# TC-DTW: Accelerating Multivariate Dynamic Time Warping Through Triangle Inequality and Point Clustering

arXiv: https://arxiv.org/abs/2101.07731 · HTML: https://mlsanity.com/paper/2101.07731/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 40 references that are in the map.
- First posted on arXiv 15 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [D3TW: Discriminative Differentiable Dynamic Time Warping for Weakly Supervised Action Alignment and Segmentation](https://mlsanity.com/paper/1901.02598/) (2019)

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

- [Mask the Redundancy: Evolving Masking Representation Learning for Multivariate Time-Series Clustering](https://mlsanity.com/paper/2511.17008/) (2025)
- [Improving Time Series Classification with Representation Soft Label Smoothing](https://mlsanity.com/paper/2408.17010/) (2024)

## Abstract (arXiv)

Dynamic time warping (DTW) plays an important role in analytics on time series. Despite the large body of research on speeding up univariate DTW, the method for multivariate DTW has not been improved much in the last two decades. The most popular algorithm used today is still the one developed seventeen years ago. This paper presents a solution that, as far as we know, for the first time consistently outperforms the classic multivariate DTW algorithm across dataset sizes, series lengths, data dimensions, temporal window sizes, and machines. The new solution, named TC-DTW, introduces Triangle Inequality and Point Clustering into the algorithm design on lower bound calculations for multivariate DTW. In experiments on DTW-based nearest neighbor finding, the new solution avoids as much as 98% (60% average) DTW distance calculations and yields as much as 25X (7.5X average) speedups.