CN110264091B - Student Cognitive Diagnosis Method - Google Patents
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Abstract
The invention discloses a student cognitive diagnosis method, which comprises the following steps: acquiring historical answer information of students, and extracting test question texts and included predefined knowledge points; calculating a knowledge point correlation vector of each test question according to the test question text and the included predefined knowledge points; and taking the set student parameters and the test question parameters containing the knowledge point relativity vector of the test questions as the input of a cognitive diagnosis model constructed by a neural network, fitting the answer results, obtaining the knowledge point relativity vector of the student through training, and completing the cognitive diagnosis of the student.
Description
Technical Field
The invention relates to the technical field of education data mining, in particular to a student cognitive diagnosis method.
Background
The cognitive diagnosis is a very important ring in intelligent education, and is an improvement and perfection of the conventional examination and evaluation. The conventional education scene adopts a coarse-granularity student evaluation mode, for example, the ability of students is evaluated by the examination scores or correct and wrong answers of the students, but the reasons of the wrong answers of the students cannot be known only by the method, and the positions of short knowledge plates of the students cannot be known accurately. For this problem, student cognitive diagnosis aims at obtaining the mastery degree of each specific knowledge point of the student hidden in the student cognitive diagnosis through analysis of the student answer records.
Cognitive diagnosis is one of the key technologies of current personalized intelligent education for the assessment of student competence. The accurate cognitive diagnosis result can provide a real knowledge state reflection for students, and a reliable basis is provided for self-evaluation of the students, subsequent coaching of teachers, resource recommendation of intelligent teaching platform and the like. Therefore, how to more accurately realize the diagnosis of the knowledge state of students has been an important research content in the field of education data mining.
The methods related to cognitive diagnosis currently exist mainly in the following two fields:
1) Educational psychology method
In educational psychology, the project reflection theory (item response theory, IRT) model and the DINA (deterministic inputs, noise "and" gate) model are two of the most typical models. The IRT is continuous and single-dimensional, and the test question difficulty, the test question distinguishing degree, the test question guessing degree and the comprehensive capability of the students are respectively represented by a continuous value scalar, and the answer result of the students is predicted through logic Style regression. IRT has a multi-dimensional modified version (MIRT) that expresses student's ability in multi-dimensional continuous vectors, but is still logistic regression in nature. On the other hand, DINA is a multidimensional discrete model, students and questions are each represented as a multidimensional 0-1 vector (the student vector has the knowledge point grasped by 1 and the question vector has no knowledge point grasped by 0, the question vector has the knowledge point contained by 1 and the question vector has no knowledge point contained by 0), and a Q matrix is applied to modeling. The Q matrix is a discrete matrix used to represent that the test questions contain knowledge points. In DINA, the relationship between knowledge points examined in a test question is considered as 'connectivity', namely, all the examined knowledge points need to be mastered to be answered, and furthermore, the problem guessing and error parameters of the test question can be further combined, so that the knowledge mastering degree of students can be excavated.
2) Matrix decomposition method
Matrix decomposition comes from the field of data mining and is also used for performing cognitive diagnosis, students and questions are respectively analogized to users and commodities in a recommendation system, and hidden features of each student and each question are respectively represented by multi-dimensional continuous vectors. Specifically, the method comprises the steps of carrying out low-rank decomposition on a record matrix of student answers, removing redundancy to obtain a student matrix representing all student characteristics and a test question matrix representing all test question characteristics, combining the two matrices based on dot multiplication, and filling up the blank part (the student does not have answer records of the questions) while restoring the original answer record matrix so as to predict the score of the student on the questions which are not answered. The low rank decomposition method may be singular value decomposition (singular value decomposition, SVD), probability matrix decomposition, etc.
