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NoMADS

Nonlocal Methods for Arbitrary Data Sources

CoordinatorTechnion – Israel Institute of Technology ; University of Twente ; UNIVERSITE DE BORDEAUX ; MEDIGUIDE LTD ; THE MATHWORKS LIMITED ; CLINICAL SCIENCE SYSTEMS ; Camelot Biomedical Systems (Italy) ; CLK GMBH ; DATEXIM ; INSTITUTO SUPERIOR TECNICO ; Delft University of Technology ; Université de Caen Basse-Normandie ; Pompeu Fabra University ; FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN NUERNBERG ; École Nationale Supérieure d'ingénieurs De Caen ; Nottingham Trent University ; Ecole Polytechnique ; ASTRAZENECA UK LIMITED ; WESTFAELISCHE WILHELMS-UNIVERSITAET MUENSTER ; Polytechnic University of Milan ; THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE ; UNI: Université de Claude Bernard Lyon F ; University of Genoa
Grant period2018-03-01 - 2023-08-31
Funding bodyEuropean Union
Call numberH2020-MSCA-RISE-2017
Grant number777826
IdentifierG:(EU-Grant)777826

Note: In NoMADS we focus on data processing and analysis techniques which can feature potentially very complex, nonlocal, relationships within the data. In this context, methodologies such as spectral clustering, graph partitioning, and convolutional neural networks have gained increasing attention in computer science and engineering within the last years, mainly from a combinatorial point of view. However, the use of nonlocal methods is often still restricted to academic pet projects. There is a large gap between the academic theories for nonlocal methods and their practical application to real-world problems. The reason these methods work so well in practice is far from fully understood. Our aim is to bring together a strong international group of researchers from mathematics (applied and computational analysis, statistics, and optimisation), computer vision, biomedical imaging, and remote sensing, to fill the current gaps between theory and applications of nonlocal methods. We will study discrete and continuous limits of nonlocal models by means of mathematical analysis and optimisation techniques, resulting in investigations on scale-independent properties of such methods, such as imposed smoothness of these models and their stability to noisy input data, as well as the development of resolution-independent, efficient and reliable computational techniques which scale well with the size of the input data. As an overarching applied theme we focus in particular on image data arising in biology and medicine, which offers a rich playground for structured data processing and has direct impact on society, as well as discrete point clouds, which represent an ambitious target for unstructured data processing. Our long-term vision is to discover fundamental mathematical principles for the characterisation of nonlocal operators, the development of new robust and efficient algorithms, and the implementation of those in high quality software products for real-world application.
     

Recent Publications

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http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Dissertation / PhD Thesis  ;  ;  ;
Consistency, Robustness and Sparsity for Learning Algorithms
FAU 217 pp. () [10.25593/OPEN-FAU-522] = Dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2024  GO OpenAccess  Download fulltext Files  Download fulltextFulltext BibTeX | EndNote: XML, Text | RIS

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article  ;  ;
Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian
The annals of applied probability 34(4), 3870 - 3910 () [10.1214/24-AAP2052]  GO OpenAccess  Download fulltext Files BibTeX | EndNote: XML, Text | RIS

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article  ;  ;
Spectral Total-Variation Processing of Shapes - Theory and Applications
ACM transactions on graphics 43(2), 3641845 () [10.1145/3641845]  GO OpenAccess  Download fulltext Files  Download fulltextFulltext Download fulltextFulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article  ;  ;
Polarized consensus-based dynamics for optimization and sampling
Mathematical programming 21, 125 - 155 () [10.1007/s10107-024-02095-y]  GO OpenAccess  Download fulltext Files  Download fulltextFulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article  ;  ;  ;
Hypergraph p-Laplacians and Scale Spaces
Journal of mathematical imaging and vision 66(4), 529-549 () [10.1007/s10851-024-01183-0] special issue: "Special Issue SSVM 2023"  GO OpenAccess  Download fulltext Files  Download fulltextFulltext BibTeX | EndNote: XML, Text | RIS

All known publications ...
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 Record created 2018-02-17, last modified 2023-02-10
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