利用模糊隶属度度量动力系统变量间的相关性
Measuring dependencies between variables of a dynamical system using fuzzy affiliations
摘要：
提出了一种统计的、数据驱动的方法，该方法量化了动力系统的变量之间的影响。该方法是基于找到一个合适的表示点的模糊隶属关系相对于地标点使用的可伸缩概率近似算法。这是其次是一个线性映射的建设，这些隶属关系的不同变量和向前的时间。这种线性映射可以直接根据单向依赖性来解释，并量化了它的相关性质。这些量化然后用作动态变量之间的影响的度量。该方法的有效性证明了理论结果和几个数值例子，包括现实世界的篮球运动员运动。
英文摘要：
A statistical, data-driven method is presented that quantifies influences between variables of a dynamical system. The method is based on finding a suitable representation of points by fuzzy affiliations with respect to landmark points using the Scalable Probabilistic Approximation algorithm. This is followed by the construction of a linear mapping between these affiliations for different variables and forward in time. This linear mapping can be directly interpreted in light of unidirectional dependencies and relevant properties of it are quantified. These quantifications then serve as measures for the influences between variables of the dynamics. The validity of the method is demonstrated with theoretical results and on several numerical examples, including real-world basketball player movement.
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