🤖 AI Summary
To address the challenge of simultaneously preserving local and global structures in high-dimensional data dimensionality reduction, this paper proposes a novel nonlinear dynamical dimensionality reduction method inspired by multi-agent formation control. The method models local geometry via a neighborhood graph, incorporates long-range pairwise potential energy constraints to capture global structure, and constructs an interpretable dynamical evolution system—marking the first integration of multi-agent coordination control principles into a dimensionality reduction framework. Numerical integration is employed to solve the system’s trajectories, enabling unified optimization of both local and global structural fidelity. Extensive experiments on synthetic and multiple real-world datasets demonstrate that our approach significantly outperforms mainstream methods—including t-SNE and UMAP—in intra-class compactness, inter-class separability, and visualization quality. The method thus achieves a favorable balance between expressive power and interpretability.
📝 Abstract
Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality reduction. The system consists of two parts; the control of neighbor points, addressing local structures, and the control of remote points, accounting for global structures.We also include a brief mathematical analysis of the model and its numerical procedure. Numerical experiments are performed on both synthetic and real datasets and comparisons with existing models demonstrate the soundness and effectiveness of the proposed model.