CN109871482A - A kind of group's educational resource recommended method based on Nash Equilibrium - Google Patents
A kind of group's educational resource recommended method based on Nash Equilibrium Download PDFInfo
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Abstract
Group's educational resource recommended method based on Nash Equilibrium that the invention proposes a kind of, comprising the following steps: obtain scoring of the group member to educational resource, group member is converted to the scoring of educational resource by approximate satisfaction by matrix decomposition；It is modeled according to individual choice of the approximate satisfaction to group member, finds Nash Equilibrium Solution by setting up pay off function, to obtain each member to the optimal selection probability of each policy entry；The preference of group is obtained by preference polymerization, recommends the educational resource for meeting the preference for group member.The invention proposes simulating the selection between group member using finding Nash Equilibrium Solution under the game scene of complete information static, the interactivity between group member is established with this.The conflict of interest between this method very good solution group member can recommend suitable educational resource for group, improve group member to the satisfaction for recommending resource.
Description
Technical field
The invention belongs to the crossing domains of information service and distributed computing, and in particular to a kind of environment in cooperative learning
The middle method for recommending educational resource to group member.
Background technique
The method of traditional recommendation is recommended to individual mostly, however as expanding economy, Internet technology
It constantly reforms, more and more activities are completed by group in actual life, recommend all receptible project to group member
Become most important.
Group is recommended it is intended that one group of user provides recommendation, how to polymerize the preference of different members in group be it is most difficult but
It is also sixty-four dollar question.It is different from towards personal service, the service of Group-oriented there are some special practice challenges, because
For the preference for needing while considering all group members.In fact, most difficult challenge is how to polymerize different groups member
Preference.Although having done some researchs both at home and abroad in terms of preference polymerization, if preference polymerization and score polymerization, group at
Reciprocation and the conflict of interest between member are still ignored.Common polymerization can not find out in group's composition that all members can
With the optimal selection of receiving, unsatisfied service may cause.
In the environment of cooperative learning, recommend the research of all receptible educational resource also seldom to group member.Tradition
Group recommending method seldom consider the conflict of interest and interactivity between group member.Simple preference fusion be difficult to solve at
The conflict of interest between member, because the certain members of some projects miss potter but may be to be difficult to receive for other members
, simple preference fusion is not avoided that the such project of recommendation, not can solve the conflict of interest between member.Traditional group
Group member is not regarded as an entirety by group recommended method, but isolated come is seen.Really during group is recommended,
It should be to generate interaction between group member, member consider the acceptance level of other members of group when making a choice,
The selection made should maximize group's interests.However existing method does not consider this interaction.
Summary of the invention
Goal of the invention: in view of the deficiencies of the prior art, the present invention proposes a kind of group's educational resource based on Nash Equilibrium
Recommended method considers the conflict of interest between group member and establishes interactivity between group member, can be group member
Recommend all acceptable educational resource, improves group member to the satisfaction of recommendation effect.
Technical solution: in order to achieve the goal above, the present invention adopts the following technical scheme:
A kind of group's educational resource recommended method based on Nash Equilibrium, comprising the following steps:
S10, scoring of the group member to educational resource is obtained, is commented educational resource group member by matrix decomposition
Divide and is converted to approximate satisfaction；
S20, pay off function is set up to find Nash Equilibrium Solution according to approximate satisfaction, obtains each member to each strategy
The optimal selection probability of item；
S30, the preference that group is obtained by preference polymerization recommend the education money for meeting the preference for group member
Source.
Preferably, step S10 includes: that group member constitutes user's factor matrix, and member constitutes the scoring of educational resource
Project factor matrix, the two matrix multiples obtain all users and score the prediction of all items, as user to project
Approximate satisfaction.
Preferably, the step S10 further include: the low-rank approximation value of satisfaction matrix is calculated, with estimation individual to not seeing
See the preference of project.
