用于评估动态系统状态空间分区的互信息统计。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0235846
Jason Lu, Michael Small
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引用次数: 0

摘要

我们提出了一种互信息统计量,用于量化动态系统状态空间分区所编码的信息。我们测量每个点在粗分区(具有少量唯一符号的分区)下的符号轨迹历史与其在细分区(具有大量唯一符号的分区)下的分区分配之间的互信息。当应用于一组测试案例时,该统计量表现出了可预测的一致行为。经验结果和该统计量的表述表明,基于轨迹历史的分区(如顺序分区)表现最佳。作为一种应用,我们介绍了加权序数分区,它是流行的序数分区的扩展,其参数可使用互信息统计量进行优化,并证明了在时间序列分析中序数分区的改进。我们还证明了加权序数分区在实际实验数据集中的适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A mutual information statistic for assessing state space partitions of dynamical systems.

We propose a mutual information statistic to quantify the information encoded by a partition of the state space of a dynamical system. We measure the mutual information between each point's symbolic trajectory history under a coarse partition (one with few unique symbols) and its partition assignment under a fine partition (one with many unique symbols). When applied to a set of test cases, this statistic demonstrates predictable and consistent behavior. Empirical results and the statistic's formulation suggest that partitions based on trajectory history, such as the ordinal partition, perform best. As an application, we introduce the weighted ordinal partition, an extension of the popular ordinal partition with parameters that can be optimized using the mutual information statistic, and demonstrate improvements over the ordinal partition in time series analysis. We also demonstrate the weighted ordinal partition's applicability to real experimental datasets.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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