A Formally Robust Time Series Distance Metric

TL;DR

This paper introduces a new time series distance metric that is robust to arbitrary data contamination and maintains computational efficiency, improving classification accuracy in contaminated datasets.

Contribution

We propose a novel, robust distance metric for time series classification that is computationally efficient and resilient to arbitrary data contamination.

Findings

The metric is robust against arbitrary data contamination.

It achieves competitive accuracy in k-NN time series classification.

The worst-case computational complexity is O(n log n).

Abstract

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 $\mathcal{O}(n\log n)$. 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.