CN115687657A - Knowledge graph-assisted test question recommendation method - Google Patents
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Abstract
The invention discloses a test question recommendation method assisted by a knowledge graph. The invention comprises the following steps: 1. constructing a discipline knowledge graph; 2. constructing a relation matrix of test questions and knowledge points; 3. diagnosing and analyzing knowledge point mastering conditions according to the historical answer data of the learner; 4. calculating the similarity of the test questions and correcting the weight relation of the test questions of the knowledge points; 5. carrying out user similarity analysis according to the diagnosis result; 6. and recommending the test questions based on the diagnosis condition of the current user and the similarity among the users. The invention solves the problems that the difference between individuals and the incidence relation between knowledge points are not considered in the existing recommendation method. The invention fuses the incidence relation among the knowledge points as auxiliary information, and can effectively reduce errors caused by hidden attributes among the knowledge points. The invention can effectively mine the knowledge which best accords with the user self-mastery condition to carry out omission and filling, continuously overcome the dependent knowledge and improve the personal ability of the user.
Description
Technical Field
The invention belongs to the fields of knowledge graphs, recommendation systems and intelligent education, and relates to a method for recommending test questions assisted by knowledge graphs.
Background
With the rise of online education, the resource data of online learning of each subject is increased explosively, question bank websites, small programs and mobile phone applications are layered endlessly, and how a person uses the questions effectively and selectively within a limited time makes up knowledge holes according to the learning characteristics of the person, improves the personal ability, and is a hotspot for personalized recommendation in current intelligent education.
In the face of massive data resources, for information consumers, it is difficult to select useful data from massive data, and then the problem of information overload occurs. The recommendation system and the search engine are both a way for helping a user to quickly find useful information, but different from the search engine, the recommendation system portrays the user by analyzing user behavior data, user tag data or context information and the like, so that information which is interesting to the user is actively pushed to the user. The intelligent education recommendation system is different from the traditional electronic commerce recommendation system, the main concerns in e-commerce recommendation are how to improve the purchase conversion rate of a user and how to dig long-tailed commodities to improve enterprise revenues, and from the starting points of education and the user, the recommendation system in education focuses on improving the learning score of the user, continuously stepping out of a user comfort area and improving the personal ability. In recent years, students refer to a traditional e-commerce recommendation method, and use a collaborative filtering method to score and predict users and test questions, but the method does not consider differences among individuals, ignores that the knowledge mastering conditions of the users are possibly different, has limitation on recommendation effect, lacks rationality of results, and is difficult to meet accurate test question recommendation in education; meanwhile, with the rapid development of psychology, personalized recommendation based on a cognitive diagnosis theory is widely used by students, an existing cognitive diagnosis model models cognition of a user from a knowledge level and ensures better interpretability, so that the existing cognitive diagnosis model is widely used for evaluating the ability level of a user examinee (namely the mastering condition of a knowledge point).
In the existing question bank, most screening structures are classified according to chapter directories, and indiscriminately convey users. With the proposal of the knowledge graph, the incidence relation between the knowledge points is organized, and the information in the graph is used as auxiliary information to be used as the input of test question recommendation, so that the user can be better trained to mine the questions which accord with the characteristics of the user.
Disclosure of Invention
The invention aims to provide a test question recommendation method assisted by a knowledge graph aiming at the defects of the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows:
step one, building a discipline knowledge graph.
And step two, constructing a relation matrix of the test question and the knowledge point.
And step three, diagnosing and analyzing knowledge point mastering conditions according to the historical answer data of the learner.
Step four, calculating the similarity of the test questions and correcting the weight relation of the test questions of the knowledge points.
And fifthly, carrying out user similarity analysis according to the diagnosis result.
And step six, recommending test questions based on the diagnosis condition of the current user and the similarity between the users.
The invention has the following beneficial effects:
the knowledge map is utilized in the cognitive diagnosis model, the incidence relation between knowledge points is fused to serve as auxiliary information, and errors caused by hidden attributes between the knowledge points can be effectively reduced; after the individuation of the user is fully utilized, the user is portrayed, the similarity between the users is discovered by utilizing the latent semantic model, and errors possibly caused by the individuation diagnosis are made up. Compared with undifferentiated delivery, the invention can effectively mine the knowledge which best meets the user self-mastery condition to check for omissions, continuously overcome the dependent knowledge and improve the personal ability of the user.
Drawings
FIG. 1 is a flow chart of a knowledge-graph-aided test question recommendation method;
FIG. 2 is an exemplary diagram of a knowledge graph constructed with knowledge points;
FIG. 3 is an exemplary graph of cognitive diagnostic results;
fig. 4 is a code example diagram of a test question recommendation method based on cognitive diagnosis and knowledge-graph.
Detailed Description
The invention is further described below with reference to the figures and examples.
As shown in fig. 1-4, a method for recommending test questions assisted by a knowledge graph specifically includes the following steps:
step one, building a discipline knowledge graph;
determining the field of disciplines, and constructing a knowledge point map according to the authoritative books of the disciplines, wherein the constructed nodes comprise chapters and sections, the chapters comprise sections, and the sections comprise knowledge points. The common attributes of the chapter and section include unique identification, name, description, and accessory attributes such as teaching targets.
And manually marking the knowledge points of the related disciplines, performing entity extraction on all test questions after training, and manually correcting to obtain the knowledge points of the disciplines.
And (4) establishing the relation between knowledge points by a domain expert, and fusing the knowledge points and the chapter relation to obtain the knowledge map.
Step two, constructing a relation matrix of the test questions and the knowledge points;
analyzing the knowledge points examined in each test question by a domain expert to obtain a test question-knowledge point matrix Q, wherein Q ik =1 test question i examined knowledge points k, Q ik =0 indicates that the test question i has not examined the knowledge point k.
Initializing a test question-knowledge point weight matrix W, representing the importance degree of knowledge points in the test question, W = Q, W ik ∈[0，1]. W is initialized to be Q, the value is 0 or 1, and the weight matrix is continuously corrected through the user question making record, wherein the value of the weight matrix is between 0 and 1. The initialized W-weight matrix is as follows:
wherein W is not less than 0 ik Less than or equal to 1, when W ik If =0, it means that the test question i does not examine the knowledge points k, W ik | A If =0, the test question i indicates that the knowledge is examinedPoint k.
Step three, diagnosing and analyzing knowledge point mastering conditions according to historical answer data of learners
The Fuzzy Cognitive Diagnosis model (Fuzzy CDF, fuzzy Cognitive Diagnosis Framework) can estimate the knowledge point mastering condition alpha of the user, the distinguishing degree a of the knowledge point to the user, the difficulty b of the knowledge point to the user, the guessing probability g of test questions, the error probability s of the test questions, the mastering condition X of the user to the test questions and the potential ability theta of the user through the answer records of the user.
And inputting the knowledge point map as auxiliary information into the fuzzy cognitive diagnosis model. The method considers that the dependency relationship of the knowledge points has similar influence with the difficulty of the knowledge points, the knowledge points which are depended more are considered to be more basic, and the formula for obtaining the mastering condition of the knowledge points by the user is as follows:
wherein alpha is uk Representing the grasping condition of the knowledge point k by the user u; a is a uk Representing the discrimination of the knowledge points; b is a mixture of uk Representing the difficulty of the knowledge points; theta u Represents the potential capability level of user u; 1.7 is an empirical constant; r is k Representing the influence of the dependency of a knowledge point k, r k The formula is as follows:
triple (k, repeat, r) represents that the knowledge point k in the knowledge graph depends on the knowledge point r, and n represents the number of all knowledge points of the section to which the current knowledge point belongs.
The mastering condition of the objective test questions is the same as that of the fuzzy cognitive diagnosis model, and the fuzzy cognition is the fuzzy interaction of the user on the mastering condition of the knowledge points. In the invention, the mastering condition of the subjective test question and the mastering condition of all knowledge points examined by the test question are related to the weight of the test question on the knowledge points.
