Molkov Ya I, Mukhin D N, Loskutov E M, Feigin A M, Fidelin G A
Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046207. doi: 10.1103/PhysRevE.80.046207. Epub 2009 Oct 15.
An alternative approach to determining embedding dimension when reconstructing dynamic systems from a noisy time series is proposed. The available techniques of determining embedding dimension (the false nearest-neighbor method, calculation of the correlation integral, and others) are known [H. D. I. Abarbanel, (Springer-Verlag, New York, 1997)] to be inefficient, even at a low noise level. The proposed approach is based on constructing a global model in the form of an artificial neural network. The required amount of neurons and the embedding dimension are chosen so that the description length should be minimal. The considered approach is shown to be appreciably less sensitive to the level and origin of noise, which makes it also a useful tool for determining embedding dimension when constructing stochastic models.
提出了一种从含噪时间序列重建动态系统时确定嵌入维数的替代方法。已知确定嵌入维数的现有技术（伪最近邻法、关联积分计算等）效率低下，即使在低噪声水平下也是如此[H. D. I. 阿巴班内尔，（施普林格出版社，纽约，1997年）]。所提出的方法基于构建人工神经网络形式的全局模型。选择所需的神经元数量和嵌入维数，以使描述长度最小。结果表明，所考虑的方法对噪声水平和噪声来源的敏感度明显较低，这使其成为构建随机模型时确定嵌入维数的有用工具。
