Visualization and Analysis of Three-Way Data Using Accumulated Concept Graphs

This paper introduces the Accumulated Concept Graph (ACG), a visualization tool based on the quantile method designed to analyze three-way data, including distributional data. Such data often have complex structures that make it difficult to identify patterns using conventional visualization techniques. The ACG represents each object with one or more monotonic line graphs. As a result, the three-way data are visualized as a set of parallel monotonic line graphs that never intersect. This non-intersecting property allows for the easy identification of both macroscopic and microscopic patterns within the data. We demonstrate the usefulness of ACGs and principal component analysis in the analysis of real three-way datasets.