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首页> 外文会议>IAPR Workshop on Cognitive Information Processing >A MUTUAL INFORMATION-BASED METHOD FOR THE ESTIMATION OF THE DIMENSION OF CHAOTIC DYNAMICAL SYSTEMS USING NEURAL NETWORKS
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A MUTUAL INFORMATION-BASED METHOD FOR THE ESTIMATION OF THE DIMENSION OF CHAOTIC DYNAMICAL SYSTEMS USING NEURAL NETWORKS

机译：基于互信息的基于信息的方法，用于使用神经网络估计混沌动力系统的维度

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摘要

In this paper, a method of estimating the dimension of dynamical systems from a time series, using neural networks, is examined. It is based (a) on the hypothesis that a member of a time series can be optimally expressed as a deterministic function of the d past series values (where d is the dimension of the system), and (b) on the observation that neural networks 'learning ability is improved rapidly when the appropriate amount of information is provided to a neural structure which is as complex as needed. To estimate the dimension of a dynamical system, neural networks are trained to learn the component of the attractor expressed by a reconstructed vector in a suitable phase space whose embedding dimension m, has been estimated using the mutual information method. More specifically, the information supplied to the networks is represented by vectors consisting of the m past values of the time series, where m varies from 1 to D + 2, D being a pre-estimation for the maximum value of the embedding dimension of the system. The current method proposes that when m meets the dimension d of the dynamical system, the neural model of the attractor remarkably improves its learning ability, minimizing locally the RMS error of the training set. The logistic and the Henon map as well as the Lorenz and the Rosler attractors expressed as systems of difference equations, were examined to test the validity of the method.
机译：在本文中，检查了一种借鉴使用神经网络的时间序列估算动态系统的维度的方法。基于（a）的假设，即时间序列的成员可以最佳地表示为D过去串联值的确定性函数（其中d是系统的尺寸），并且（b）关于神经网络的观察当提供适当的信息量以根据需要进行复杂的神经结构时，网络的学习能力快速提高。为了估计动态系统的维数，神经网络被训练学习由重构矢量在合适的相空间，其嵌入维μm表示的吸引子的成分，一直使用的互信息的方法来估计。更具体地，提供到网络的信息由以下各项组成的米过去的时间序列，其中，m从1变化到d + 2的值矢量表示的，d是预先估计的嵌入尺寸的最大值系统。当前方法提出，当M符合动态系统的尺寸D时，吸引器的神经模型显着提高了其学习能力，最小化训练集的RMS误差。逻辑和HENON地图以及LORENZ和ROSLLER吸引子表示为差分方程式的系统，以测试该方法的有效性。

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