A Clustering Method using Entropy for Grouping Students

Abstract

This study suggests a novel clustering method using entropy in information theory for setting cut-scores. Based on item response vectors from the examinees, we construct the Ordered Item Booklets (OIBs) based on the Rasch model which is a kind of Item Response Theory (IRT). The approach of the proposed method is to partition the scores into n-clusters and to construct probability distribution tables separately for each cluster from the item response vector. Using these probability distribution tables, mutual information and relative entropy (Kullback-leibler divergence) were computed between each of the clusters and then cut-scores were determined by the cluster’s partition to minimize mutual information values. Experimental results show that the approach of this proposed entropy method has a realistic possibility of application as a clustering evaluation method.