knowledge state for knowledge point 2, and the third line is the learner's knowledge state for knowledge point 3. The first column is the learner's initial learning parameters for 3 knowledge points; the second column is the learner's learning ability parameters for 3 knowledge points; the third column is the learner's guess parameters for 3 knowledge points and the fourth column is the learner's miss parameters for 3 knowledge points.
(5) Bayes knowledge tracking algorithm in knowledge tracking model according to ks 1 And calculating the predicted value of the 2 nd answer performance of the learner.
p(C 2 )＝L 1 *(1-S 1 )+(1-L 1 )*G 1
＝(0.3，0.1，0.15)*(0.9，0.95，0.85) T +(0.7，0.9，0.85)*(0.1，0.05，0.15) T
＝0.735
Since 0.735 < 0.95, the learner is predicted to have the wrong answer for the second time.
(6) Fully connected neural network generation evolution weight w in knowledge tracking model 1 ＝(0.2，0.3，0.1，0.4) T Change it by Δ ks from the whole 1 ＝(||L 1 -L 0 ||，||T 1 -T 0 ||，||G 1 -G 0 ||，||S 1 -S 0 | |) combinations as evolution terms
Figure BDA0003082954360000111
Figure BDA0003082954360000112
(7) Incorporating evolutionary terms into a loss function
Figure BDA0003082954360000113
And training the knowledge tracking model reversely to be optimal. Where f (-) is a commonly used cross entropy loss function.
(8) Time step 2 … … (loop through steps 2-7 above).
The invention also provides a knowledge tracking system based on learner knowledge state evolution expression, which comprises:
the statistical cognition data module is used for acquiring statistical cognition data sets of a plurality of learners on a plurality of knowledge point samples;
the knowledge state representation module is used for generating knowledge state representation of a learner and building a knowledge tracking model on the basis of a long-short term memory neural network, a full-connection neural network and a Bayesian knowledge tracking algorithm;
the forecasting module is used for generating a forecasting value of the future answer expression of the learner and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the forecasting value of the future answer expression of the learner;
the evolution module is used for generating evolution items and calculating the difference value of the state matrixes in the adjacent sequences so as to represent the overall change of the knowledge state of the learner in the adjacent answers;
and the optimization module is used for incorporating the evolution item into the loss function and optimizing the evolution item, the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
As a further improvement of the present invention, the cognitive data set in the statistical cognitive data module includes a plurality of time series, one time series includes a plurality of time step data, and the plurality of time step data represent the answering situation of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
As a further improvement of the invention, the input of the long-short term memory neural network in the knowledge state representation module is the acquired cognitive data set, and the output is the low-level feature representation-distributed vector of the knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is a high-level feature representation of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner.
As a further improvement of the present invention, in the evolution module, the difference value of the state matrix in the adjacent sequence is calculated to represent the overall change of the knowledge state of the learner in the adjacent answer, specifically: and generating evolution weights by using the established knowledge tracking model, quantifying the action of each state column in the state matrix in the overall change, and combining the evolution weights and the overall change of the knowledge state into an evolution item to express the accurate change of the knowledge state of the learner in the adjacent answers.
As a further improvement of the present invention, the step of defining the loss function in the optimization module comprises: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating the evolution item to obtain the loss function of the knowledge tracking model, and realizing the training target of the knowledge tracking model by optimizing the loss function and enabling the loss function to find the global minimum value or the local minimum value, and further minimizing the loss function by using a random gradient descent method commonly used in the field, so that the knowledge tracking model reaches the optimal state.
As a further improvement of the invention, the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
Figure BDA0003082954360000121
wherein, ks t The state matrix generated at the t-th time step, i belongs to {1, 2.. the., n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state row represents the knowledge state of the learner on the knowledge point i, and the knowledge state comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively as follows: p is a radical of i (L t ) E (0, 1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical of formula i (T t ) E (0, 1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical of formula i (G t ) E (0, 1) is a guess parameter and represents a guess probability value when the learner does not learn the knowledge point i; p is a radical of i (S t ) E (0, 1) is a fault parameter and represents the probability value of the fault answering of the learner at the learned knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l is t Initial learning parameters representing all n knowledge points; t is a unit of t A learning ability parameter representing n knowledge points; g t Guess parameters representing n knowledge points; s t Fault parameters representing n knowledge points.
