CN105512770A - Student ability prediction method based on hybrid decomposition technology - Google Patents

Abstract

The invention relates to a student ability prediction method based on a hybrid decomposition technology, comprising the following steps: establishing a training set matrix based on the performance of a learner in a training set; predicting the learner by use of a matrix decomposition method; using a deviation matrix decomposition model to correct user deviation and task deviation; and predicting possible performance of the student in other tasks, and recommending an appropriate task for the learner. Thus, the learning efficiency of learners is improved, and time is saved for learners. The method can be applied to an education recommendation system.

Description

A kind of student ability Forecasting Methodology based on hybrid decomposition technique

Technical field

The invention belongs to educational data excavation applications, further relate to the prediction of student performance, specifically a kind of method predicting student ability based on hybrid decomposition technique.

Background technology

Commending system is widely used in every field, especially in ecommerce.One of its fundamental purpose is liked by the history of user, dopes user to the interested degree of their sundry item, after knowing that user is interested in which product, just can recommend for them.At present, commending system also starts to be applied in e-learning field.Educational data method for digging comes from the process extracting meaningful data in educational system, and the potential information excavated in these data can provide service for educator, learner, supvr etc.In current educational system, a main data mining task is prediction student performance, in this task, we need to understand student be how to learn, student adapts to the speed degree of a new problem, or whether likely directly infer from student performance data its to deal with problems required for the knowledge that possesses.When system can after their performance of Accurate Prediction, can be just that they recommend more suitably exercise or task.Like this, we can filter out the task of having better performance because of too simple, or filter out the task of having poor performance because of too difficult.

Many commending systems relate to education sector, specifically:

The people such as Garacia utilize correlation rule to excavate useful information by the student performance of IF-THEN rule format in paper " Anarchitectureformakingrecommendationstocoursewareauthor susingassociationruleminingandcollaborativefiltering " (" UserModelingandUser-AdaptedInteraction "), produce recommend according to these rules;

The people such as Ge propose to carry out personalized recommendation course selection module in conjunction with Cempetency-based education and collaborative filtering at paper " CoursewareRecommendationinE-LearningSystem " (" InternationalConferenceonWeb-basedLearning ").

The people such as Khribi adopt content-based Web digging technology and collaborative filtering to carry out technology at paper " AutomaticRecommendationsforE-LearningPersonalizationBase donWebUsageMiningTechniquesandInformationRetrieval " (" Proceedingsofthe8thIEEEInternationalConferenceonAdvanced LearningTechnologies ") and recommend learner's peer link.

In the problem of student performance prediction, also there is correlative study:

The people such as Romero in paper " DataMiningAlgorithmstoClassifyStudents " (" 1stInternationalConferenceonEducationalataMining ") more different data digging method and technology (as neural network, decision tree, genetic algorithm etc.), based on the data that student uses in Moodle system, final mark is added in respective course.

Bekele and Menzel uses Bayesian network to predict student's result at paper " ABayesianApproachtoPredictPerformanceofaStudent (BAPPS): ACasewithEthiopianStudents " (" ArtificialIntelligenceandApplications ").

More than predict that the method for student performance is also short of to some extent in the accuracy of prediction, seldom consider the dependent latency of user.

Summary of the invention

The object of the invention is to the deficiency overcoming above-mentioned prior art, a kind of student ability Forecasting Methodology based on hybrid decomposition technique is proposed, existing performance according to learner predicts the outcome, suitable exercise scheme is recommended to it, thus save the quality time of learner, improve the learning efficiency of learner.

