FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3182376623> ?p ?o ?g. }

• W3182376623 endingPage "e2100473118" @default.
• W3182376623 startingPage "e2100473118" @default.
• W3182376623 abstract "Most high-dimensional datasets are thought to be inherently low-dimensional-that is, data points are constrained to lie on a low-dimensional manifold embedded in a high-dimensional ambient space. Here, we study the viability of two approaches from differential geometry to estimate the Riemannian curvature of these low-dimensional manifolds. The intrinsic approach relates curvature to the Laplace-Beltrami operator using the heat-trace expansion and is agnostic to how a manifold is embedded in a high-dimensional space. The extrinsic approach relates the ambient coordinates of a manifold's embedding to its curvature using the Second Fundamental Form and the Gauss-Codazzi equation. We found that the intrinsic approach fails to accurately estimate the curvature of even a two-dimensional constant-curvature manifold, whereas the extrinsic approach was able to handle more complex toy models, even when confounded by practical constraints like small sample sizes and measurement noise. To test the applicability of the extrinsic approach to real-world data, we computed the curvature of a well-studied manifold of image patches and recapitulated its topological classification as a Klein bottle. Lastly, we applied the extrinsic approach to study single-cell transcriptomic sequencing (scRNAseq) datasets of blood, gastrulation, and brain cells to quantify the Riemannian curvature of scRNAseq manifolds." @default.
• W3182376623 created "2021-07-19" @default.
• W3182376623 creator A5036478105 @default.
• W3182376623 creator A5047847184 @default.
• W3182376623 creator A5056164433 @default.
• W3182376623 date "2021-07-16" @default.
• W3182376623 modified "2023-10-08" @default.
• W3182376623 title "Computing the Riemannian curvature of image patch and single-cell RNA sequencing data manifolds using extrinsic differential geometry" @default.
• W3182376623 cites W1479704546 @default.
• W3182376623 cites W1494826373 @default.
• W3182376623 cites W1528911722 @default.
• W3182376623 cites W1966949944 @default.
• W3182376623 cites W1984462878 @default.
• W3182376623 cites W1991566301 @default.
• W3182376623 cites W2001141328 @default.
• W3182376623 cites W2012388631 @default.
• W3182376623 cites W2024691638 @default.
• W3182376623 cites W2038254572 @default.
• W3182376623 cites W2053129129 @default.
• W3182376623 cites W2060300932 @default.
• W3182376623 cites W2071391326 @default.
• W3182376623 cites W2101933716 @default.
• W3182376623 cites W2102212449 @default.
• W3182376623 cites W2103975664 @default.
• W3182376623 cites W2104339857 @default.
• W3182376623 cites W2107385756 @default.
• W3182376623 cites W2116016979 @default.
• W3182376623 cites W2117684310 @default.
• W3182376623 cites W2120023453 @default.
• W3182376623 cites W2121281425 @default.
• W3182376623 cites W2124731682 @default.
• W3182376623 cites W2135937351 @default.
• W3182376623 cites W2141376824 @default.
• W3182376623 cites W2144044408 @default.
• W3182376623 cites W2157878484 @default.
• W3182376623 cites W2164435545 @default.
• W3182376623 cites W2295124130 @default.
• W3182376623 cites W2413133914 @default.
• W3182376623 cites W2509957998 @default.
• W3182376623 cites W2522224202 @default.
• W3182376623 cites W2561429117 @default.
• W3182376623 cites W2586637063 @default.
• W3182376623 cites W2592449894 @default.
• W3182376623 cites W2607384979 @default.
• W3182376623 cites W2766437506 @default.
• W3182376623 cites W2783380616 @default.
• W3182376623 cites W2805619986 @default.
• W3182376623 cites W2832881433 @default.
• W3182376623 cites W2902652978 @default.
• W3182376623 cites W2912031427 @default.
• W3182376623 cites W2912272542 @default.
• W3182376623 cites W2917576966 @default.
• W3182376623 cites W2950336271 @default.
• W3182376623 cites W2954066696 @default.
• W3182376623 cites W2976645955 @default.
• W3182376623 cites W2992037634 @default.
• W3182376623 cites W2999304916 @default.
• W3182376623 cites W3010470448 @default.
• W3182376623 cites W3102292222 @default.
• W3182376623 cites W3121267967 @default.
• W3182376623 cites W3133287152 @default.
• W3182376623 cites W4213171111 @default.
• W3182376623 cites W4235974481 @default.
• W3182376623 cites W4246954948 @default.
• W3182376623 doi "https://doi.org/10.1073/pnas.2100473118" @default.
• W3182376623 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/8307776" @default.
• W3182376623 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/34272279" @default.
• W3182376623 hasPublicationYear "2021" @default.
• W3182376623 type Work @default.
• W3182376623 sameAs 3182376623 @default.
• W3182376623 citedByCount "2" @default.
• W3182376623 countsByYear W31823766232021 @default.
• W3182376623 countsByYear W31823766232022 @default.
• W3182376623 crossrefType "journal-article" @default.
• W3182376623 hasAuthorship W3182376623A5036478105 @default.
• W3182376623 hasAuthorship W3182376623A5047847184 @default.
• W3182376623 hasAuthorship W3182376623A5056164433 @default.
• W3182376623 hasBestOaLocation W31823766231 @default.
• W3182376623 hasConcept C114614502 @default.
• W3182376623 hasConcept C12089564 @default.
• W3182376623 hasConcept C12520029 @default.
• W3182376623 hasConcept C127413603 @default.
• W3182376623 hasConcept C134306372 @default.
• W3182376623 hasConcept C154945302 @default.
• W3182376623 hasConcept C181104567 @default.
• W3182376623 hasConcept C184720557 @default.
• W3182376623 hasConcept C192939610 @default.
• W3182376623 hasConcept C195065555 @default.
• W3182376623 hasConcept C2524010 @default.
• W3182376623 hasConcept C2779668893 @default.
• W3182376623 hasConcept C33923547 @default.
• W3182376623 hasConcept C41008148 @default.
• W3182376623 hasConcept C41608201 @default.
• W3182376623 hasConcept C529865628 @default.
• W3182376623 hasConcept C78519656 @default.
• W3182376623 hasConceptScore W3182376623C114614502 @default.
• W3182376623 hasConceptScore W3182376623C12089564 @default.
• W3182376623 hasConceptScore W3182376623C12520029 @default.

• next