基于马尔可夫链粗粒化的多变量时间序列同步簇检测
Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains
摘要：
同步聚类分析是一种从二元同步指数矩阵R出发，检测多元时间序列数据集潜在结构的方法。以前的方法利用R的特征向量进行聚类识别，类似于最近几次尝试使用相关矩阵的特征向量进行组识别。所有这些方法都假设了主特征向量和聚类之间的一一对应关系，然而在重要的情况下，这已经被证明是错误的。我们澄清了有用的特征值分解同步聚类分析的问题翻译成随机过程的语言，并得到一个增强的聚类方法利用最近的见解，从粗粒化的有限状态马尔可夫过程。我们说明了我们的方法使用耦合洛伦兹振荡器的模拟系统的操作，我们证明了其优越的性能比以前的方法。最后，我们调查的问题，对小样本量的算法的鲁棒性，这是很重要的现场应用。
英文摘要：
Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.
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