While these above-described cognitive diagnostic methods have demonstrated their effectiveness in past applications, they are all linear combinations between student vectors and test question vectors, often failing to accurately model complex relationships between students and test questions. The student vector obtained by the partial method (IRT, matrix decomposition, etc.) can be used for predicting the answer result although reflecting the abstract characteristics of the student, but has no meaning which can be practically interpreted, and the mastery degree of the student on each specific knowledge point can not be known, so that the understanding and the further utilization of the diagnosis result are not facilitated. In addition, the design of the function mapping (such as logistic regression in IRT and dot multiplication in matrix decomposition) in a specific vector combination mode requires more expertise, is time-consuming and labor-consuming, and has limited types of test questions to which the designed function is generally applicable.
Disclosure of Invention
The invention aims to provide a student cognitive diagnosis method, which can accurately obtain the mastering degree of students on each specific predefined knowledge point by analyzing the student answer records and combining the knowledge points of test questions and the text information of the test questions.
The invention aims at realizing the following technical scheme:
a student cognitive diagnostic method comprising:
acquiring historical answer information of students, and extracting test question texts and included predefined knowledge points;
calculating a knowledge point correlation vector of each test question according to the test question text and the included predefined knowledge points;
and taking the set student parameters and the test question parameters containing the knowledge point relativity vector of the test questions as the input of a cognitive diagnosis model constructed by a neural network, fitting the answer results, obtaining the knowledge point relativity vector of the student through training, and completing the cognitive diagnosis of the student.
According to the technical scheme provided by the invention, the analysis of the student answer records by the method can accurately acquire the mastering condition of the student at each specific knowledge point, and the cognitive diagnosis result can be used for auxiliary teaching such as visual diagnosis report, education resource recommendation and the like.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a student cognitive diagnosis method according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
The embodiment of the invention provides a student cognitive diagnosis method, which is characterized in that the neural network technology is applied to cognitive diagnosis by considering the strong learning capacity and function fitting capacity of the neural network, the complex relationship between students and test questions is automatically learned through answer records, and the knowledge mastering condition of the students is obtained.
The neural network is a popular algorithm in the current machine learning field, nonlinear transformation is carried out on input features through a multi-layer perceptron, model parameters are adjusted through a gradient descent algorithm in the model training process, and any continuous function can be fitted theoretically, so that the neural network is suitable for modeling complex relations between students and test questions. However, the neural network has a characteristic of 'black box' so that the parameters of the neural network lack of interpretation in most cases, and although a neural network model for predicting the answer result of the student exists at present, the obtained student vector cannot represent the mastery degree of the student at each specific knowledge point. Therefore, the neural network is used for realizing the cognitive diagnosis of students, and the explanatory problem of the cognitive diagnosis is required to be solved. The student cognitive diagnosis method provided by the embodiment of the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the student cognitive diagnosis method provided by the embodiment of the invention mainly includes the following steps:
and 11, acquiring historical answer information of students, and extracting test question texts and included predefined knowledge points.
The historical answer information of each student comprises test questions including: knowledge points, test question text and answer results (answer pairs, answer errors or scores), wherein the test question text comprises: question face, answer and/or resolution;
in the answer record, N students, M test questions and K knowledge points are shared, and the student set is S= { S 1 ,s 2 ,...,s N The test question set is E= { E } 1 ,e 2 ,...,e M Knowledge point set K nowledge ＝{k 1 ,k 2 ,...,k K Each answer record is expressed as a triplet (s, e, r), and the result of the test question e by the student s is represented as r; wherein if the test questions are divided into only right and wrong questions,then answer pair r=1, answer error r=0; let r=score/total score if the test question is scored.
And step 12, calculating a knowledge point correlation vector of each test question according to the test question text and the included predefined knowledge points.
The embodiment of the invention provides two knowledge point correlation vector calculation methods of test questions:
the method comprises the following steps:
numbering the test question text and the predefined knowledge points respectively, and constructing a test question-knowledge point association matrix Q:
the test question-knowledge point association matrix Q is an MxK matrix, wherein the row vector Q m As test question e m Knowledge point correlation vector of (a).
