一个强大的时间延迟选择标准,应用于融合交叉映射
R S Martin1, C M Greve2, C E Huerta3
1DEVCOM ARL Army Research Office, Research Triangle Park, Durham, North Carolina 27709, USA.
Chaos (Woodbury, N.Y.)
|September 4, 2024
概括
本研究引入了一种通过优化相互信息来选择动态系统中的时间延迟的新方法. 这种方法比现有方法更可靠,特别是在有噪音的数据中,改善了因果关系的检测.
科学领域:
- 动态系统理论 动态系统理论
- 非线性动力学是一种非线性动力学.
- 信息理论是信息理论.
背景情况:
- 选择适当的时间延迟对于准确嵌入动态系统至关重要.
- 现有的方法通常依赖于相互信息的局部最小值,在噪音条件下可能不可靠.
- 强大的时间延迟选择对于可靠的因果关系检测至关重要.
研究的目的:
- 介绍一个新的启发式的时间延迟选择在动态系统.
- 为了优化全球最大的相互信息在orthonormal坐标.
- 与当地的最低方法相比,证明其稳定性和更好的性能.
主要方法:
- 利用基于优化全球最大的相互信息的启发式.
- 在系统嵌入中使用正态坐标.
- 将性能与使用融合交叉映射的本地最小方法进行比较.
- 使用杂的洛伦茨系统和实验性等离子体数据进行测试.
主要成果:
- 全球最大值方法比局部最小值方法更强大,特别是在有噪音的情况下.
- 建议的启发式保证在所选择的坐标系中存在一个全局最大值.
- 该方法在因果关系检测的时间滞后选择中显示出更好的一致性和准确性.
- 来自振荡等离子体源的实验数据验证了这些发现.
结论:
- 优化全球最大的相互信息的启发式优化为时间延迟选择提供了更可靠的方法.
- 这种方法提高了动态系统中因果关系检测的准确性,特别是在噪音条件下.
- 这些发现表明,复杂系统的时间序列分析取得了重大进展.
更多相关视频
07:12Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time
Published on: July 1, 2014
12.3K
08:45Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example
Published on: October 24, 2012
14.6K
相关概念视频
01:20Region of Convergence of Laplace Tarnsform
512
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
512
01:17Region of Convergence
401
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
401
01:24Properties of DTFT I
375
In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
375