Becchi Matteo, Fantolino Federico, Pavan Giovanni M
Department of Applied Science and Technology, Politecnico di Torino, Torino 10129, Italy.
Department of Innovative Technologies, University of Applied Sciences and Arts of Southern Switzerland, Lugano, Viganello 6962, Switzerland.
Proc Natl Acad Sci U S A. 2024 Aug 13;121(33):e2403771121. doi: 10.1073/pnas.2403771121. Epub 2024 Aug 7.
Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe "": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data.
复杂系统通常具有错综复杂的内部动力学，往往难以阐明。理想情况下，这需要能够以无监督方式检测和分类系统中发生的微观动力学事件的方法。然而，将统计相关的涨落与内部噪声解耦通常仍然并非易事。在此，我们描述了一种简单的迭代无监督聚类方法，它能有效地检测和分类有噪声时间序列数据中的统计相关涨落。我们通过分析各种具有复杂内部动力学的系统的模拟和实验轨迹来证明其有效性，这些系统涵盖从原子尺度到微观尺度，处于平衡态和非平衡态。该方法基于一种迭代的检测 - 分类 - 存档方法。就像剥去洋葱的外部（明显）层会露出内部隐藏的层一样，该方法首先对系统中最密集的动力学环境及其特征噪声进行检测/分类。然后将这种动力学簇的信号从时间序列数据中去除，并对去除噪声后的剩余部分再次进行分析。在每次迭代中，通过不断增加（且自适应）的相关性与噪声比来促进对隐藏动力学子域的检测。该过程不断迭代，直到无法再发现新的动力学域，作为输出，揭示出能够根据分析的时间分辨率以统计稳健方式有效区分/分类的簇的数量。该方法具有通用性且具有清晰的物理解释性。我们期望它将有助于分析各种复杂的动力学系统和时间序列数据。
