# A flat persistence diagram for improved visualization of persistent homology

## TL;DR

The paper introduces flat persistence diagrams, a new visualization method for persistent homology that reduces visual bias and enhances interpretability, aiding the practical application of topological data analysis.

## Contribution

It proposes a novel flat persistence diagram that improves visualization of persistent homology by providing an intuitive reference axis and reducing visual bias.

## Key findings

- Flat persistence diagrams display equivalent information to traditional diagrams.
- They offer a more intuitive horizontal reference axis.
- They reduce visual bias, leading to deeper insights.

## Abstract

Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted insight into the geometry underlying complex datasets, visualization of even single-parameter persistent homology has significant room for improvement. Here, we propose a modification to the conventional persistence diagram - the flat persistence diagram - that more efficiently displays information relevant to persistent homology and simultaneously corrects for visual bias present in the former. Flat persistence diagrams display equivalent information as their predecessor, while providing researchers with an intuitive horizontal reference axis in contrast to the usual diagonal reference line. Reducing visual bias through the use of appropriate graphical displays not only provides more accurate, but also deeper insights into the topology that underlies complex datasets. Introducing flat persistence diagrams into widespread use would bring researchers one step closer to practical application of topological data analysis.