Visualizing Symmetric Square Matrices with Rainbow Boxes: Methods and Application to Character Co-occurrence Matrices in Literary Texts

A symmetric square matrix is a type of dataset frequently found in various domains. An example is character co-occurrence matrices in digital humanities. However, the visualization of these matrices is difficult. In this paper, we propose a method for visualizing symmetric square matrices, by transforming a matrix into overlapping sets, and then by visualizing these overlapping sets using rainbow boxes, a recent set visualization technique. We apply this method to the visualization of character matrices in novels, using two datasets: a small one (21 characters) and a large one (80 characters). We show that this visualization allows the finding of several insights. Finally, we discuss the advantages and drawbacks of this method, and we compare it to other approaches in the literature.

I. Introduction

Symmetric square matrices and co-occurrence matrices are a kind of dataset that can be encountered in many domains [1]. Any undirected graph can be represented by an adjacency matrix, leading to a symmetric square matrices. Such matrices are frequently encountered in visual text analysis [2], which applies information visualization methods to digital humanities. When the structure of the text is not preserved by the visualization, this is called distant reading (by opposition to close reading). In particular, character co-occurrence matrices can be extracted from novels and narrative texts, and visualized with various techniques. An example of a symmetric square matrix, representing the relations between the 21 main characters in a novel, is shown in Figure 2. Figure 1.

Rainbow boxes displaying groups of interrelated characters in a novel. Characters are in columns, and each rectangular box corresponds to a group of characters. In a given group, each character is related to each other character of the same group. Box colors indicate the part of the novel during which a character joins the group.