Persistent Homology of Attractors For Action Recognition

TL;DR

This paper introduces a topological data analysis framework using persistent homology of attractors for human action recognition from 3D motion data, showing improved performance over existing methods.

Contribution

It presents a novel approach combining phase-space reconstruction and persistent homology to extract topological features for action recognition.

Findings

Outperforms baseline methods in action recognition accuracy

Effectively captures topological features of dynamical systems

Incorporates temporal adjacency in homology computation

Abstract

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.