# Interpretable Classification of Time Series Using Euler Characteristic Surfaces

arXiv: https://arxiv.org/abs/2603.15079 · HTML: https://mlsanity.com/paper/2603.15079/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 38 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Euler Characteristic Surfaces](https://mlsanity.com/paper/2102.08260/) (2021)
- [Fluctuations in EEG band power at subject-specific timescales over minutes to days explain changes in seizure evolutions](https://mlsanity.com/paper/2012.07105/) (2020)

## Built on by (most cited first, 1 of 1)

- [Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map in Small-Diameter Vertical Pipes](https://mlsanity.com/paper/2604.06167/) (2026)

## Abstract (arXiv)

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic (chi) -- a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures the nontrivial topological differences between the limit cycle and the strange attractor in the R"ossler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On textitECG5000, our single-feature ECS classifier achieves 98% accuracy with O(n+R· T) complexity, compared to 62% reported by a recent PH-based method. An AdaBoost extension raises accuracy to 98.6%, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on textitTwoLeadECG (94.1%) and textitEpilepsy2 (92.6%).