Wherein eta is ui Shows how the user u grasps the test question i, W ik Is the weight of the knowledge point k in the test question i, alpha uk The knowledge point k is grasped by the user u.
The fuzzy cognitive diagnosis model adopts Monte Carlo (MCMC, markov chain Monte Carlo) algorithm to alpha uk 、a uk 、b uk And theta u Estimating, and outputting a final model as a knowledge point mastering condition alpha, a distinguishing degree a of the knowledge point to the user, difficulty b of the knowledge point to the user, a guessing probability g of the test question, a failure probability s of the test question, a mastering condition X of the user to the test question and a potential ability theta of the user.
Step four, calculating the similarity of the test questions and correcting the weight relation of the test questions of the knowledge points
And calculating the similarity of the test questions by correcting the weight relationship between the knowledge points and the test questions, searching for similar test questions in the wrong questions of the user in the recommendation method, and consolidating the knowledge points.
And calculating the distance of the test question by using the weight matrix:
the closer sim (i, o) is to 1, the higher its similarity is.
Continuously adjusting the weight matrix W through the measured response of a user, wherein the adjusting mode is as follows:
equation (5) shows that when the user's knowledge of the knowledge point may or may not answer the question, actually as predicted, i in equation (5) is the questionIndex, k is knowledge point index, X i For the predicted grasping condition of the test question i, a is the number of users. λ is the influence coefficient, λ ∈ [0,1 ]](ii) a In a special case, when the knowledge point k is an isolated node, i.e., the knowledge point k is a base knowledge point, and is the lowest layer to be relied on in the graph, λ =1, i.e., the influence of the relied point is 0.
Representing pairs of knowledge points W on which knowledge points k depend ik R is the index of the dependent knowledge points, L is the number of dependent knowledge points, Q ir | A =0 indicates that the test question i examined the knowledge point r.
The formula (6) shows that when the user knows the condition, the user can answer the question, but does not answer the question, the question may be wrong, and the probability that the error rate is correct is subtracted; the user knows that the situation cannot answer the question, but answers the question correctly, which may be guess. Wherein, g i Expressing the guess probability, s, of the test question i i The probability of failure of the test question i is shown.
Step five, carrying out user similarity analysis according to the diagnosis result
And selecting the target knowledge point t as a knowledge point to be recommended.
The source is as follows: 1. mapping the position of the user u in the whole map, namely G u E.g. G, wherein G u All of the knowledge points in (1) belong to points to which topics have already been done by the user u. G u As an input of the LFM Model (patent Factor Model), a knowledge point that the current cognitive level of the user may grasp is obtained.
2. The user selects the target knowledge point t by himself, and it is assumed that the user can select only knowledge points that do not contain any child nodes (base nodes). Predicting by using an LFM model, comprising the following steps:
preprocessing the cognitive diagnosis result user-knowledge point grasping condition alpha, and recording the matrix after preprocessing as alpha c . Considering the mastery condition alpha of the user to the knowledge point uk When the value is smaller than the median, it is considered that the prediction is not known, and the value is recorded as 0, i.e., α uk < mean (k), then
Performing matrix decomposition on the processed user-knowledge point master matrix: alpha is alpha c ＝p·q T Randomly initializing the matrices p and q, and associating the diagnosis result of the user-knowledge point grasping matrix with the corresponding p u And
the value obtained by the point multiplication establishes a squared error loss function, wherein the loss function is defined as:
λ is the regularization coefficient, r ui Is a function of the actual value of the measured value,
in order to predict the value of the target,
optimizing a loss function by using a gradient descent method, iterating for certain times to obtain matrixes p and q, and predicting a matrix alpha p 。
Step six, recommending test questions based on the diagnosis condition of the current user and the similarity between users
From the prediction matrix alpha p And obtaining the knowledge point t which is most suitable for learning of the current user u. And (3) searching and describing relevant questions of the target knowledge point t:
the target user u is defined as u, if the target user u does not grasp the dependent knowledge point k (the median smaller than the knowledge point is considered as not grasping), namely alpha uk If the number of the knowledge points is less than mean (k), the knowledge points k are enqueued, because the knowledge points are the knowledge needed by the target user u to learn the knowledge points t, after the knowledge points k are established, the topics most relevant to the knowledge points k are found according to the weight matrix W, wherein the measuring method comprises the following steps:
i is the test question with the most knowledge points in the investigation subject, i is the queuing QR,
the sum of the weights of all knowledge points examined by the test question i is represented. Searching for test questions N, N enqueue QR, hat which are related to the current knowledge point k and are similar to the wrong questions in the wrong question record of the user u k = QR. Where hat is the set of predicted knowledge points and topics, and QR is the topics that can be recommended.