The second method is as follows:
to reduce the problems of inaccuracy, incompleteness and the like caused by subjectivity of manual labeling, the test question-knowledge point correlation matrix Q is optimized to obtain an optimized matrixThe optimized knowledge point relevance vector of each test question is obtained, and the preferred implementation mode is as follows:
word segmentation is carried out on test question text to obtain word sequencesVectorizing each word and then splicing to obtain a primary characterization vector of the test question text> wherein ,wl Represents the first word, w l For the word vector corresponding to the first word, N e For the number of words, d 0 Is the dimension of the word vector.
Alternatively, word vectorization may be achieved by replacing each Word with a pre-trained Word2 Vec.
Training a test question knowledge point prediction model by using a neural network, taking a primary characterization vector of a test question as input of the test question knowledge point prediction model, taking a corresponding row vector of the test question in a test question-knowledge point correlation matrix Q as a training label, training, and outputting a prediction vector; the output predictive vector is a knowledge point predictive vector equal to the line vector of the test question-knowledge point association matrix Q, wherein each dimension represents the probability that the test question contains the corresponding knowledge point.
Alternatively, assuming that a test question knowledge point prediction model is trained by using a convolution network (convolutional neural network, CNN), a hidden layer is obtained through a convolution network wherein ：
wherein phi is an activation function;i.e. d 1 A convolution kernel of length c; />Representing w l Is the j-th dimensional element value of (2); />Is a bias term;
the convolution layer is followed by a pooling layer, and a multi-layer convolution-pooling operation is adopted; the number of neurons at the last layer of the network is consistent with the number K of knowledge points, a sigmoid activation function can be used for limiting the value of each dimension to (0, 1), and a prediction vector o epsilon (0, 1) is output 1×K The method comprises the steps of carrying out a first treatment on the surface of the Calculating a loss function according to the prediction vector o and a label y, wherein the label y is a knowledge point vector marked by manpower, namely test question-knowledgeThe corresponding row of the point association matrix Q. Alternatively, the loss function selects cross entropy: wherein yi An ith element of y, o i The i-th element of o.
In addition, knowledge point prediction can also adopt structures such as a cyclic neural network (recurrent neural network, RNN), and the like, and the embodiment of the invention does not limit the specific structure of the hidden layer inside the network. Training of the knowledge point prediction model is independently carried out, and subsequent steps are carried out after training is completed. After training, the output vector corresponding to each test question is the knowledge point prediction vector of the test question.
Test question e m The k knowledge points with the largest value in the knowledge point prediction vector areThe following steps are carried out>Combining with the test question-knowledge point correlation matrix Q to obtain an optimized matrix +.>
Defining partial order relationshipsThe method comprises the following steps:
b, if Q ma =1 and Q mb =0 and->
Wherein a and b represent different knowledge points, and a partial order relation set D is defined v ：
In an optimized matrixIn { ()>And Q is mn =0, where m=1, 2,..m and n=1, 2,..k } values are all set to 0; set matrix->Is subject to Gaussian distribution +.> Is->In row m, defined as->The value satisfies the partial order relation->Conditional probability of->Obeying the function distribution:
where λ is the hyper-parameter, then the matrixWith respect to the partial order relation set D v The posterior conditional probability distribution of (2) is:
wherein ,is->Has been previously provided with each dimension obeying a Gaussian distribution +.>Sigma is the standard deviation; c is a constant and is ignored in the optimization; />
For a pair ofAll non-0 values of (i.e. not +)>After the activation function is converted into the (0, 1) value range, the test question e is obtained m Knowledge correlation vector of (c).
Training of (a) in combination with a cognitive diagnostic model, +.>Will be used in the loss function of the joint training, see later in detail.
And 13, taking the set student parameters and the test question parameters containing the knowledge point relativity vector of the test questions as the input of a cognitive diagnosis model constructed by a neural network, fitting the answer results, obtaining the knowledge point masteriness vector of the student through training, and completing the cognitive diagnosis of the student.
