The algorithm for the detection of lag synchronization from time series data is presented in this paper. Multi-variate time series data are re-organized into a sequence of perfect matrices of delayed Lagrange differences and mapped into a two-dimensional pattern of discriminants. The minimization of this pattern yields a discrete sequence of time lags with a high resolution in time. The proposed technique is capable to detect lag synchronization between chaotic signals contaminated by noise. The proposed technique is also exploited as the feature extraction algorithm for the detection of cyclic alternating patterns in sleep. Computational experiments are used to demonstrate the efficacy of the proposed algorithm.

本文提出了一种从时间序列数据中检测滞后同步的算法。多变量时间序列数据被重新组织成延迟拉格朗日差的完美矩阵序列，并映射成判别式的二维模式。这种模式的最小化产生了具有高分辨率时间的离散时间滞后序列。所提出的技术能够检测被噪声污染的混沌信号之间的滞后同步。所提出的技术也被用作检测睡眠中循环交替模式的特征提取算法。计算实验用于证明所提出算法的有效性。