User u has to recommended test question ki Answering, finding hat according to W matrix ki Point of knowledge P with emphasis on investigation i And checking the mastery condition of each knowledge point, P i A set of knowledge points examined for test question i. If all knowledge points are mastered, the knowledge points are considered to master the knowledge for researching the related questions, and the knowledge point P is obtained i Section C, (P) i E.g. C), acquiring a next knowledge point needing learning in the section of the current knowledge point, and predicting t. If the chapter is all mastered, the next chapter is followed.
User u pairs recommended test questions hat ki And (6) wrong answering. Searching knowledge points on which the knowledge points k depend and preamble knowledge points of the knowledge points k under the section C, wherein the reason of wrong answer may be that the dependent knowledge points are not mastered or the preamble knowledge points of the knowledge points are not mastered, sequentially traversing the mastering conditions of all knowledge point sets, and if the knowledge points are larger than a threshold value, skipping and considering the mastering; and if the user does not know the related topic, recommending the related topic.
As shown in FIG. 1, a test question recommendation method flow chart assisted by a knowledge graph is characterized in that a subject knowledge graph is constructed by original data, personalized diagnosis is carried out depending on entity relations in the knowledge graph in the cognitive diagnosis process, then similarity analysis is carried out by using a latent semantic model, and finally a test question which is most suitable for learning of a user is obtained according to an analysis result and the graph.
As shown in fig. 2, a knowledge graph example diagram constructed by knowledge points is shown, wherein chapters, sections and knowledge points are used as entities of the knowledge graph, and relationships among the entities include relationships such as inclusion and dependency, wherein an entity chapter includes an entity section, the entity section includes each basic knowledge point, and there is a dependency relationship among the basic knowledge points, for example, a section of a garbage collector includes knowledge points such as G1 and CMS, the CMS depends on a knowledge point marking-compression algorithm, and the marking-compression algorithm depends on a knowledge point reachability analysis algorithm;
fig. 3 is an exemplary graph of cognitive diagnosis results, which shows how a user grasps each knowledge point, where the internal nodes are the degrees of user grasping each knowledge point, and as shown in the figure, the degree of user grasping knowledge point 2 is the highest, and the degree of user grasping knowledge point 4 is the lowest;
fig. 4 shows an example of codes of a test question recommendation method based on cognitive diagnosis and a knowledge graph, which indicates that a target knowledge point t is determined, first, whether the knowledge point on which the knowledge point t depends reaches a mastery degree is found, if not, a question with the highest correlation with the depended knowledge point and a test question similar to the depended knowledge point in a historical question set are found, and finally, a test question conforming to the learning of a user is output.
Claims (6)
1. A knowledge graph-assisted test question recommendation method is characterized by comprising the following steps:
step one, building a discipline knowledge graph;
step two, constructing a relation matrix of the test questions and the knowledge points;
step three, diagnosing and analyzing knowledge point mastering conditions according to the historical answer data of the learner;
step four, calculating the similarity of the test questions and correcting the weight relation of the test questions of the knowledge points;
fifthly, carrying out user similarity analysis according to the diagnosis result;
and step six, recommending test questions based on the diagnosis condition of the current user and the similarity between the users.
