Visualization of Clusters in an Educational Data Set Based on Convex-Hull Shape Preservation Algorithm

摘要

We study the problem of visualization of clusters in an educational data set based on convex-hull shape preservation algorithm. This problem considers multidimensional data with preestablished classes with the requirement of elements of different classes must be presented at distinctive regions. Such problem is commonly found on economic and social data, where visualization is important to understand a phenomenon before further analysis. In this paper, we propose an algorithm that uses a nonlinear transformation to preserve some data distance properties and display in a convenient format to interpretation. The proposed visualization algorithm is a partition-conforming projection, as defined by Kleinberg [An impossibility theorem for clustering, Adv. Neural Inform. Processing Syst. 15: Proc. 2002 Conf., 2003, The MIT Press, p. 463.], and completely separates the convex hull of data classes by applying locally linear operations. We applied this algorithm to visualize data from an important exam applied for over four million students of the Brazilian educational system Exame Nacional do Ensino Medio (ENEM). Results show that the proposed algorithm successfully separates unintelligible data and presents it more accessible to further visual analysis.