Exploring Common and Individual Characteristics of Students via Matrix Recovering

TL;DR

This paper introduces a matrix recovering framework that simultaneously identifies shared group characteristics and individual traits of students, enhancing personalized education strategies.

Contribution

It proposes a novel matrix decomposition approach combining low-rank and sparse matrices to detect both common and individual student characteristics.

Findings

Effectively detects meaningful student groups similar to state-of-the-art biclustering.

Identifies individual student characteristics alongside group patterns.

Demonstrates the method's effectiveness through experiments.

Abstract

Balancing group teaching and individual mentoring is an important issue in education area. The nature behind this issue is to explore common characteristics shared by multiple students and individual characteristics for each student. Biclustering methods have been proved successful for detecting meaningful patterns with the goal of driving group instructions based on students' characteristics. However, these methods ignore the individual characteristics of students as they only focus on common characteristics of students. In this article, we propose a framework to detect both group characteristics and individual characteristics of students simultaneously. We assume that the characteristics matrix of students' is composed of two parts: one is a low-rank matrix representing the common characteristics of students; the other is a sparse matrix representing individual characteristics of students. Thus, we treat the balancing issue as a matrix recovering problem. The experiment results show the effectiveness of our method. Firstly, it can detect meaningful biclusters that are comparable with the state-of-the-art biclutering algorithms. Secondly, it can identify individual characteristics for each student simultaneously. Both the source code of our algorithm and the real datasets are available upon request.