Random Sampling Effects on e-Learners Cluster Sizes Using Clustering Algorithms

Abstract

e-Learners represent an increasing audience and a target of most higher education institutions (that include universities and colleges). However, few studies focus on their progress and interactions during the learning process through various educational tools. This study looks at the assessment of e-learners for Open University Learning Analytics in the UK. This paper deploys a model-based clustering and The Bayesian Information Criterion for k-means (BIC) to support the classification (e.g. density-based clustering and k-means) and definition of the cluster size. The study found out that, during assessment, students might belong to two to three clusters. The novelty of this study lies in its initial deployment of unsupervised learning (model-based clustering) to discover the number of clusters amongst on-line learners. Secondly, the study tests the validity of clusters by applying two algorithms - k-means and density-estimate clustering - when randomly splitting a training set by 40% and 60%. This form of semi-supervised learning (that meant assigning the number of clusters to k-means algorithms and density estimate clustering) was used to test the effect of two clustering algorithms (e.g. the Density clustering and K-means algorithms) on the cluster size by fixing the sample number and the percentage when splitting the dataset. While an exception, the cluster percentage case only occurs with two clusters and when using a density estimation clustering method. Thus, both algorithms, k-means and density-based clustering using k-means, have a similar effect on the cluster sizes, with the exception of the density-based method when clustering two clusters.