用新型神经网络从时间序列中挖掘隐藏的共同驱动源。
Inference of hidden common driver dynamics by anisotropic self-organizing neural networks
- 基于时延嵌入与内在维数估计，设计各向异性自组织网络。
- 重建的隐含驱动序列与真实驱动高度相关（相关系数高）。
- 适合研究复杂系统中隐藏共同驱动的科学家与工程师。
我们提出一种新方法，通过分析两个受控动力系统的时间序列数据，推断隐藏的共同驱动源的动力学特性。该方法基于时延嵌入、对观测系统及其相互维数的估计，并引入一种新型各向异性训练技术用于柯亨自组织映射，有效学习受控系统的吸引子并将其分解为对应于自身动态和共享动态的子流形。通过模拟实验，使用不同混沌映射在非线性耦合下驱动两个系统，结果表明重建的隐含驱动时间序列与真实隐藏驱动序列具有高相关性，优于多种现有方法，包括线性方法（PCA、ICA）和非线性方法（动态成分分析、典型相关分析、深度典型相关分析）。
原文摘要 · Abstract (English)
We are introducing a novel approach to infer the underlying dynamics of hidden common drivers, based on analyzing time series data from two driven dynamical systems. The inference relies on time-delay embedding, estimation of the intrinsic dimension of the observed systems, and their mutual dimension. A key component of our approach is a new anisotropic training technique applied to Kohonen's self-organizing map, which effectively learns the attractor of the driven system and separates it into submanifolds corresponding to the self-dynamics and shared dynamics. To demonstrate the effectiveness of our method, we conducted simulated experiments using different chaotic maps in a setup, where two chaotic maps were driven by a third map with nonlinear coupling. The inferred time series exhibited high correlation with the time series of the actual hidden common driver, in contrast to the observed systems. The quality of our reconstruction were compared and shown to be superior to several other methods that are intended to find the common features behind the observed time series, including linear methods like PCA and ICA as well as nonlinear methods like dynamical component analysis, canonical correlation analysis and even deep canonical correlation analysis.
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