A Measure of Multivariate Phase Synchrony Using Hyperdimensional Geometry
A Measure of Multivariate Phase Synchrony Using Hyperdimensional Geometry
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DOI：
10.1109/tsp.2016.2529586
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发表时间：
2016-06-01
影响因子：
5.4
通讯作者：
Aviyente, Selin
中科院分区：
文献类型：
--
作者：
Al-Khassaweneh, Mahmood;Villafane-Delgado, Marisel;Aviyente, Selin
相位同步已被用于研究组成复杂系统的子系统的动力学。目前的相位同步测度大多是双变量的，关注的是时间序列对之间的同步。二元测量不一定能得出复杂系统内全球相互作用的完整图景。当前的多变量同步度量要么基于对所有可能的成对同步值的平均，要么基于对双变量同步矩阵的特征分解。这些方法对二元同步性指标的准确性比较敏感，计算复杂，对多元同步性进行量化的方法比较间接。最近，我们提出了一种利用超维坐标系计算多变量相位同步的方法。这种方法被称为超球面相位同步（HPS），它依赖于相位差的顺序。在本文中，我们提出了一种更一般的超球坐标系以及一种新的高维流形表示，以消除对信号相位顺序的依赖。这个新框架被称为超环同步（Hyper-Torus Synchrony， HTS），它被证明相当于一组足够的锁相值平方的均方根，这些锁相值的相位差包含了网络中所有振荡器的信息。分析给出了高温超导的统计特性，并对其在合成信号和实际信号下的性能进行了全面评价。
Phase synchrony has been used to investigate the dynamics of subsystems that make up a complex system. Current measures of phase synchrony are mostly bivariate focusing on the synchrony between pairs of time series. Bivariate measures do not necessarily lead to a complete picture of the global interactions within a complex system. Current multivariate synchrony measures are based on either averaging all possible pairwise synchrony values or eigendecomposition of the pairwise bivariate synchrony matrix. These approaches are sensitive to the accuracy of the bivariate synchrony indices, computationally complex and indirect ways of quantifying the multivariate synchrony. Recently, we had proposed a method to compute the multivariate phase synchrony using a hyperdimensional coordinate system. This method, referred to as Hyperspherical Phase Synchrony (HPS), has been found to be dependent on the ordering of the phase differences. In this paper, we propose a more general hyper-spherical coordinate system along with a new higher-dimensional manifold representation to eliminate the dependency on the ordering of the signals' phases. This new framework, referred to as Hyper-Torus Synchrony (HTS), is shown to be equivalent to the root-mean-square of a sufficient set of squared phase-locking values whose phase differences contain information about all oscillators in the network. The statistical properties of HTS are given analytically and its performance is evaluated thoroughly for both synthetic and real signals.