Cover Image

A nonlocal graph-PDE and higher-order geometric integration for image labeling

Show other versions (1)

Multigrid modeling algorithms are a technique used to accelerate iterative method models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods. Using an objective function derived from a graph-dist...

Full description

Saved in:
Bibliographic Details
Main Authors: Sitenko, Dmitrij (Author) , Boll, Bastian (Author) , Schnörr, Christoph (Author)
Format: Article (Journal)
Language:English
Published: March 30, 2023
In: SIAM journal on imaging sciences
Year: 2023, Volume: 16, Issue: 1, Pages: 501-567
ISSN:1936-4954
DOI:10.1137/22M1496141
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/22M1496141
Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/22M1496141
Get full text
Author Notes:Dmitrij Sitenko, Bastian Boll, and Christoph Schnörr

MARC

LEADER 00000caa a2200000 c 4500
001 1850434247
003 DE-627
005 20230706203226.0
007 cr uuu---uuuuu
008 230616s2023 xx |||||o 00| ||eng c
024 7 |a 10.1137/22M1496141  |2 doi 
035 |a (DE-627)1850434247 
035 |a (DE-599)KXP1850434247 
035 |a (OCoLC)1389529114 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 27  |2 sdnb 
100 1 |a Sitenko, Dmitrij  |d 1991-  |e VerfasserIn  |0 (DE-588)1269603604  |0 (DE-627)1818104296  |4 aut 
245 1 2 |a A nonlocal graph-PDE and higher-order geometric integration for image labeling  |c Dmitrij Sitenko, Bastian Boll, and Christoph Schnörr 
264 1 |c March 30, 2023 
300 |a 67 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 16.06.2023 
520 |a Multigrid modeling algorithms are a technique used to accelerate iterative method models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods. Using an objective function derived from a graph-distance metric, we perform orthogonally-constrained optimization to find optimal prolongation and restriction maps between graphs. We compare and contrast several methods for performing this numerical optimization, and additionally present some new theoretical results on upper bounds of this type of objective function. Once calculated, these optimal maps between graphs form the core of multiscale artificial neural network (MsANN) training, a new procedure we present which simultaneously trains a hierarchy of neural network models of varying spatial resolution. Parameter information is passed between members of this hierarchy according to standard coarsening and refinement schedules from the multiscale modeling literature. In our machine learning experiments, these models are able to learn faster than training at the fine scale alone, achieving a comparable level of error with fewer weight updates (by an order of magnitude). 
700 1 |a Boll, Bastian  |d 1996-  |e VerfasserIn  |0 (DE-588)1241416443  |0 (DE-627)1770926682  |4 aut 
700 1 |a Schnörr, Christoph  |e VerfasserIn  |0 (DE-588)1023033348  |0 (DE-627)717351017  |0 (DE-576)168404540  |4 aut 
773 0 8 |i Enthalten in  |a Society for Industrial and Applied Mathematics  |t SIAM journal on imaging sciences  |d Philadelphia, Pa. : SIAM, 2008  |g 16(2023), 1 vom: März, Seite 501-567  |h Online-Ressource  |w (DE-627)561317917  |w (DE-600)2418483-4  |w (DE-576)279226195  |x 1936-4954  |7 nnas 
773 1 8 |g volume:16  |g year:2023  |g number:1  |g month:03  |g pages:501-567  |g extent:67  |a A nonlocal graph-PDE and higher-order geometric integration for image labeling 
856 4 0 |u https://doi.org/10.1137/22M1496141  |x Verlag  |x Resolving-System  |z lizenzpflichtig  |3 Volltext 
856 4 0 |u https://epubs.siam.org/doi/10.1137/22M1496141  |x Verlag  |z lizenzpflichtig  |3 Volltext 
951 |a AR 
992 |a 20230616 
993 |a Article 
994 |a 2023 
998 |g 1023033348  |a Schnörr, Christoph  |m 1023033348:Schnörr, Christoph  |d 110000  |d 110200  |d 110000  |d 110400  |e 110000PS1023033348  |e 110200PS1023033348  |e 110000PS1023033348  |e 110400PS1023033348  |k 0/110000/  |k 1/110000/110200/  |k 0/110000/  |k 1/110000/110400/  |p 3  |y j 
998 |g 1241416443  |a Boll, Bastian  |m 1241416443:Boll, Bastian  |d 110000  |d 110200  |d 110000  |d 110400  |e 110000PB1241416443  |e 110200PB1241416443  |e 110000PB1241416443  |e 110400PB1241416443  |k 0/110000/  |k 1/110000/110200/  |k 0/110000/  |k 1/110000/110400/  |p 2 
999 |a KXP-PPN1850434247  |e 4339809209 
BIB |a Y 
SER |a journal 
JSO |a {"person":[{"family":"Sitenko","display":"Sitenko, Dmitrij","role":"aut","given":"Dmitrij"},{"role":"aut","given":"Bastian","display":"Boll, Bastian","family":"Boll"},{"role":"aut","given":"Christoph","family":"Schnörr","display":"Schnörr, Christoph"}],"note":["Gesehen am 16.06.2023"],"title":[{"title_sort":"nonlocal graph-PDE and higher-order geometric integration for image labeling","title":"A nonlocal graph-PDE and higher-order geometric integration for image labeling"}],"origin":[{"dateIssuedKey":"2023","dateIssuedDisp":"March 30, 2023"}],"type":{"media":"Online-Ressource","bibl":"article-journal"},"language":["eng"],"physDesc":[{"extent":"67 S."}],"name":{"displayForm":["Dmitrij Sitenko, Bastian Boll, and Christoph Schnörr"]},"recId":"1850434247","id":{"eki":["1850434247"],"doi":["10.1137/22M1496141"]},"relHost":[{"note":["Gesehen am 05.03.20"],"origin":[{"dateIssuedDisp":"2008-","publisherPlace":"Philadelphia, Pa.","dateIssuedKey":"2008","publisher":"SIAM"}],"title":[{"title":"SIAM journal on imaging sciences","title_sort":"SIAM journal on imaging sciences"}],"titleAlt":[{"title":"Journal on imaging sciences"},{"title":"SIIMS"}],"type":{"bibl":"periodical","media":"Online-Ressource"},"part":{"extent":"67","volume":"16","year":"2023","text":"16(2023), 1 vom: März, Seite 501-567","pages":"501-567","issue":"1"},"language":["eng"],"corporate":[{"display":"Society for Industrial and Applied Mathematics","role":"aut"}],"disp":"Society for Industrial and Applied MathematicsSIAM journal on imaging sciences","id":{"eki":["561317917"],"issn":["1936-4954"],"zdb":["2418483-4"]},"name":{"displayForm":["Society for Industrial and Applied Mathematics"]},"physDesc":[{"extent":"Online-Ressource"}],"pubHistory":["1.2008 -"],"recId":"561317917"}]} 
SRT |a SITENKODMINONLOCALGR3020 

Similar Items