A comparative analysis of matrix reordering algorithms regarding canonical data patterns

Abstract

Matrix reordering is an Information Visualization topic that aims to study how to reveal information hidden within matrix-based visualizations, through appropriate reordering of its rows and columns. Considering the plethora of algorithms currently available to perform this task, and the set of matrix patterns presented in the visualization literature, we noted a lack of a comprehensive comparative analysis related to a subset of these patterns, known as canonical data patterns. Thus, this work aimed to perform a broad comparison of 37 state-of-the-art reordering algorithms by measuring the efficiency (execution time) and effectiveness (which combines objective functions as Moore Neighborhood, Minimal Span Loss Function and Circular Correlation, and a qualitative approach by visually assessing the output matrices) of the algorithms. We used as input a large synthetic matrix data set with different canonical data patterns. As a result, it was possible to indicate the most appropriate reordering algorithms for each pattern considered.