# Tropical time series, iterated-sums signatures and quasisymmetric functions

arXiv: https://arxiv.org/abs/2009.08443 · HTML: https://mlsanity.com/paper/2009.08443/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [FRUITS: Feature Extraction Using Iterated Sums for Time Series Classification](https://mlsanity.com/paper/2311.14549/) (2023)
- [Aggregating time-series and image data: functors and double functors](https://mlsanity.com/paper/2504.05274/) (2025)
- [Tensor-to-Tensor Models with Fast Iterated Sum Features](https://mlsanity.com/paper/2506.06041/) (2025)

## Abstract (arXiv)

Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a central, and our motivating example. It leads to features of (real-valued) time series that are not easily available using existing signature-type objects. We demonstrate how the signature extracts chronological aspects of a time series, and that its calculation is possible in linear time. We identify quasisymmetric expressions over semirings as the appropriate framework for iterated-sums signatures over semiring-valued time series.