# Amercing: An Intuitive, Elegant and Effective Constraint for Dynamic Time Warping

arXiv: https://arxiv.org/abs/2111.13314 · HTML: https://mlsanity.com/paper/2111.13314/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 26 Nov 2021.

## Builds on (most cited first, 5 of 5)

- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [TS-CHIEF: A Scalable and Accurate Forest Algorithm for Time Series Classification](https://mlsanity.com/paper/1906.10329/) (2019)
- [Proximity Forest: An effective and scalable distance-based classifier for time series](https://mlsanity.com/paper/1808.10594/) (2018)
- [Improving the Accuracy of Global Forecasting Models using Time Series Data Augmentation](https://mlsanity.com/paper/2008.02663/) (2020)
- [Early Abandoning and Pruning for Elastic Distances including Dynamic Time Warping](https://mlsanity.com/paper/2102.05221/) (2021)

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

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Deep Learning for Time Series Classification and Extrinsic Regression: A Current Survey](https://mlsanity.com/paper/2302.02515/) (2023)

## Abstract (arXiv)

Dynamic Time Warping (DTW), and its constrained (CDTW) and weighted (WDTW) variants, are time series distances with a wide range of applications. They minimize the cost of non-linear alignments between series. CDTW and WDTW have been introduced because DTW is too permissive in its alignments. However, CDTW uses a crude step function, allowing unconstrained flexibility within the window, and none beyond it. WDTW's multiplicative weight is relative to the distances between aligned points along a warped path, rather than being a direct function of the amount of warping that is introduced. In this paper, we introduce Amerced Dynamic Time Warping (ADTW), a new, intuitive, DTW variant that penalizes the act of warping by a fixed additive cost. Like CDTW and WDTW, ADTW constrains the amount of warping. However, it avoids both abrupt discontinuities in the amount of warping allowed and the limitations of a multiplicative penalty. We formally introduce ADTW, prove some of its properties, and discuss its parameterization. We show on a simple example how it can be parameterized to achieve an intuitive outcome, and demonstrate its usefulness on a standard time series classification benchmark. We provide a demonstration application in C++.