{"id":1385,"date":"2025-01-23T07:04:02","date_gmt":"2025-01-23T07:04:02","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/01\/23\/2501-12582\/"},"modified":"2025-01-23T07:04:02","modified_gmt":"2025-01-23T07:04:02","slug":"2501-12582","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/01\/23\/2501-12582\/","title":{"rendered":"Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA"},"content":{"rendered":"<p>    Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2501.12582v1 Announce Type: new<br \/>\nAbstract: 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.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Pei Chen, Yaofang Suo, Rui Liu, Luonan Chen<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2501.12582\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA arXiv:2501.12582v1 Announce Type: new 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 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[1437,661,1010],"class_list":["post-1385","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-critical","tag-spatial","tag-temporal"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1385"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=1385"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1385\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1385"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=1385"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=1385"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}