Modeling and Analysis of Students’ Performance Trajectories using Diffusion Maps and Kernel Two-Sample Tests

Modeling and analysis of students’ performance is a common task that is aimed at identifying important factors that affect the learning process. Typically, the analysis uses one-dimensional input parameters. However, with the advancement of data collections tools, many of the gathered educational datasets have become high-dimensional. Hence, the use of standard statistical methods may be limited in cases that the initial data unit is a vector. This paper proposes to use vector input units, which consist of student performance trajectories, for identifying statistical differences in college performances for several populations of college students. Two kernel based methods named diffusion maps and the kernel two-sample test are utilized. Diffusion maps generates a low-dimensional representation of the data, in which important characteristic factors are identified. The kernel two-sample test is a statistical test for comparing whether high-dimensional samples are drawn from two different probability distributions. The two methods are combined into a unified framework. Two case studies, which are processed similarly, are presented. The first tests for significant distributional differences between students with or without learning disabilities. Our results show that these groups’ performances is significantly different. The second case-study analyzes whether the SAT score impacts students’ performance throughout their 4-year of studies. It was found that significant distribution differences in performance are only present for groups of students having a very high or a very low SAT score. Thus, the SAT score is only weakly correlated to students’ college performance.