# Topological Analysis for Detecting Anomalies (TADA) in Time Series

arXiv: https://arxiv.org/abs/2406.06168 · HTML: https://mlsanity.com/paper/2406.06168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 50 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Exathlon: A Benchmark for Explainable Anomaly Detection over Time Series](https://mlsanity.com/paper/2010.05073/) (2020)
- [Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Series](https://mlsanity.com/paper/2303.01272/) (2023)
- [Minimum Covariance Determinant and Extensions](https://mlsanity.com/paper/1709.07045/) (2017)
- [Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection](https://mlsanity.com/paper/2307.08390/) (2023)
- [The density of expected persistence diagrams and its kernel based estimation](https://mlsanity.com/paper/1802.10457/) (2018)
- [Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks](https://mlsanity.com/paper/1906.05795/) (2019)
- [Robust Bregman Clustering](https://mlsanity.com/paper/1812.04356/) (2018)
- [Adaptive Anomaly Detection in Chaotic Time Series with a Spatially Aware Echo State Network](https://mlsanity.com/paper/1909.01709/) (2019)
- [Spectral Dependence](https://mlsanity.com/paper/2103.17240/) (2021)
- [A provable initialization and robust clustering method for general mixture models](https://mlsanity.com/paper/2401.05574/) (2024)
- [Time topological analysis of EEG using signature theory](https://mlsanity.com/paper/2404.15328/) (2024)

## Abstract (arXiv)

This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed approach is lean enough to handle large scale datasets, and extensive numerical experiments back the intuition that it is more suitable for detecting global changes of correlation structures than existing methods. Some theoretical guarantees for quantization algorithms based on dependent time sequences are also provided.