Research On The Application Of Binary Matrix Completion In Personalized Learning

Educational Data Mining(EDM)is a cross-research field of data mining,machine learning,statistical measurement and educational psychology.EDM aims to mine the large amount of data of students learning behave or relate automatically from educational scenarios,and obtain the inherent information of education and learning,so as to better serve the teachers and learners.In many applications of this field,predicting students'learning behaviors and finding or improving existing forecasting models are very challenging research topics.The analysis of student feedback data is a very meaningful research work.On the one hand,it can help students to do questions targetedly and improve learning efficiency.On the other hand,educators can better understand the students' performance and learning process according to the analysis results,so as to achieve the improvement of teaching methods.However,due to the absence of the system or the fact that the students have not done some problems,many feedback data are missing,which has caused great difficulties to the researchers.Prediction of missing data is a typical matrix completion problem.Classical research methods can be used to predict and complete missing data,such as alternating direction method of multipliers and singular value thresholding.But most of the current matrix completion methods are performed in the real number domain.The feedback data of students is usually a binary matrix composed of 0 or 1,whereas there are few studies on missing data completion of binary matrix.In this paper,the main research topic is to predict and complement the missing data of binary valued matrix.This paper is based on previous research,and the research work is divided into two parts:In the first part,we compare the classical matrix completion method,and propose the SPARFA-Zero algorithm based on the sparse factor analysis model.Since the SPARFA-Zero algorithm avoids the problem of complex parameter selection and simplifies the gradient projection method,it can reduce the running time of the algorithm without affecting the decrease of matrix complementation accuracy.However,the output of this algorithm is a numerical value in the form of a probability.In the second part,according to the project response theory,clustering algorithms in machine learning and the potential characteristics of student test questions,We propose a personalized completion method of binary valued matrix based on fuzzy C means model(BMPC-FCM)and make binary discretization processing of the output of matrix completion result.The algorithms proposed in this paper are validated on the simulated data and real data sets respectively,we use some standards such as TIME,COR,AUC and LIK to evaluate the effectiveness and feasibility of the proposed methods.Experimental results show that the SPARFA-Zero algorithm proposed in this paper improves the running speed,the BMPC-FCM method not only makes the result of matrix completion be a binary valued matrix of 0-1 form,but also improves the accuracy of matrix completion.