Preferably, the step S20 includes:
S21, pay off function p (i, S are set upx) indicate member UiTo specific policy configuration file SxIncome:
Itemsim (j, k) is project I in formulajWith project IkSimilarity, R be member UiTo the satisfaction of project, | G | be
The quantity of member, itemsim are indicated are as follows:
S22, Nash Equilibrium point is found, at least one Nash Equilibrium, table can achieve to the simulation of individual choice in group
It is shown as:
NA=(NA1,...,NAG)
According to the last group member U of above formulaiIt will be showed in the form of optimal selection probability to the selection of project S, N table
Show the number of entry,Indicate member UiTo the select probability of j-th of project.
Preferably, the step S30 is by the latent space preference polymerization based on matrix decomposition, from evaluation space
Obtain final group's preference.
The utility model has the advantages that
1, recommended method of the invention can significantly improve group member to the satisfaction of educational resource, avoid in group
There is a minority to the unsatisfied situation of the educational resource of recommendation.
2, method of the invention really produces reciprocation between group member, with traditional group recommending method phase
The interactivity of user is embodied than being not simple by weighing factor, but group's composition is simulated by finding Nash Equilibrium Solution
The process of member's selection, this process are the effects for really producing interaction, and substantially increasing last preference fusion, are
The effect that group is recommended has laid extraordinary basis.
3, this method considers the conflict of interest between group member, between very good solution member to different educational
The acceptance level of resource, so that group member when making a choice, is not the favorite educational resource of simple consideration oneself, and
It is that can select the most suitable educational resource for entire group, substantially increases the effect of last preference fusion.
4, this method combines existing relatively good preference fusion method, very good solution group recommend in preference fusion
This maximum problem.And can be approached by low-rank matrix come the preference of smooth group member, to few members and residue
The different extreme preference of other members is filtered.And this method can also be controlled smoothly by the parameter in change method
Degree, accordingly even when having extreme member in group also has good recommendation effect.
Detailed description of the invention
Fig. 1 is the relational graph of group's educational resource recommended method based on Nash Equilibrium；
Fig. 2 is the work flow diagram based on Nash Equilibrium group educational resource recommended method.
Specific embodiment
Technical solution of the present invention is described further with reference to the accompanying drawing.
The present invention uses for reference the method that Nash Equilibrium Solution is found in game theory, with reference to existing group recommending method, really
The interactivity and the conflict of interest between group member are considered, by finding Nash Equilibrium Solution and using common preference fusion side
Method, which combines, recommends educational resource for group member, achievees the purpose that improve recommendation effect satisfaction.Referring to Fig.1, this method
Technical Architecture mainly include three parts: personal preference (Personalpreference), Nash Equilibrium (Nash
Equilibrium) and group's preference (Group preference), by setting up reasonable pay off function to personal preference
(Payoff function) solves the conflict of interest between group member, is simulated by finding the process of Nash Equilibrium Solution
The process of group member selection merges (Preference finally by preference so that generating interaction between group member
Aggregation final group's preference) is obtained, to recommend all receptible educational resource for group member.
Fig. 2 shows the flow charts based on Nash Equilibrium group educational resource recommended method.
Step S10 obtains scoring of the group member to educational resource, by matrix decomposition by group member to educational resource
Scoring be converted to approximate satisfaction.
In one embodiment, student prepares to write simply using the cooperation of Python programming language in the environment of cooperation
Function first allows each student to make scoring to educational resource (such as solve a problem practice and Working Examples), then will by matrix decomposition
Student is approximately personal preference of the student to educational resource to the scoring of educational resource.In the specific implementation, group member is constituted
One user's factor matrix, member constitute a project factor matrix to the scoring of educational resource, the two matrix multiples can be with
It obtains all users to score to the prediction of all items, in this, as user to the satisfaction of project.
Further, it can also estimate that individual to the preference for not seeing project, avoids omitting by setting up evaluating matrix
The potential strategy of some members.Its basic thought is that preference of the student to project is considered as to a sparse matrix, it is desirable to its sky
The value of cell is predicted, is consistent its value with satisfaction existing in matrix.This can be by calculating satisfaction square
The low-rank approximation value of battle array is realized.