To achieve these goals, the technical solution adopted in the present invention comprises the following steps:

(1) matrix model X is set up, X ∈ R ^{u × I}be original two-dimensional matrix, U represents the student in training set, and I represents task corresponding to training set middle school student;

(2) the matrix model X of step (1) is decomposed, X ≈ WH ^t, obtain matrix W and matrix H;

Wherein: W ∈ R ^{u × K1}be a matrix, K1 is the latent factor quantity of test set Middle school students ' learning ability, H ∈ R ^{i × K2}be a matrix, K2 is the latent factor quantity of task in test set;

(3) obtain test set student according to following formula (1) to attempt first time whether successfully predicting the outcome;

${\hat{p}}_{ui}=\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}={\left({\mathrm{WH}}^T\right)}_{u,i}---\left(1\right)$

represent test set middle school student attempt whether successfully predicting the outcome first time; w _ukand h _ikbe respectively the element of W and H, K=K1=K2;

(4) attempt first time whether successfully predicting the outcome and the actual result p of training set middle school student with the test set middle school student of step (3) gained _uicompare, calculate the error amount err of prediction;

$err=\underset{(u,i)\∈D^{train}}{\Σ}{(p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik})}^2---\left(2\right)$

D ^trainit is training set;

(5) adopt gradient descent method determination training set medial error minimum value, the computing formula of gradient descent method is:

$\frac{\∂}{\∂w_{uk}}{e^2}_{ui}=-2e_{ui}{h}_{ik}=-2(p_{ui}-{\hat{p}}_{ui})h_{ik}---\left(3\right)$

$\frac{\∂}{\∂h_{ik}}{e^2}_{ui}=-2e_{ui}{w}_{uk}=-2(p_{ui}-{\hat{p}}_{ui})w_{uk}---\left(4\right)$

Wherein $e_{ui}=p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}.$

(6) according to the error minimum value in step (5) gained training set, the learning ability utilizing following formula (5) and (6) to calculate each student in test set predicts the outcome;

${w^{\′}}_{uk}=w_{uk}-\mathrm{\β}\frac{\∂}{\∂w_{uk}}{e^2}_{ui}=w_{uk}+2{\mathrm{\βe}}_{ui}{h}_{ik}---\left(5\right)$

$h_{ik}^{\′}=h_{ik}-\mathrm{\β}\frac{\∂}{\∂h_{ik}}{e^2}_{ui}=h_{ik}+2{\mathrm{\βe}}_{ui}{w}_{uk}---\left(6\right)$

β is learning rate, and value is 0.15;

(7) by adding standardizing factor, predict the outcome to step (6) calculating gained and correct, updating formula is:

${{\hat{p}}_{ui}}^{\′}={(p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik})}^2+\mathrm{\λ}\left(\right|\left|W\right|{|}^2+\left|\right|H\left|{|}^2\right)---\left(7\right)$

Wherein: λ is regularization parameter;

Obtain the comparatively figure of merit that test set middle school student u attempts the first time of Given task i whether successfully predicting the outcome

Step (8) is also comprised, specifically: what whether successfully predict the outcome in the first time trial of step (7) gained adds student deviation b compared with on the basis of the figure of merit after above-mentioned steps (7) _uwith task deviation b _i, obtain the prediction optimal value that test set middle school student finish the work

${\hat{p}}_{ui}=\mathrm{\μ}+b_u+b_i+{{\hat{p}}_{ui}}^{\′}$

Wherein: μ represents the mean value of prediction, b _urepresent the degree of student's deviation average, b _ithe degree of expression task deviation average.

Above-mentioned μ, b _uand b _icomputing formula be respectively:

$\mathrm{\μ}=\frac{{\Σ}_{p\∈D^{train}}p}{\left|D^{train}\right|}$

$b_u=\frac{{\Σ}_{p^u\∈D^{train}}(p^u-\mathrm{\μ})}{|p^u\∈D^{train}|}$

$b_i=\frac{{\Σ}_{p^i\∈D^{train}}(p^i-\mathrm{\μ})}{|p^i\∈D^{train}|}$

Wherein: P is training set D ^trainin mean predicted value, p ^ufor training set D ^trainin student's deviation, p ⁱfor training set D ^trainin task deviation.

