# A Formally Robust Time Series Distance Metric

arXiv: https://arxiv.org/abs/2008.07865 · HTML: https://mlsanity.com/paper/2008.07865/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2020.

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

- [Anomaly Detection in Event-triggered Traffic Time Series via Similarity Learning](https://mlsanity.com/paper/2506.16855/) (2025)
- [Task-aware Similarity Learning for Event-triggered Time Series](https://mlsanity.com/paper/2207.08159/) (2022)

## Abstract (arXiv)

Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various different distance metrics or measures dedicated to particular aspects of real-world time series data, yet there is an important aspect that has not been considered so far: Robustness against arbitrary data contamination. In this work, we propose a novel distance metric that is robust against arbitrarily "bad" contamination and has a worst-case computational complexity of O(nlog n). We formally argue why our proposed metric is robust, and demonstrate in an empirical evaluation that the metric yields competitive classification accuracy when applied in k-Nearest Neighbor time series classification.