1. The European Conference on e-learing ，2017/10
On Predicting Student Performance Using Low-Rank Matrix Factorization Techniques
Stephan Lorenze University of Copenhagen
The European Conference on e-learing ，2017/10

2. Question
Analysis
DataSet

3. Accurate prediction of Student’s abilities
Purpose
Teachers provide remedial support to weak students and to recommend appropriate tasks to excellent students.
Accurate prediction of Student’s abilities

4. how a student perform on an unseen quiz
Question
predicting the score of students in the quiz system of the Clio Online learning platform
how a student perform on an unseen quiz
Matrix completion

5. A conclusion
We conclude that since the active students in the platform perform very similar and the current version of the data set is very sparse, the very low-rank approximation can capture enough information.

6. assumption
there are a small number of latent features revealing the students and tasks preferences.
Such assumption is natural and has been widely used in research and application work in educational data (Barnes 2005; Desmarais 2011; van der Linden and Hambleton 2010, Bydzovska 2016 ).
It is worth noting that there are prior work using matrix factorization for predicting student performance (Desmarais 2011; Elbadrawy et al. 2016; Thai- Nghe et al. 2010).
Since matrix factorization in general requires iterative methods (Koren, Bell and Volinsky 2009; Lee and Seung 2000; Srebro and Jaakkola 2003) to solve the non- convex optimization, the initialization stage is essential in the design of successful methods.

7. Further
If we do not restrict the number of degrees of freedom in the completed matrix, this problem is underdetermined since we can assign any arbitrary values to the missing entries. Therefore, one often tries to estimate a low-rank matrix from the sparse,observed matrix
we can cast the matrix completion problem as the weighted low-rank matrix factorization (LRMF)

8. Therefore the weighted
low-rank matrix factorization (LRMF) where the weights are 1s for observed entries and 0s for missing entries

9. Function
standard weighted LRMF
weighted non-negative LRMF

10. Contribution
We view the problem of predicting the scores of students from their partial observed scores as the weighted LRMF problem. We study the well-known Expectation-Maximization procedure (EM) (EM algorithm n.d.) for solving it.
We investigate the non-negative constrained problem, i.e. all entries of the estimated low-rank matrices U, V are non-negative, and make use of the EM method for solving the non-negative constrained problem.
Since the behaviour of the EM method is sensitive to the initial values, we propose using the singular value decomposition (SVD) (Golub and Loan 1999) and the non-negative double SVD (Boutsidis and Gallopoulos 2008) as the initialization stages for the standard weighted and non-negative weighted LRMF, respectively. Experimental results show that the proposed initialization methods lead to fast convergence ratio for both constrained and non-constrained problems.

11. Contribution
We implement and measure the performance of the proposed methods on new real-life data from a Clio Online learning platform. We compare the mean squared error of the EM method with the simple baseline approach based on the global mean score and student/quiz bias. Surprisingly, the advanced EM method is only slightly better or comparable to the baseline approach. We visualize the eigenvalue spectrum of a dense subset of the data set to explain our interesting findings.
We conclude that since the active students in the platform perform very similarly and the current version of the data set is very sparse, the very low-rank approximation can capture enough information. This means that the simple baseline approach (rank at most 2) achieves similar performance compared to other advanced methods. We believe that by restricting the quiz data set, e.g. only including quizzes with a time limit, students will behave differently and the advanced EM methods might improve the prediction accuracy

12. DATA
data from the Danish online learning platform Clio Online (Clio Online n.d.)
all repeated attempts at the same quiz are removed, so that only the first attempt remains.
the data consists of a list of tuples (i,j,v)
Their platform includes texts, videos, quizzes, exercises, and more, spanning several different elementary school subjects. We study the performance of students on the quizzes

13. Process the DataSet What we get A large sparse matrix
So extract a subset of the data until
Each student si, the set contains at least 15 tuples for that student, and for each quiz qj, the set contains at least 15 tuples for that quiz. This means that each student/quiz has at least 15 answers
The resulting data set contains data for n = 1141 students and m = 245 quizzes.