Student ability Forecasting Methodology based on hybrid decomposition technique of the present invention, it is based on the performance of learner in training set, set up training set matrix, matrix decomposition method is utilized to predict learner afterwards, deviation matrix decomposition model is adopted to correct user's deviation and task deviation again, dope this student may show in other tasks, thus recommend suitable task for learner, thus improve the learning efficiency of learner and save the time of learner, can be applied in education commending system, compared with prior art the present invention mainly has the following advantages:

First, because the present invention adopts the method for matrix decomposition to predict student performance, to compare traditional sorting technique or homing method, matrix decomposition technology can consider a lot of latency, therefore the importance of proposed method does not just dope student performance, also can recommend the task of their level of learning applicable for student, and can to dope which task to them are difficulties or simple.Such as, have the exercise database that huge, student loses a large amount of time because exercise is too difficult or too simple.When system can predict their performance, can recommend more suitably to practise for them.

Second, because the present invention considers student's deviation and task deviation, in fact predicted data a lot changes due to the impact separately of student or task self, student's qualification difference and task difficulty difference all can have influence on and predict the outcome, therefore student's deviation and task deviation are concerning being an important factor prediction, can make like this to predict the outcome more accurate.

Embodiment

Now be described the student ability Forecasting Methodology based on hybrid decomposition technique of the present invention, it is specifically realized by following steps in conjunction with the embodiments:

(1) matrix model X is set up, X ∈ R ^{u × I}be original two-dimensional matrix, U represents the student in training set, and I represents task corresponding to training set middle school student.

Give one example, as table 1shown in, suppose that training set is the two-dimensional matrix X that 6 students and 5 exercises (task) form.Each task is the value calculating y when a given particular value x, such as y=-2x, and student has completed some tasks, and first time attempts solving this Mission Success and is denoted as 1, mistakebe denoted as 0.Whether the problem that will solve now is: dope student and attempt successful to the task first time that they did not do.

table 1the row of training set table

(2) matrix model X is decomposed, X ≈ WH ^t, obtain matrix W and matrix H;

Matrix decomposition technology is that a matrix decomposition is become two or more forms be multiplied compared with minor matrix, and the subject matter of this technology how to find a best parameter W and H given rule.

Wherein: W ∈ R ^{u × K1}be a matrix, K1 is the latent factor quantity of test set Middle school students ' learning ability, H ∈ R ^{i × K2}be a matrix, K2 is the latent factor quantity of test set task;

(3) obtain test set student according to following formula to attempt first time whether successfully predicting the outcome;

${\hat{p}}_{ui}=\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}={\left({\mathrm{WH}}^T\right)}_{u,i}---\left(1\right)$

represent test set middle school student attempt whether successfully predicting the outcome first time; w _ukand h _ikbe respectively the element of W and H; K=K1=K2;

(4) attempt first time whether successfully predicting the outcome and the actual result p of training set middle school student with the test set middle school student of step (3) gained _uicompare, calculate the error amount err of prediction,

$err=\underset{(u,i)\∈D^{train}}{\Σ}{(p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik})}^2---\left(2\right)$

D ^trainit is training set;

(5) adopt gradient descent method determination training set medial error minimum value, wherein most crucial step is exactly obtain the partial derivative of each variable in formula, and the computing formula of gradient descent method is:

$\frac{\∂}{\∂w_{uk}}{e^2}_{ui}=-2e_{ui}{h}_{ik}=-2(p_{ui}-{\hat{p}}_{ui})h_{ik}---\left(3\right)$

$\frac{\∂}{\∂h_{ik}}{e^2}_{ui}=-2e_{ui}{w}_{uk}=-2(p_{ui}-{\hat{p}}_{ui})w_{uk}---\left(4\right)$

Wherein: $e_{ui}=p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}.$

(6) utilize the error minimum value in the training set of step (5) gained, the learning ability being obtained each student in test set by following formula is predicted the outcome.Can in the hope of the local minimum of function along the negative gradient direction of certain variable at function point place by gradient descent method.

${w^{\′}}_{uk}=w_{uk}-\mathrm{\β}\frac{\∂}{\∂w_{uk}}{e^2}_{ui}=w_{uk}+2{\mathrm{\βe}}_{ui}{h}_{ik}---\left(5\right)$

$h_{ik}^{\′}=h_{ik}-\mathrm{\β}\frac{\∂}{\∂h_{ik}}{e^2}_{ui}=h_{ik}+2{\mathrm{\βe}}_{ui}{w}_{uk}---\left(6\right)$

β is learning rate, for this data set value 0.15.