As a further improvement of the invention, the probability vector p (C) of correct prediction of answer of the learner at the current time step t and the t +1 th future time step t+1 ) The expression of (a) is:
p(C t+1 )＝L t *(1-S t )+(1-L t )*G t
wherein the probability vector p (C) t+1 ) The ith dimension in (b) is the probability value of the learner's correct answer knowledge point i at the t +1 th time step in the future, the probability vector p (C) t+1 ) Performing dot product operation with the knowledge point vector of the t +1 time step response to calculate the probability value of the correct response of the learner at the next time step, and predicting that the learner will correctly respond when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
As a further improvement of the invention, at the current time step t, the evolution term e t The expression of (a) is:
Figure BDA0003082954360000131
wherein, w t ＝(w 1 ，w 2 ，w 3 ，w 4 )∈(0，1) 4 Is the evolution weight, Δ ks t The integral change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the integral change of the knowledge state is different, and the evolution weight accurately models each time stepThe specific role of the status column.
As a further improvement of the invention, in the knowledge tracking model, the loss function of a time series is as follows:
Figure BDA0003082954360000132
wherein f (-) is a cross entropy function,
Figure BDA0003082954360000133
a predicted value of the learner's future answer performance t+1 Is the actual value of the learner's future answer performance, e t Is an evolution item representing the accurate change of the knowledge state, E belongs to N * Is the total number of questions answered by the learner sequence, N * Is a natural number set.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein when the processor runs the computer program, the steps of the knowledge tracking method based on the learner knowledge state evolution representation are executed.
The present invention also provides a computer readable storage medium storing a computer program that causes a computer to perform the steps of the previously disclosed knowledge tracking method based on an evolving representation of a learner's knowledge state.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A knowledge tracking method based on learner knowledge state evolution representation is characterized by comprising the following steps:
s1, acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
s2, generating knowledge state representation of the learner, and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of the long-term and short-term memory neural network and the input of the full-connection neural network are cognitive data sets, and the output of the long-term and short-term memory neural network and the full-connection neural network is a state matrix; the input of the long-short term memory neural network is an acquired cognitive data set, and the output is a low-level feature representation-distributed vector of a knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix represented by the high-level characteristics of knowledge states, and the state matrix is a representation method of the knowledge states of learners; the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, and are knowledge states of all knowledge points in the cognitive data set by a learner;
s3, generating a predicted value of the future answer expression of the learner, wherein in the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner;
s4, generating an evolution item, combining the evolution weight and the integral change of the knowledge state into the evolution item to express the accurate change of the knowledge state of the learner in the adjacent answers, and specifically: generating evolution weights by utilizing the established knowledge tracking model, combining the evolution weights and the integral change of the knowledge state into an evolution item by quantifying the action of each state column in the integral change in the state matrix, and generating the evolution item e at the current time step t t The expression of (a) is:
Figure FDA0003614274240000011
wherein w t ＝(w 1 ，w 2 ，w 3 ，w 4 )∈(0，1) 4 Is the evolution weight, Δ ks t Is the overall change of knowledge state at t time steps and t-1 time steps, is the difference of state matrixes of adjacent time steps, namely the difference of state columns of adjacent time steps, and the overall change of knowledge state of different state columnsThe evolution weights accurately model the specific action of each state column;
and S5, incorporating the evolution item into a loss function and optimizing, wherein the training target of the knowledge tracking model is to generate an accurate predicted value of the learner's future answer performance and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
2. The knowledge tracking method based on the learner knowledge state evolution representation as claimed in claim 1, wherein the cognitive data set in step S1 includes a plurality of time series, a time series includes a plurality of time step data, a plurality of time step data represent the answering situation of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
3. The knowledge tracking method based on learner knowledge state evolution representation as claimed in claim 1, wherein the state matrix ks in step S2 is represented as:
Figure FDA0003614274240000021
wherein, ks t The state matrix generated at the t-th time step, i belongs to {1, 2, … … n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state line represents the knowledge state of the learner on the knowledge point i, and the i-th state line comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively: p is a radical of i (L t ) E (0, 1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical of i (T t ) E (0, 1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical of i (G t ) The element (0, 1) is a guess parameter and represents a guess probability value when a learner does not learn the knowledge point i; p is a radical of i (S t ) Belongs to (0, 1) as a fault parameter, and indicates that the learner is in the process ofWhen learning the probability value of wrong answer when the knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l is t Initial learning parameters representing all n knowledge points; t is t A learning ability parameter representing n knowledge points; g t Guess parameters representing n knowledge points; s. the t Fault parameters representing n knowledge points.
