# Time-warping invariants of multidimensional time series

arXiv: https://arxiv.org/abs/1906.05823 · HTML: https://mlsanity.com/paper/1906.05823/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Stability of Deep Neural Networks via discrete rough paths](https://mlsanity.com/paper/2201.07566/) (2022)
- [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)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)

## Abstract (arXiv)

In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties.