用单个变量捕捉复杂系统动态，提前预警关键转折点。
Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA
- 基于非线性延迟嵌入理论，将高维空间信息压缩为单一时间变量。
- 仅用一个潜变量就完整保留原始数据的时间特性，准确识别临界点。
- 适用于临床重症监护等真实数据，可为每位患者提供可靠预警信号。
在高维时间序列数据分析中，发现主导模式并探索动态行为，尤其是关键状态转换与突变点，是研究现实复杂系统的重要挑战。这类任务需要可解释的数据表示，以帮助理解原始数据空间中的时空信息。本文提出一种通用且解析的超低维降维方法——时空主成分分析（stPCA），仅用一个潜在变量即可无失真地完全表征高维时间序列的动力学特性。该方法基于非线性延迟嵌入理论，将高维空间信息转化为一维时间信息。此单变量的动力学过程可解析求解，理论上保持了原始高维时间序列的时间属性，从而能准确、可靠地识别即将发生的关键转变前的临界点。该方法在个体化异质性重症监护记录等真实数据集上的应用表明，stPCA能定量且稳健地为每位患者提供临界/突变状态的早期预警信号。
原文摘要 · Abstract (English)
Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand interpretable data representations to facilitate comprehension of both spatial and temporal information within the original data space. Here, we proposed a general and analytical ultralow-dimensionality reduction method for dynamical systems named spatial-temporal principal component analysis (stPCA) to fully represent the dynamics of a high-dimensional time-series by only a single latent variable without distortion, which transforms high-dimensional spatial information into one-dimensional temporal information based on nonlinear delay-embedding theory. The dynamics of this single variable is analytically solved and theoretically preserves the temporal property of original high-dimensional time-series, thereby accurately and reliably identifying the tipping point before an upcoming critical transition. Its applications to real-world datasets such as individual-specific heterogeneous ICU records demonstrated the effectiveness of stPCA, which quantitatively and robustly provides the early-warning signals of the critical/tipping state on each patient.
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