Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA

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 comprehensi...

Full description

Saved in:
Bibliographic Details
Main Authors: Pei Chen, Yaofang Suo, Kazuyuki Aihara, Ye Li, Dan Wu, Rui Liu, Luonan Chen
Format: Article
Language:English
Published: Wiley 2025-05-01
Series:Advanced Science
Subjects:
Online Access:https://doi.org/10.1002/advs.202408173
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849434500729143296
author Pei Chen
Yaofang Suo
Kazuyuki Aihara
Ye Li
Dan Wu
Rui Liu
Luonan Chen
author_facet Pei Chen
Yaofang Suo
Kazuyuki Aihara
Ye Li
Dan Wu
Rui Liu
Luonan Chen
author_sort Pei Chen
collection DOAJ
description 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. This study proposes 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 demonstrate the effectiveness of stPCA, which quantitatively and robustly provides the early‐warning signals of the critical/tipping state on each patient.
format Article
id doaj-art-c3ef2dcc209f453c9ffe29f1a6425ffb
institution Kabale University
issn 2198-3844
language English
publishDate 2025-05-01
publisher Wiley
record_format Article
series Advanced Science
spelling doaj-art-c3ef2dcc209f453c9ffe29f1a6425ffb2025-08-20T03:26:38ZengWileyAdvanced Science2198-38442025-05-011220n/an/a10.1002/advs.202408173Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCAPei Chen0Yaofang Suo1Kazuyuki Aihara2Ye Li3Dan Wu4Rui Liu5Luonan Chen6School of Mathematics South China University of Technology Guangzhou 510640 ChinaSchool of Mathematics South China University of Technology Guangzhou 510640 ChinaInternational Research Center for Neurointelligence Institutes for Advanced Study The University of Tokyo Tokyo 113‐0033 JapanShenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen 518055 ChinaShenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen 518055 ChinaSchool of Mathematics South China University of Technology Guangzhou 510640 ChinaSchool of Mathematical Sciences School of AI Shanghai Jiao Tong University Shanghai 200240 ChinaAbstract 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. This study proposes 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 demonstrate the effectiveness of stPCA, which quantitatively and robustly provides the early‐warning signals of the critical/tipping state on each patient.https://doi.org/10.1002/advs.202408173critical state transitioninterpretable data representationspatial‐temporal PCAultralow‐dimensionality reduction
spellingShingle Pei Chen
Yaofang Suo
Kazuyuki Aihara
Ye Li
Dan Wu
Rui Liu
Luonan Chen
Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA
Advanced Science
critical state transition
interpretable data representation
spatial‐temporal PCA
ultralow‐dimensionality reduction
title Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA
title_full Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA
title_fullStr Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA
title_full_unstemmed Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA
title_short Ultralow‐Dimensionality Reduction for Identifying Critical Transitions by Spatial‐Temporal PCA
title_sort ultralow dimensionality reduction for identifying critical transitions by spatial temporal pca
topic critical state transition
interpretable data representation
spatial‐temporal PCA
ultralow‐dimensionality reduction
url https://doi.org/10.1002/advs.202408173
work_keys_str_mv AT peichen ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca
AT yaofangsuo ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca
AT kazuyukiaihara ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca
AT yeli ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca
AT danwu ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca
AT ruiliu ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca
AT luonanchen ultralowdimensionalityreductionforidentifyingcriticaltransitionsbyspatialtemporalpca