In the embodiment of the invention, the set student parameter is recorded as h s The method comprises the steps of carrying out a first treatment on the surface of the The test question parameters include: knowledge point relevance vector of test question (i.e. Q e or ) Difficulty vector h for investigation of test question knowledge points diff And test question distinguishing degree h disc ；
For the convenience of mathematical expression and model realization, assume that the knowledge point mastery degree matrix is A, the test question knowledge point investigation difficulty matrix is B, the test question distinction degree matrix is D, and the one-hot vector of the student is x s (0-1 vector with length N, only dimension corresponding to student id is 1, and the rest dimension is 0), and one-hot vector of test question is x e (0-1 vector of length M, only dimension corresponding to question id is 1, and the remaining dimensions are 0), then:
h s ＝sigmoid(x s ×A)，
h diff ＝sigmoid(x e ×B)，
h disc ＝sigmoid(x e ×D)，
Q e ＝x e×Q, or
Wherein A, B and D are all learnable matrixes;
after the student parameters and the test question parameters are fused, through the transformation of the cognitive diagnosis model, the answer result of the student is predicted through training, the answer result is expressed in a vector form (namely, the knowledge point mastery degree vector), and each dimension represents the mastery degree of the student on the corresponding knowledge point.
As described above, the neural network lacks interpretability of its parameters in most cases due to its own "black box", and therefore, embodiments of the present invention are designed to ensure student parameter h s Is performed on the student parameters, and the monotonicity assumption is converted into the property of the neural network mapping function.
The monotonicity assumption is that the probability of predicting the answering of a student to a test question increases monotonically about the grasping degree of any knowledge point of the student; that is, in the case that the grasping degree of other knowledge points of the student is unchanged, if the grasping degree of a certain knowledge point is increased, the probability of answering the test questions by the student is unchanged or increased, and the probability of answering the test questions by the student is not reduced.
Embodiments of the present invention do not limit the implementation of specific monotonicity assumptions in the network architecture.
Alternatively, if the cognitive diagnostic model is constructed by multiple fully connected layers, monotonicity assumption can be achieved by limiting the weight of each fully connected layer to be non-negative.
The first layer of the network is:
or ,
wherein the symbol omicron represents multiplication by element; then a plurality of layers are full-connection layers with non-negative weight values;
assuming that the number of full connection layers is 3, then:
f 1 ＝φ(W 1 ×x T +b 1 )
f 2 ＝φ(W 2 ×f 1 +b 2 )
y＝φ(W 3 ×f 2 +b 3 )
wherein ,W1 ，W 2 ，W 3 For the weight matrix, each element value of the weight matrix is non-negative, phi=sigmoid () is selected as an activation function, and the final output value y is a probability prediction value of input student answers to test questions.
In the embodiment of the invention, the cross entropy is selected as a loss function trained by a cognitive diagnosis model (step 13):
wherein ,ri For the answer result of the student to the ith test question in the training sample, y is obtained from the history answer information of the student i Is the corresponding predicted value;
if the knowledge point correlation vector of the test question uses Q (i.e., obtained by the method one described above), the training loss function loss=loss of the cognitive diagnostic model CDM The method comprises the steps of carrying out a first treatment on the surface of the If the knowledge point correlation vector of the test question is used(i.e. obtained by the method II), the whole model (comprising the optimized test question-knowledge point correlation matrix +.>And cognitive diagnostic model) training loss function +.>
According to the scheme provided by the embodiment of the invention, the analysis of the student answer records can accurately acquire the mastering conditions of students at each specific knowledge point, and the diagnosis results can be used for auxiliary teaching such as visual diagnosis report, education resource recommendation and the like.
