"Layer-by-layer" Unsupervised Clustering of Statistically Relevant Fluctuations in Noisy Time-series Data of Complex Dynamical Systems

Abstract

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 unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often non-trivial. Here we describe "Onion Clustering": 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 similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection and 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 sub-domains 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 statistically robust way as a function of the time-resolution of the analysis. Onion Clustering 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.

29 pages, 9 figures. Errors in labels in Fig5 corrected

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Cited by in corpus (5)

• "Layer-by-layer" Unsupervised Clustering of Statistically Relevant Fluctuations in Noisy Time-series Data of Complex Dynamical Systems
• Data-driven assessment of optimal spatiotemporal resolutions for information extraction in noisy time series data
• Relevant, hidden, and frustrated information in high-dimensional analyses of complex dynamical systems with internal noise
• A data driven approach to classify descriptors based on their efficiency in translating noisy trajectories into physically-relevant information
• Maximum Information Extraction Via Clustering and Minimization of Shannon Entropy