(7) in order to prevent overfitting, the present invention improves error function, the basis of err function is added its standardizing factor, makes WH ^tcan obtain good approximation with X, and need not comprise a large amount of sundry items, correct predicting the outcome of step (6), updating formula is:

${{\hat{p}}_{ui}}^{\′}={(p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik})}^2+\mathrm{\λ}\left(\right|\left|W\right|{|}^2+\left|\right|H\left|{|}^2\right)---\left(7\right)$

Wherein: λ is regularization parameter;

Obtain the comparatively figure of merit that student u attempts the first time of Given task i whether successfully predicting the outcome

${{\hat{p}}_{ui}}^{\′}=\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}.$

(8) the first time of step (7) gained attempt whether successfully predicting the outcome compared with the basis of the figure of merit being added student deviation bu and task deviation bi, thus obtain optimal value.Because much other changes may be also had in score value to be the independent impacts due to user or project, they are referred to as deviation, and in educational environment, user's deviation and project deviation correspond to student's deviation and task deviation respectively.Because student's qualification is different, the student of qualification difference compared to pass student for same task, its performance may be more far short of what is expected than the performance of pass student, or extremely clever student compared to pass student for same task, its performance may be well more a lot of than pass student.Equally, task also has deviation, the very difficult task that all student can not solve, or the simple task that all student can solve, and it predicts the outcome and also has impact.Specifically:

${\hat{p}}_{ui}=\mathrm{\μ}+b_u+b_i+{{\hat{p}}_{ui}}^{\′}$

Wherein: μ represents the mean value of prediction, b _urepresent the degree of student's deviation average, b _ithe degree of expression task deviation average;

$\mathrm{\μ}=\frac{{\Σ}_{p\∈D^{train}}p}{\left|D^{train}\right|}$

$b_u=\frac{{\Σ}_{p^u\∈D^{train}}(p^u-\mathrm{\μ})}{|p^u\∈D^{train}|}$

$b_i=\frac{{\Σ}_{p^i\∈D^{train}}(p^i-\mathrm{\μ})}{|p^i\∈D^{train}|}$

Wherein: P is training set D ^trainin mean predicted value, p ^ufor training set D ^trainin student's deviation, p ⁱfor training set D ^trainin task deviation.

The latent factor number setting student and task in the training stage is K=2, by having calculated optimum matrix W and H, sees respectively table 2shown in 3.

table 2calculate the row of gained Optimal matrix W table

Zhang San	0.64	0.75
			Li Si	0.66	0.75
Xiao Ming	0.70	0.69
			Little Hua	0.90	0.94
Little red	0.27	0.93
			Little Huang	0.75	0.64

table 3for calculating the row of gained Optimal matrix H table

y＝3x-4	y＝-2x	y＝1/x	y＝-x-1	y＝x
					0.71	0.51	1.02	0.36	0.72
0.70	0.56	0.41	0.96	0.69

The performance value of prediction Xiao Ming to task y=-x-1 is: $\hat{p}=\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}=0.7*0.36+0.69*0.96=\mathrm{0.91.}$

Predict the outcome from this and can see that Xiao Ming can correctly have very high confidence (0.91) to finish the work.

In a similar fashion, can also predict that other students are to still abortive performance.In addition, make in this way, not only can predict student performance, similar task (exercise) or any task difficult a little can also be recommended to student.Such as, have the exercise database that huge, student wastes them and solves too difficulty or too simple question the most of the time, can by the performance of prediction student, and system just can automatically for they recommend suitable exercise.

