Exploratory data analysis of interval-valued symbolic data with matrix visualization

Symbolic data analysis (SDA) has gained popularity over the past few years because of its potential for handling data having a dependent and hierarchical nature. Amongst many methods for analyzing SDA data, exploratory data analysis (EDA: Tukey, (1977)) with graphical presentation is an important one. Recent developments of graphical and visualization tools for SDA include zoom star, closed shapes, and parallel-coordinate-plots. Other studies project high dimensional SDA data into lower dimensional space using SDA versions of principal component analysis, multidimensional scaling, and self-organizing maps. Most graphical and visualization approaches for exploring SDA data structure inherit the advantages of their counterparts for conventional (non-SDA) data, but also their disadvantages. Here we introduce matrix visualization (MV) for visualizing and clustering SDA data using interval-valued symbolic data as an example; it is by far the most popular SDA data type in the literature and the most commonly encountered one in practice. Many MV techniques for visualizing and clustering conventional data are converted to SDA data, and several techniques are newly developed for SDA data. Various examples of data with simple to complex structures are brought in to illustrate the proposed methods.