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...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2025-05-01
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| Series: | Advanced Science |
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| Online Access: | https://doi.org/10.1002/advs.202408173 |
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| _version_ | 1849434500729143296 |
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| 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 |
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