Claims (3)

1., based on a student ability Forecasting Methodology for hybrid decomposition technique, it is characterized in that comprising the following steps:

(1) matrix model X is set up, X ∈ R ^{u × I}be original two-dimensional matrix, U represents the student in training set, and I represents task corresponding to training set middle school student;

(2) the matrix model X of step (1) is decomposed, X ≈ WH ^t, obtain matrix W and matrix H;

Wherein: W ∈ R ^{u × K1}be a matrix, K1 is the latent factor quantity of test set Middle school students ' learning ability, H ∈ R ^{i × K2}be a matrix, K2 is the latent factor quantity of task in test set;

(3) obtain test set student according to following formula (1) to attempt first time whether successfully predicting the outcome;

${\hat{p}}_{ui}=\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}={\left({\mathrm{WH}}^T\right)}_{u,i}---\left(1\right)$

represent test set middle school student attempt whether successfully predicting the outcome first time; w _ukand h _ikbe respectively the element of W and H, K=K1=K2;

(4) attempt first time whether successfully predicting the outcome and the actual result p of training set middle school student with the test set middle school student of step (3) gained _uicompare, calculate the error amount err of prediction;

$err=\underset{(u,i)\∈D^{train}}{\Σ}{(p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik})}^2---\left(2\right)$

D ^trainit is training set;

(5) adopt gradient descent method determination training set medial error minimum value, the computing formula of gradient descent method is:

$\frac{\∂}{\∂w_{uk}}{e^2}_{ui}=-2e_{ui}{h}_{ik}=-2(p_{ui}-{\hat{p}}_{ui})h_{ik}---\left(3\right)$

$\frac{\∂}{\∂h_{ik}}{e^2}_{ui}=-2e_{ui}{w}_{uk}=-2(p_{ui}-{\hat{p}}_{ui})w_{uk}---\left(4\right)$

Wherein $e_{ui}=p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik}$

(6) according to the error minimum value in step (5) gained training set, the learning ability utilizing following formula (5) and (6) to calculate each student in test set predicts the outcome;

$w_{uk}^{\′}=w_{uk}-\mathrm{\β}\frac{\∂}{\∂w_{uk}}{e^{\′}}_{ui}=w_{uk}+2{\mathrm{\βe}}_{ui}{h}_{ik}---\left(5\right)$

$h_{ik}^{\′}=h_{ik}-\mathrm{\β}\frac{\∂}{\∂h_{ik}}{e^2}_{ui}=h_{ik}+2{\mathrm{\βe}}_{ui}{w}_{uk}---\left(6\right)$

β is learning rate, and value is 0.15;

(7) by adding standardizing factor, predict the outcome to step (6) calculating gained and correct, updating formula is:

${{\hat{p}}_{ui}}^{\′}={(p_{ui}-\underset{k=1}{\overset{K}{\Σ}}{w}_{uk}{h}_{ik})}^2+\mathrm{\λ}\left(\right|\left|W\right|{|}^2+\left|\right|H\left|{|}^2\right)---\left(7\right)$

Wherein: λ is regularization parameter;

Obtain the comparatively figure of merit that student u attempts the first time of Given task i whether successfully predicting the outcome

2. the student ability Forecasting Methodology based on hybrid decomposition technique according to claim 1, is characterized in that: after step (7), also comprise step (8), specifically:

The comparatively figure of merit whether successfully predicted the outcome is attempted in the first time of step (7) gained basis on add student deviation b _uwith task deviation b _i, obtain the prediction optimal value that test set middle school student finish the work

${\hat{p}}_{ui}=\mathrm{\μ}+b_u+b_i+{{\hat{p}}_{ui}}^{\′}$

Wherein: μ represents the mean value of prediction, b _urepresent the degree of student's deviation average, b _ithe degree of expression task deviation average.

3. the student ability Forecasting Methodology based on hybrid decomposition technique according to claim 2, is characterized in that: described μ, b _uand b _icomputing formula be respectively:

$\mathrm{\μ}=\frac{{\mathrm{\Σ}}_{p\∈D^{train}}p}{\left|D^{train}\right|}$

$b_u=\frac{{\mathrm{\Σ}}_{p^u\∈D^{train}}(p^u-\mathrm{\μ})}{|p^u\∈D^{train}|}$

$b_i=\frac{{\mathrm{\Σ}}_{p^i\∈D^{train}}(p^i-\mathrm{\μ})}{|p^i\∈D^{train}|}$

Wherein: P is training set D ^trainin mean predicted value, p ^ufor training set D ^trainin student's deviation, p ⁱfor training set D ^trainin task deviation.