Model-Free Information Extraction in Enriched Nonlinear Phase-Space

Abstract: Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise contamination. When representative physical models and large labeled data sets are unavailable, as is the case with most real-world applications, model-dependent Bayesian approaches would yield misleading results, and most supervised learning machines would also fail to reliably resolve the intricately evolving systems. Here, we propose an unsupervised machine-learning approach that operates in a well-constructed function space, whereby the evolving nonlinear dynamics are captured through a linear functional representation determined by the Koopman operator. This breakthrough leverages on the time-feature embedding and the ensuing reconstruction of a phase-space representation of the dynamics, thereby permitting the reliable identification of critical global signatures from the whole trajectory. This dramatically improves over commonly used static local features, which are vulnerable to unknown transitions or noise. Thanks to its data-driven nature, our method excludes any prior models and training corpus. We benchmark the astonishing accuracy of our method on three diverse and challenging problems in: biology, medicine, and engineering. In all cases, it outperforms existing state-of-the-art methods. As a new unsupervised information processing paradigm, it is suitable for ubiquitous nonlinear dynamical systems or end-users with little expertise, which permits an unbiased excavation of underlying working principles or intrinsic correlations submerged in unlabeled data flows.