4. The knowledge tracking method according to claim 3, wherein the state matrix is inputted into a Bayesian knowledge tracking algorithm in step S3 to calculate the predicted value of the learner 'S future answer performance, and the probability vector p (C) of the learner' S correct prediction of the answer at the current time step t for the t +1 th time step in the future is calculated t+1 ) The expression of (c) is:
p(C t+1 )＝L t *(1-S t )+(1-L t )*G t
wherein the probability vector p (C) t+1 ) The ith dimension in (b) is the probability value of the learner's correct answer knowledge point i at the t +1 th time step in the future, the probability vector p (C) t+1 ) Performing dot product operation with the knowledge point vector answered at the t +1 th time step to calculate the probability value of correct answer at the next time step of the learner, and predicting that the learner will correctly answer when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
5. The knowledge tracking method based on the evolving representation of the learner knowledge state as claimed in claim 1, wherein the step of defining the loss function in step S5 includes: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating into an evolution item to obtain a loss function of the knowledge tracking model, and finding a global minimum value or a local minimum value by optimizing the loss function to realize the training target of the knowledge tracking model, and further minimizing the loss function by using a random gradient descent method commonly used in the field to make the knowledge tracking model reach an optimal state, wherein the loss function of a time sequence in the knowledge tracking model is as follows:
Figure FDA0003614274240000031
wherein f (-) is a cross entropy function,
Figure FDA0003614274240000032
for the learner's predicted value of future answer performance, a t+1 Is the actual value of the learner's future answer performance, e t Is an evolution term representing the accurate change of the knowledge state, E belongs to N * Is the total number of questions answered by the learner sequence, N * Is a natural number set.
6. A knowledge tracking system based on an evolving representation of a learner's knowledge state, the system comprising:
the statistical cognitive data module is used for acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
the knowledge state representation module generates knowledge state representation of learners and builds a knowledge tracking model on the basis of a long-short term memory neural network, a full-connection neural network and a Bayesian knowledge tracking algorithm; the input of the long-short term memory neural network is an acquired cognitive data set, and the output is a low-level feature representation-distributed vector of a knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a high-level feature representation-state matrix of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner; the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, and are knowledge states of all knowledge points in the cognitive data set by a learner;
the forecasting module is used for generating a forecasting value of the future answer expression of the learner and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the forecasting value of the future answer expression of the learner;
the evolution module is used for generating evolution items and calculating the difference value of the state matrixes in the adjacent sequences so as to represent the overall change of the knowledge state of the learner in the adjacent answers, and specifically comprises the following steps: generating evolution weights by using the established knowledge tracking model, quantizing the action of each state column in the state matrix in the overall change, combining the evolution weights and the overall change of the knowledge state into evolution items, and generating the evolution item e at the current time step t t The expression of (a) is:
Figure FDA0003614274240000033
wherein, w t ＝(w 1 ，w 2 ，w 3 ，w 4 )∈(0，1) 4 Is the evolution weight, Δ ks t The overall change of the knowledge state at t time steps and t-1 time steps is the difference value of state matrixes of adjacent time steps, namely the difference value of state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight;
and the optimization module is used for incorporating the evolution item into the loss function and optimizing the evolution item, the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
7. An electronic device, characterized in that: comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to perform the steps of a knowledge tracking method according to any one of claims 1 to 5 based on an evolving representation of a knowledge state of a learner.
8. A computer-readable storage medium storing a computer program for causing a computer to perform the steps of a knowledge tracking method based on an evolving representation of a learner's knowledge state as claimed in any one of claims 1 to 5.
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