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

TL;DR

This paper introduces a novel ultralow-dimensionality reduction method called spatial-temporal PCA (stPCA) that effectively captures the dynamics of high-dimensional time-series data, enabling early detection of critical transitions and tipping points in complex systems.

Contribution

The paper presents a new analytical ultralow-dimensionality reduction technique that preserves temporal properties and accurately identifies critical transitions in high-dimensional data.

Findings

Successfully applied to ICU data for early warning of critical states

Accurately detects tipping points before critical transitions

Provides robust and quantitative early-warning signals

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.