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arXiv · 2501.12582

Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA

Pei Chen·Yaofang Suo·Rui Liu·Luonan Chen
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Abstract

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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Pei Chen, Yaofang Suo, Rui Liu, Luonan Chen. 2025-01-22. Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA. https://arxiv.org/abs/2501.12582

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