2. The method for recommending test questions assisted by a knowledge graph according to claim 1, wherein the method for constructing a relation matrix of test questions and knowledge points is specifically realized as follows:
analyzing the knowledge points examined in each test question by a domain expert to obtain a test question knowledge point matrix Q, wherein Q ik =1 test question i examined knowledge points k, Q ik =0 indicates that the test question i has not examined the knowledge point k;
initializing a test question-knowledge point weight matrix W, representing the importance degree of the knowledge points in the test question, W = Q, W ik ∈[0，1](ii) a Initializing W into Q with the value of 0 or 1, and continuously correcting the weight matrix through user question making record, wherein the value of the weight matrix is between 0 and 1; the initialized W-weight matrix is as follows:
wherein W is not less than 0 ik Less than or equal to 1, when W ik If =0, the test question i has no investigation knowledge points k and W ik ! If =0, this indicates that the knowledge point k is considered in the test question i.
3. The knowledge-graph-aided test question recommendation method according to claim 2, wherein the diagnosis and analysis of knowledge point mastering conditions according to the learner's historical answer data is implemented as follows:
inputting the knowledge point map as auxiliary information into a fuzzy cognitive diagnosis model; the method considers that the dependency relationship of the knowledge points has similar influence with the difficulty of the knowledge points, the knowledge points which are depended more are considered to be more basic, and the formula for obtaining the mastering condition of the knowledge points by the user is as follows:
wherein alpha is uk Representing the grasping condition of the knowledge point k by the user u; a is uk Representing the discrimination of the knowledge points; b uk Representing the difficulty of the knowledge points; theta u Represents the potential capability level of user u; r is k Representing the influence of the dependency of a knowledge point k, r k The formula is as follows:
triple (k, repeat, r) represents that knowledge points k in the knowledge graph depend on knowledge points r, and n represents the number of all knowledge points of the section to which the current knowledge points belong;
the mastering condition of the test questions is the same as that of the fuzzy cognitive diagnosis model, and the fuzzy cognitive diagnosis model is a fuzzy deal of the user on the mastering condition of the knowledge points; the method considers that the mastering condition of the test questions and the mastering conditions of all knowledge points examined by the test questions are related to the weight of the test questions on the knowledge points;
wherein eta is ui Shows how the user u grasps the test question i, W ik Is the weight of the knowledge point k in the test question i, alpha uk The mastering condition of the knowledge point k for the user u;
the fuzzy cognitive diagnosis model adopts a Monte Carlo algorithm to pair alpha uk 、a uk 、b uk And theta u Estimating, and outputting a final model as a knowledge point mastering condition alpha, a distinguishing degree a of the knowledge point to the user, difficulty b of the knowledge point to the user, a guessing probability g of the test question, a failure probability s of the test question, a mastering condition X of the user to the test question and a potential ability theta of the user.
4. The method for recommending test questions assisted by a knowledge graph according to claim 2 or 3, wherein the method for calculating the similarity of the test questions and correcting the weight relationship of the test questions of the knowledge points is specifically realized as follows:
calculating the similarity of the test questions by correcting the weight relationship between the knowledge points and the test questions, searching for similar test questions in the user wrong questions in the recommendation method, and consolidating the knowledge points;
and calculating the distance of the test questions by using the weight matrix:
when sim (i, o) is closer to 1, it is said that the similarity is higher;
continuously adjusting the weight matrix W through the measured response of a user, wherein the adjusting mode is as follows:
the expression (5) shows that when the user's mastery condition of the knowledge point may or may not answer the question, actually as predicted, in the expression (5), i is the index of the test question, k is the index of the knowledge point, and X is the index of the knowledge point i A is the number of users for the predicted mastering condition of the test question i; λ is the influence coefficient, λ ∈ [0,1 ]](ii) a In a special case, when a knowledge point k is an isolated node, namely the knowledge point k is a basic knowledge point and is the lowest layer of dependence in the graph, λ =1, namely the influence of the dependent point is 0;
representing pairs of knowledge points W on which knowledge points k depend ik R is the index of the dependent knowledge points, L is the number of the dependent knowledge points, Q ir ! =0 indicates that the test question i examines the knowledge point r;
the formula (6) shows that when the user knows the condition, the user can answer the question, but the user does not answer the question, but the question may be missed, and the probability that the error rate is correct is subtracted; the user knows that the situation cannot answer the question, but answers the question correctly, which may be guess; wherein, g i Expressing the guess probability, s, of the test question i i The probability of failure of the test question i is shown.