Step S20 sets up pay off function according to approximate satisfaction to find Nash Equilibrium Solution, obtains each member to each
The optimal selection probability of policy entry.
Invention emulates a static non-cooperative game scenes with Complete Information, then find its Nash Equilibrium Solution.
The following steps are included:
Step S21 sets up suitable pay off function, considers acceptable journey when group member makes a choice to other members
Degree, this makes it possible to the conflict of interest for solving group member during finding Nash Equilibrium Solution, group member is being selected
When can consider other members in group actively for bigger income preference, rather than simple selection oneself it is favorite that
One project.
Member will obtain different incomes from different policing options in this method, with pay off function p (i, Sx) carry out table
The person of being shown as UiTo specific policy configuration file SxIncome, S herexRefer to the set of strategies of the selection to project:
Itemsim (j, k) is project I in formulajWith project IkSimilarity, R is member U obtained in step S10iTo item
Purpose satisfaction, | G | it is the quantity of member.
Itemsim can be indicated are as follows:
R (1:| G |, j) indicates R (1:j) ..., the transposition of R (| G |, j).
This pay off function means UiIncome can be obtained by interests expectation from the selection to project, there is this
A pay off function is just that the searching Nash Equilibrium Solution of next step lays a solid foundation, and ensures that depositing for Nash Equilibrium Solution
?.
Step S22 finds Nash Equilibrium point, in the case where having found Nash Equilibrium Solution, if other group members are not
Change factum, and the group member having one's choice also is unwilling to change the selection of oneself, then has reached Nash Equilibrium.Group
All members in group can obtain acceptable income from Nash Equilibrium Solution, and only Nash Equilibrium Solution can meet simultaneously
All members.And it can capture the interaction of member during group member makes a choice, find Nash Equilibrium Solution side
Method solves the conflict of interest between group member to the full extent.When reaching Nash Equilibrium Solution, group member is all unwilling
Actively change the strategy of itself, the state of a balance has just been reached between member.
According to Nash Equilibrium theorem it is found that if mixed strategy is received, the game with limited participant and strategy
At least one Nash Equilibrium.Therefore, the simulation that this method selects an individual in population can achieve at least one receive it is assorted
Equilibrium indicates are as follows:
NA=(NA1,...,NAG)
According to the last group member U of above formulaiIt will be showed in the form of optimal selection probability to the selection of project S.
The quantity of participant and the quantity of strategy are limited, and member selection is allowed to have the strategy of probability.For example, U1It can choose general
The optimal item I that rate is 0.43, select probability be 0.6 another optimal item I5.N indicates the number of entry, NAjI indicates member UiIt is right
The select probability of j-th of project after each member makes a choice, calculates income, income obtained will not be high again, and member is just
The strategy that motivation changes oneself is not had, this has just reached Nash Equilibrium.
Step S30 obtains the preference of group by preference polymerization, recommends the religion for meeting the preference for group member
Educate resource.
After reaching Nash Equilibrium, group member is an optimum probability distribution to the selection of educational resource, so needing logical
The preference that preference polymerization obtains group to the end is crossed, the present invention uses the latent space preference polymerization side based on matrix decomposition
Method obtains final group's preference in evaluation space.
Every group of optional project/strategy is expressed as latent space first, is decomposed herein using singular value matrix:
A is member characteristic matrix, and D is diagonal weight matrix, and V is policy characteristics matrix.| G | number of members, | IS | project
Quantity.
Further, the effect for reducing dimension can be reached approximately by low order matrix:
W indicates the quantity of residue character, and D (k, k) indicates that k multiplies the diagonal matrix of k.Parameter alpha controls smoothness or denoising journey
Degree, for example, working as α smaller (w is also smaller), smoothness is bigger.This process is necessary, especially when the preference of member occurs very
When big conflict.