From the description of the above embodiments, it will be apparent to those skilled in the art that the above embodiments may be implemented in software, or may be implemented by means of software plus a necessary general hardware platform. With such understanding, the technical solutions of the foregoing embodiments may be embodied in a software product, where the software product may be stored in a nonvolatile storage medium (may be a CD-ROM, a U-disk, a mobile hard disk, etc.), and include several instructions for causing a computer device (may be a personal computer, a server, or a network device, etc.) to perform the methods of the embodiments of the present invention.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (3)
1. A student cognitive diagnosis and application method, comprising:
acquiring historical answer information of students, and extracting test question texts and included predefined knowledge points;
calculating a knowledge point correlation vector of each test question according to the test question text and the included predefined knowledge points;
the set student parameters and test question parameters containing knowledge point relativity vectors of the test questions are used as input of a cognitive diagnosis model constructed by a neural network, answer results are fitted, knowledge point masteriness vectors of students are obtained through training, cognitive diagnosis of the students is completed, and education resource recommendation is carried out according to the cognitive diagnosis results; the method comprises the steps of carrying out monotonicity assumption on student parameters, converting the monotonicity assumption into the property of a neural network mapping function, and if a cognitive diagnosis model is constructed through a plurality of fully-connected layers, realizing the monotonicity assumption by a method of limiting the weight of each fully-connected layer to be a non-negative value; the monotonicity assumption is that the probability of predicting the answering of a student to a test question increases monotonically about the grasping degree of any knowledge point of the student; that is, under the condition that the mastering degree of other knowledge points of the student is unchanged, if the mastering degree of a certain knowledge point is increased, the probability of answering the test questions by the student is unchanged or increased;
the historical answer information of each student comprises test questions including: knowledge points, test question texts and answer results, wherein the test question texts comprise: question face, answer and/or resolution;
in the answer record, N students, M test questions and K knowledge points are shared, and the student set is S= { S 1 ,s 2 ,...,s N The test question set is E= { E } 1 ,e 2 ,...,e M Knowledge point set K nowledge ＝{k 1 ,k 2 ,...,k K Each answer record listShown as a triplet (s, e, r), and the result of the test question e by the representative student s is r; if the test questions are divided into only right and wrong directions, answering the right and wrong directions r=1 and r=0; let r = score/total score if the test question has a score;
the calculating the knowledge point relevance vector of each test question according to the test question text and the included predefined knowledge points comprises the following steps:
numbering the test question text and the predefined knowledge points respectively, and constructing a test question-knowledge point association matrix Q:
the test question-knowledge point association matrix Q is an MxK matrix, wherein the row vector Q m As test question e m Is a knowledge point correlation vector; wherein M is the number of questions, K is the number of knowledge points;
the calculating the knowledge point relevance vector of each test question according to the test question text and the included predefined knowledge points further comprises: optimizing the test question-knowledge point association matrix Q to obtain an optimized matrixThereby obtaining the optimized knowledge point relevance vector of each test question:
word segmentation is carried out on test question text to obtain word sequencesVectorizing each word and then splicing to obtain a primary characterization vector of the test question text> wherein ,wl Represents the first word, w l For the word vector corresponding to the first word, N e For the number of words, d 0 Is the dimension of the word vector;
training a test question knowledge point prediction model by using a neural network, taking a primary characterization vector of a test question as input of the test question knowledge point prediction model, taking a corresponding row vector of the test question in a test question-knowledge point correlation matrix Q as a training label, training, and outputting a prediction vector;
test question e m The k knowledge points with the largest value in the knowledge point prediction vector areThe following steps are carried out>Combining with the test question-knowledge point correlation matrix Q to obtain an optimized matrix +.>
