# Visualizing a Million Time Series with the Density Line Chart

arXiv: https://arxiv.org/abs/1808.06019 · HTML: https://mlsanity.com/paper/1808.06019/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2018.

## Built on by (most cited first, 2 of 2)

- [Data-driven modeling of time-domain induced polarization](https://mlsanity.com/paper/2107.14796/) (2021)
- [TiVy: Time Series Visual Summary for Scalable Visualization](https://mlsanity.com/paper/2507.18972/) (2025)

## Abstract (arXiv)

Data analysts often need to work with multiple series of data---conventionally shown as line charts---at once. Few visual representations allow analysts to view many lines simultaneously without becoming overwhelming or cluttered. In this paper, we introduce the DenseLines technique to calculate a discrete density representation of time series. DenseLines normalizes time series by the arc length to compute accurate densities. The derived density visualization allows users both to see the aggregate trends of multiple series and to identify anomalous extrema.