Then, in order to which by integrating equilibrium solution, group membership's sets of preferences in the latent space after decomposition is got up, we will
Each group of ideal item Feature prototype (being expressed as IFP) is defined as:
In preference smoothly and after aggregation, IFP can be considered as the ideal item in latent factor space.
Then the project grading prototype of defining ideal are as follows:
IIP is the ideal item or prototype for polymerizeing single preference in grading space.
Result to the end is obtained finally by the distance for calculating ideal project:
In order to measure each candidate item IjDifference/similitude between IIP, we are by ideal item distance IID (Ij, IIP)
It calculates are as follows:
IID(Ij, IIP)=| | R (1:| G |, Ij)-IIP||2
||·||2Indicate Euclid's normal form.
The polymerization is with two big advantages: first, it is concluded that the feature of group's preference, inclined rather than just group
Good scoring, because a pair of similar project can have different scorings but should have similar feature.Second, energy
It is enough to be approached by low-rank matrix come the preference of smooth group member, the extreme preference of few members and other members were carried out
Filter.It also can control smoothness by the parameter in change method.Thus reach and recommends educational resource towards group member
Purpose can be good at improving group member to the satisfaction for recommending educational resource.
Claims (6)
1. a kind of group's educational resource recommended method based on Nash Equilibrium, which is characterized in that the described method comprises the following steps:
S10, scoring of the group member to educational resource is obtained, is turned group member to the scoring of educational resource by matrix decomposition
It is changed to approximate satisfaction；
S20, pay off function is set up to find Nash Equilibrium Solution according to approximate satisfaction, obtains each member to each policy entry
Optimal selection probability；
S30, the preference that group is obtained by preference polymerization recommend the educational resource for meeting the preference for group member.
2. group's educational resource recommended method according to claim 1 based on Nash Equilibrium, which is characterized in that the step
Rapid S10 includes: that group member constitutes user's factor matrix, and member constitutes project factor matrix to the scoring of educational resource, this two
A matrix multiple obtains all users and scores the prediction of all items, as user to the approximate satisfaction of project.
3. group's educational resource recommended method according to claim 1 based on Nash Equilibrium, which is characterized in that the step
Rapid S10 further include: the low-rank approximation value of satisfaction matrix is calculated, with estimation individual to the preference for not seeing project.
4. group's educational resource recommended method according to claim 1 based on Nash Equilibrium, which is characterized in that the step
Suddenly S20 includes:
S21, pay off function p (i, S are set upx) indicate member UiTo specific policy configuration file SxIncome:
Itemsim (j, k) is project I in formulajWith project IkSimilarity, R be member UiTo the satisfaction of project, | G | it is member
Quantity, itemsim indicate are as follows:
S22, Nash Equilibrium point is found, at least one Nash Equilibrium can achieve to the simulation of individual choice in group, indicated are as follows:
NA=(NA1,...,NA|G|)
According to the last group member U of above formulaiIt will be showed in the form of optimal selection probability to the selection of project S, N indicates item
Mesh number amount,Indicate member UiTo the select probability of j-th of project.
5. group's educational resource recommended method according to claim 1 based on Nash Equilibrium, which is characterized in that the step
Rapid S30 obtains final group's preference by the latent space preference polymerization based on matrix decomposition from evaluation space.
6. group's educational resource recommended method according to claim 5 based on Nash Equilibrium, which is characterized in that the base
In matrix decomposition latent space preference polymerization the following steps are included:
S31, every group of optional project/strategy is expressed as latent space, is decomposed using singular value matrix:
A is member characteristic matrix, and D is diagonal weight matrix, and V is policy characteristics matrix；| G | number of members, | IS | the number of entry；
S32, the effect for reducing dimension is reached approximately by low order matrix, wherein w indicates the quantity of residue character:
The project grading prototype of S33, defining ideal are as follows:
S34, result to the end is obtained by calculating the distance of ideal project:
IID(Ij, IIP)=| | R (1:| G |, Ij)-IIP||2
Wherein | | | |2Indicate Euclid's normal form.
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