# Elastic Similarity and Distance Measures for Multivariate Time Series

arXiv: https://arxiv.org/abs/2102.10231 · HTML: https://mlsanity.com/paper/2102.10231/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 57 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 18 of 18)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [A Time Series Forest for Classification and Feature Extraction](https://mlsanity.com/paper/1302.2277/) (2013)
- [TS-CHIEF: A Scalable and Accurate Forest Algorithm for Time Series Classification](https://mlsanity.com/paper/1906.10329/) (2019)
- [The Canonical Interval Forest (CIF) Classifier for Time Series Classification](https://mlsanity.com/paper/2008.09172/) (2020)
- [Fast and Accurate Time Series Classification with WEASEL](https://mlsanity.com/paper/1701.07681/) (2017)
- [Proximity Forest: An effective and scalable distance-based classifier for time series](https://mlsanity.com/paper/1808.10594/) (2018)
- [Deep Echo State Network (DeepESN): A Brief Survey](https://mlsanity.com/paper/1712.04323/) (2017)
- [Scalable Dictionary Classifiers for Time Series Classification](https://mlsanity.com/paper/1907.11815/) (2019)
- [A tale of two toolkits, report the third: on the usage and performance of HIVE-COTE v1.0](https://mlsanity.com/paper/2004.06069/) (2020)
- [Elastic bands across the path: A new framework and methods to lower bound DTW](https://mlsanity.com/paper/1808.09617/) (2018)
- [Early Abandoning and Pruning for Elastic Distances including Dynamic Time Warping](https://mlsanity.com/paper/2102.05221/) (2021)

## Built on by (most cited first, 8 of 8)

- [A Review and Evaluation of Elastic Distance Functions for Time Series Clustering](https://mlsanity.com/paper/2205.15181/) (2022)
- [Time-Series Classification in Smart Manufacturing Systems: An Experimental Evaluation of State-of-the-Art Machine Learning Algorithms](https://mlsanity.com/paper/2310.02812/) (2023)
- [Proximity Forest 2.0: A new effective and scalable similarity-based classifier for time series](https://mlsanity.com/paper/2304.05800/) (2023)
- [Deep Unsupervised Domain Adaptation for Time Series Classification: a Benchmark](https://mlsanity.com/paper/2312.09857/) (2023)
- [CENTS: Generating synthetic electricity consumption time series for rare and unseen scenarios](https://mlsanity.com/paper/2501.14426/) (2025)
- [Rock the KASBA: Blazingly Fast and Accurate Time Series Clustering](https://mlsanity.com/paper/2411.17838/) (2024)
- [MRMS-Net and LMRMS-Net: Scalable Multi-Representation Multi-Scale Networks for Time Series Classification](https://mlsanity.com/paper/2603.19315/) (2026)
- [Soft-MSM: Differentiable Context-Aware Elastic Alignment for Time Series](https://mlsanity.com/paper/2605.00069/) (2026)

## Abstract (arXiv)

This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures are a class of similarity measures that can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.