Dauwels J, Vialatte F, Weber T, Musha T, Cichocki A
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Neural Comput. 2009 Aug;21(8):2203-68. doi: 10.1162/neco.2009.11-08-899.
Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, events are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, the companion letter in this issue, one-dimensional events are considered; this letter concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly more difficult combinatorial problem and therefore is nontrivial. Also in the multidimensional case, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (1) estimate the SES parameters from a given pairwise alignment; (2) with the resulting estimates, refine the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the one-dimensional case. The pairwise alignment (step 2) can no longer be obtained through dynamic programming, since the state space becomes too large. Instead it is determined by applying the max-product algorithm on a cyclic graphical model. In order to test the robustness and reliability of the SES method, it is first applied to surrogate data. Next, it is applied to detect anomalies in EEG synchrony of mild cognitive impairment (MCI) patients. Numerical results suggest that SES is significantly more sensitive to perturbations in EEG synchrony than a large variety of classical synchrony measures.
随机事件同步是一种量化信号对相似性的技术。首先，从两个给定的时间序列中提取事件。接下来，尝试将一个时间序列中的事件与另一个时间序列中的事件进行对齐。对齐效果越好，两个时间序列就被认为越相似。在本期的配套文章第一部分中，考虑了一维事件；本文涉及多维事件。尽管基本思想相似，但向多维点过程的扩展涉及一个明显更困难的组合问题，因此并非易事。同样在多维情况下，联合计算成对对齐和SES参数的问题被转化为一个统计推断问题。这个问题通过坐标下降法解决，更具体地说，是通过交替以下两个步骤：(1) 从给定的成对对齐中估计SES参数；(2) 根据得到的估计值，改进成对对齐。SES参数通过最大后验 (MAP) 估计来计算（步骤1），这与一维情况类似。成对对齐（步骤2）不能再通过动态规划获得，因为状态空间变得太大。相反，它是通过在循环图形模型上应用最大乘积算法来确定的。为了测试SES方法的稳健性和可靠性，首先将其应用于替代数据。接下来，将其应用于检测轻度认知障碍 (MCI) 患者脑电图同步中的异常情况。数值结果表明，与多种经典同步测量方法相比，SES对脑电图同步中的扰动明显更敏感。
