Formation-Controlled Dimensionality Reduction
This work addresses dimensionality reduction for data analysis, but it appears incremental as it builds on existing models with a novel method.
The authors tackled the problem of dimensionality reduction by proposing a nonlinear dynamical system inspired by formation control of mobile agents, which effectively handles both local and global structures, and demonstrated its soundness and effectiveness through numerical experiments on synthetic and real datasets.
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.