5. The method for recommending test questions assisted by a knowledge graph according to claim 4, wherein the similarity analysis of the users is performed according to the diagnosis results, and the specific analysis is as follows:
selecting a target knowledge point t as a knowledge point to be recommended;
1. mapping the position of the user u in the whole map, namely G u E.g. G, wherein G u All the knowledge points in (1) belong to points related to topics already done by the user u; g u As the input of an LFM (tension Factor Model), acquiring a knowledge point which can be mastered by the current cognitive level of a user;
2. the user selects a target knowledge point t by himself, and the user is supposed to select only knowledge points which do not contain any child nodes (basic nodes); predicting by using an LFM model, comprising the following steps:
preprocessing the user-knowledge point grasping condition alpha of the result of the cognitive diagnosis, and recording the matrix after preprocessing as alpha c (ii) a Considering the mastery condition alpha of the user to the knowledge point uk When the value is smaller than the median, it is considered that the prediction is not known, and the value is recorded as 0, i.e., α uk < mean (k), then
Performing matrix decomposition on the processed user-knowledge point master matrix: alpha is alpha c ＝p·q T Randomly initializing matrixes p and q, and grasping the diagnosis result of the matrix by the user-knowledge points and corresponding pu sums
The value obtained by the point multiplication establishes a squared error loss function, wherein the loss function is defined as:
λ is the regularization coefficient, r ui In the form of an actual value of the value,
in order to predict the value of the target,
optimizing a loss function by using a gradient descent method, iterating for a certain number of times to obtain matrixes p and q and predicting a matrix alpha p 。
6. The knowledge-graph-assisted test question recommendation method according to claim 5, wherein the recommendation of the test questions is realized based on the diagnosis condition of the current user and the similarity between the users, and is specifically realized as follows:
from the prediction matrix alpha p Obtaining a knowledge point t which is most suitable for learning of a current user u; and (3) searching and describing relevant questions of the target knowledge point t:
the target user is defined as u, if the target user u does not know the dependent knowledge point k, namely alpha uk If the number of the knowledge points is less than the mean (k), the knowledge point k enqueues, because the knowledge point is the knowledge required by the target user u to learn the knowledge point t, after the knowledge point k is established, the most relevant topic of the knowledge point k is found out according to the weight matrix W, wherein the measuring method comprises the following steps:
i, the test question with the most knowledge points in the investigation subject, i, the queuing QR,
representing the weight sum of all knowledge points examined by the test question i; searching for test questions N, N enqueue QR, hat which are related to the current knowledge point k and are similar to the wrong questions in the wrong question record of the user u k = QR; wherein hat is a set of prediction knowledge points and topics, and QR is a topic which can be recommended;
user u has to recommended test question ki Answering, finding hat according to W matrix ki Knowledge point P with emphasis on investigation i And checking the mastery condition of each knowledge point, P i To test question i instituteA set of investigated knowledge points; if all knowledge points are mastered, the knowledge points are considered to master the knowledge of related topic investigation, and the knowledge point P is obtained i Section C, (P) i E to C), acquiring a knowledge point needing learning next to the current knowledge point in the section, and predicting t; if the chapter is completely mastered, the next chapter;
user u has to recommended test question ki Wrong answer; searching knowledge points on which the knowledge points k depend and preamble knowledge points of the knowledge points k under the section C, wherein the reason of wrong answer may be that the dependent knowledge points are not mastered or the preamble knowledge points of the knowledge points are not mastered, sequentially traversing the mastering conditions of all knowledge point sets, and if the knowledge points are larger than a threshold value, skipping and considering the mastering; less than that, it is considered that it is not mastered, and the relevant topic is recommended for it.
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