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 observation 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.

翻译：降维是将高维数据生成低维表示的过程。受移动智能体编队控制的启发，我们提出一种用于降维的非线性动力系统。该系统由两部分组成：控制邻近点以处理局部结构，以及控制远端点以考虑全局结构。我们还对该模型及其数值计算过程进行了简要的数学分析。在合成数据集和真实数据集上进行了数值实验，与现有模型的比较表明所提模型的合理性与有效性。