# Persistent Homology of Attractors For Action Recognition

arXiv: https://arxiv.org/abs/1603.05310 · HTML: https://mlsanity.com/paper/1603.05310/

## Key facts

- Cited by 10 papers in the map (data through 13 Oct 2026).
- First posted on arXiv 16 Mar 2016.

## Built on by (most cited first, 10 of 10)

- [TopoFR: A Closer Look at Topology Alignment on Face Recognition](https://mlsanity.com/paper/2410.10587/) (2024)
- [Stability and Machine Learning Applications of Persistent Homology Using the Delaunay-Rips Complex](https://mlsanity.com/paper/2303.01501/) (2023)
- [Quantum Persistent Homology for Time Series](https://mlsanity.com/paper/2211.04465/) (2022)
- [Classification of Stochastic Processes with Topological Data Analysis](https://mlsanity.com/paper/2206.03973/) (2022)
- [Classification based on Topological Data Analysis](https://mlsanity.com/paper/2102.03709/) (2021)
- [A Topological Data Analysis Based Classifier](https://mlsanity.com/paper/2111.05214/) (2021)
- [A Time-Series Foundation Model by Universal Delay Embedding](https://mlsanity.com/paper/2509.12080/) (2025)
- [A Topological Approach for Motion Track Discrimination](https://mlsanity.com/paper/2102.05705/) (2021)
- [Quantum Distance Approximation for Persistence Diagrams](https://mlsanity.com/paper/2402.17295/) (2024)
- [A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams](https://mlsanity.com/paper/2402.14489/) (2024)

## Abstract (arXiv)

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system. We reconstruct the phase-space of time series corresponding to actions using time-delay embedding, and compute the persistent homology of the phase-space reconstruction. In order to better represent the topological properties of the phase-space, we incorporate the temporal adjacency information when computing the homology groups. The persistence of these homology groups encoded using persistence diagrams are used as features for the actions. Our experiments with action recognition using these features demonstrate that the proposed approach outperforms other baseline methods.