# Robust Time Series Dissimilarity Measure for Outlier Detection and Periodicity Detection

arXiv: https://arxiv.org/abs/2206.02956 · HTML: https://mlsanity.com/paper/2206.02956/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Trend Filtering on Graphs](https://mlsanity.com/paper/1410.7690/) (2014)
- [CloudRCA: A Root Cause Analysis Framework for Cloud Computing Platforms](https://mlsanity.com/paper/2111.03753/) (2021)
- [Learning Discriminative Prototypes with Dynamic Time Warping](https://mlsanity.com/paper/2103.09458/) (2021)
- [RobustTrend: A Huber Loss with a Combined First and Second Order Difference Regularization for Time Series Trend Filtering](https://mlsanity.com/paper/1906.03751/) (2019)
- [RobustPeriod: Time-Frequency Mining for Robust Multiple Periodicity Detection](https://mlsanity.com/paper/2002.09535/) (2020)
- [A General Optimization Framework for Dynamic Time Warping](https://mlsanity.com/paper/1905.12893/) (2019)

## Built on by (most cited first, 5 of 5)

- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Improving Time Series Encoding with Noise-Aware Self-Supervised Learning and an Efficient Encoder](https://mlsanity.com/paper/2306.06579/) (2023)
- [LoFT-LLM: Low-Frequency Time-Series Forecasting with Large Language Models](https://mlsanity.com/paper/2512.20002/) (2025)
- [Adapting to the Unknown: Robust Meta-Learning for Zero-Shot Financial Time Series Forecasting](https://mlsanity.com/paper/2504.09664/) (2025)
- [Unsupervised Discovery of Long-Term Spatiotemporal Periodic Workflows in Human Activities](https://mlsanity.com/paper/2511.14945/) (2025)

## Abstract (arXiv)

Dynamic time warping (DTW) is an effective dissimilarity measure in many time series applications. Despite its popularity, it is prone to noises and outliers, which leads to singularity problem and bias in the measurement. The time complexity of DTW is quadratic to the length of time series, making it inapplicable in real-time applications. In this paper, we propose a novel time series dissimilarity measure named RobustDTW to reduce the effects of noises and outliers. Specifically, the RobustDTW estimates the trend and optimizes the time warp in an alternating manner by utilizing our designed temporal graph trend filtering. To improve efficiency, we propose a multi-level framework that estimates the trend and the warp function at a lower resolution, and then repeatedly refines them at a higher resolution. Based on the proposed RobustDTW, we further extend it to periodicity detection and outlier time series detection. Experiments on real-world datasets demonstrate the superior performance of RobustDTW compared to DTW variants in both outlier time series detection and periodicity detection.