# TopoLines: Topological Smoothing for Line Charts

## TL;DR

TopoLines introduces a topological smoothing method for line charts that preserves important peaks in noisy data, enhancing visual analysis without losing critical features.

## Contribution

It applies topological data analysis to develop a smoothing technique that retains peaks, addressing limitations of traditional smoothing methods.

## Key findings

- Outperforms traditional smoothing methods in peak preservation.
- Reduces residual error while maintaining data features.
- Effective across multiple application domains.

## Abstract

Line charts are commonly used to visualize a series of data values. When the data are noisy, smoothing is applied to make the signal more apparent. Conventional methods used to smooth line charts, e.g., using subsampling or filters, such as median, Gaussian, or low-pass, each optimize for different properties of the data. The properties generally do not include retaining peaks (i.e., local minima and maxima) in the data, which is an important feature for certain visual analytics tasks. We present TopoLines, a method for smoothing line charts using techniques from Topological Data Analysis. The design goal of TopoLines is to maintain prominent peaks in the data while minimizing any residual error. We evaluate TopoLines for 2 visual analytics tasks by comparing to 5 popular line smoothing methods with data from 4 application domains.