# Parameterizing the cost function of Dynamic Time Warping with application to time series classification

arXiv: https://arxiv.org/abs/2301.10350 · HTML: https://mlsanity.com/paper/2301.10350/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [HIVE-COTE 2.0: a new meta ensemble for time series classification](https://mlsanity.com/paper/2104.07551/) (2021)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [MultiRocket: Multiple pooling operators and transformations for fast and effective time series classification](https://mlsanity.com/paper/2102.00457/) (2021)
- [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)
- [shapeDTW: shape Dynamic Time Warping](https://mlsanity.com/paper/1606.01601/) (2016)
- [Improving the Accuracy of Global Forecasting Models using Time Series Data Augmentation](https://mlsanity.com/paper/2008.02663/) (2020)
- [A General Optimization Framework for Dynamic Time Warping](https://mlsanity.com/paper/1905.12893/) (2019)

## Built on by (most cited first, 3 of 3)

- [Proximity Forest 2.0: A new effective and scalable similarity-based classifier for time series](https://mlsanity.com/paper/2304.05800/) (2023)
- [Deep Time Warping for Multiple Time Series Alignment](https://mlsanity.com/paper/2502.16324/) (2025)
- [Warping and Matching Subsequences Between Time Series](https://mlsanity.com/paper/2506.15452/) (2025)

## Abstract (arXiv)

Dynamic Time Warping (DTW) is a popular time series distance measure that aligns the points in two series with one another. These alignments support warping of the time dimension to allow for processes that unfold at differing rates. The distance is the minimum sum of costs of the resulting alignments over any allowable warping of the time dimension. The cost of an alignment of two points is a function of the difference in the values of those points. The original cost function was the absolute value of this difference. Other cost functions have been proposed. A popular alternative is the square of the difference. However, to our knowledge, this is the first investigation of both the relative impacts of using different cost functions and the potential to tune cost functions to different tasks. We do so in this paper by using a tunable cost function λγ with parameter γ. We show that higher values of γ place greater weight on larger pairwise differences, while lower values place greater weight on smaller pairwise differences. We demonstrate that training γ significantly improves the accuracy of both the DTW nearest neighbor and Proximity Forest classifiers.