Visualizing Symbolic Data by Closed Shapes

Abstract

In the framework of Factorial Data Analysis on Symbolic Objects (SO’s), we propose new kinds of SO’s visualizations on factorial planes alternative to rectangular shapes (Minimum Covering Area Rectangle MCAR). MCAR were mainly proposed in PCA on SO’s to represent in reduced bi-dimensional subspace symbolic data described by interval variables and represented by hypercubes. The new representations of SO’s are based on the convex hulls (CH) of the projected hypercube vertices. In particular, we propose a compromise between the MCAR and CH visualizations by means of particular closed shapes, that contains the CH and it is contained by MCAR. The main advantage of this kind of SO representation is its interpretation and lower over-fitting than MCAR. Furthermore, some indexes of quality of representation and over-fitting are developed.