Defining partial order relationshipsThe method comprises the following steps:
if Q ma =1 and Q mb =0 and->
Wherein a and b represent different knowledge points, and a partial order relation set D is defined v ：
In an optimized matrixIn { ()>And Q is mn =0, where m=1, 2,..m and n=1, 2,..k } values are all set to 0; set matrix->Is subject to Gaussian distribution +.> Is->In row m, defined as->The value satisfies the partial order relation->Conditional probability of->Obeying the function distribution:
where λ is the hyper-parameter, then the matrixWith respect to the partial order relation set D v The posterior conditional probability distribution of (2) is:
wherein ,is->Has been previously provided with each dimension obeying a Gaussian distribution +.>Sigma is the standard deviation; c is a constant and is ignored in the optimization; />
For a pair ofNot 0, i.e. not { }>And Q is mn After the activation function is converted into the (0, 1) value range }, the test question e is obtained m Knowledge correlation vector of (a);
the step of fitting the answer result by taking the set student parameters and the test question parameters containing the knowledge point relativity vector of the test questions as the input of the cognitive diagnosis model constructed by the neural network, and the step of obtaining the knowledge point relativity vector of the student through training comprises the following steps:
the set student parameter is recorded as h s The method comprises the steps of carrying out a first treatment on the surface of the The test question parameters include: knowledge point correlation vector of test questions and test question knowledge point investigation difficulty vector h diff And test question distinguishing degree h disc ；
Assuming that the knowledge point mastery degree matrix is A, the test question knowledge point investigation difficulty matrix is B, the test question distinction matrix is D, and the one-hot vector of the student is x s The one-hot vector of the test question is x e Then:
h s ＝sigmoid(x s ×A)，
h diff ＝sigmoid(x e ×B)，
h disc ＝sigmoid(x e ×D)，
Q e ＝x e×Q, or
Wherein A, B and D are all learnable matrixes;
after the student parameters and the test question parameters are fused, through the transformation of the cognitive diagnosis model, the answer result of the student is predicted through training, the answer result is expressed in a vector form, and each dimension represents the mastery degree of the student on the corresponding knowledge point;
the first layer of the network is:
or ,
wherein the symbols areRepresenting multiplication by element; then a plurality of layers are full-connection layers with non-negative weight values;
assuming that the number of full connection layers is 3, then:
f 1 ＝φ(W 1 ×x T +b 1 )
f 2 ＝φ(W 2 ×f 1 +b 2 )
y＝φ(W 3 ×f 2 +b 3 )
wherein ,W1 ，W 2 ，W 3 For the weight matrix, each element value of the weight matrix is non-negative, phi=sigmoid () is selected as an activation function, and the final output value y is a probability prediction value of input student answers to test questions.
2. The method for student cognitive diagnosis and application of claim 1, wherein,
assuming that a convolutional network is used for training a test question knowledge point prediction model, obtaining a hidden layer through a layer of convolutional network wherein ：
wherein phi is an activation function;i.e. d 1 A convolution kernel of length c; />Representing w l Is the j-th dimensional element value of (2);is a bias term;
the convolution layer is followed by a pooling layer, and a multi-layer convolution-pooling operation is adopted; the number of neurons of the last layer of the network is consistent with the number K of knowledge points, the value of each dimension is limited to (0, 1) by adopting an activation function, and a prediction vector o epsilon (0, 1) is output 1×K The method comprises the steps of carrying out a first treatment on the surface of the Calculating a loss function according to the prediction vector o and the label y, and selecting cross entropy by the loss function:wherein the label y is a knowledge point vector marked manually, namely a corresponding row of the test question-knowledge point association matrix Q, y i An ith element of y, o i The i-th element of o.
3. The method for student cognitive diagnosis and application of claim 1, wherein,
cross entropy is selected as a loss function for cognitive diagnostic model training:
wherein ,ri For the answer result of the student to the ith test question in the training sample, y is obtained from the history answer information of the student i Is the corresponding predicted value;
if the knowledge point correlation vector of the test question uses Q, the training loss function loss=loss of the cognitive diagnostic model CDM The method comprises the steps of carrying out a first treatment on the surface of the If the knowledge point correlation vector of the test question is usedOptimizing the test question-knowledge point correlation matrix +.>And training loss function of cognitive diagnostic model +.>
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