# Identifying manifolds underlying group motion in Vicsek agents

arXiv: https://arxiv.org/abs/1508.02809 · HTML: https://mlsanity.com/paper/1508.02809/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2015.

## Built on by (most cited first, 6 of 6)

- [Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling](https://mlsanity.com/paper/2202.07022/) (2022)
- [Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders](https://mlsanity.com/paper/2110.10428/) (2021)
- [Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions](https://mlsanity.com/paper/2203.02600/) (2022)
- [Real-time Forecasting of Time Series in Financial Markets Using Sequentially Trained Many-to-one LSTMs](https://mlsanity.com/paper/2205.04678/) (2022)
- [Fraud Detection Using Optimized Machine Learning Tools Under Imbalance Classes](https://mlsanity.com/paper/2209.01642/) (2022)
- [Efficient and Robust Remote Sensing Image Denoising Using Randomized Approximation of Geodesics' Gramian on the Manifold Underlying the Patch Space](https://mlsanity.com/paper/2504.10820/) (2025)

## Abstract (arXiv)

Collective motion of animal groups often undergoes changes due to perturbations. In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents. To characterize such manifolds, first we introduce a simple mapping of agents between time-steps. Then, we construct a novel metric which is susceptible to variations in the collective motion, thus revealing distinct underlying manifolds. The method is validated through three sample scenarios simulated using a Vicsek model, namely switching of speed, coordination, and structure of a group. Combined with a dimensionality reduction technique that is used to infer the dimensionality of the embedding manifold, this approach provides an effective model-free framework for the analysis of collective behavior across animal species.