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H2020Staff exchange2018–2023

NoMADS · Nonlocal Methods for Arbitrary Data Sources

Horizon 2020 — Marie Skłodowska-Curie Actions

Duration
2018-03-01 → 2023-08-31
EU contribution
€1,111,500
Participants
27
Scheme
MSCA-RISE

Lines connect the coordinator with its partners. CORDIS does not always give exact coordinates for projects before 2014. These points are placed at city or country level.

Results in brief

Nonlocal Methods for Arbitrary Data Sources

This research network addresses problems with data that can be interpreted and/or processed via nonlocal relationships. Typical examples include 3D point-cloud data used in several industrial applications, data derived from imaging techniques in biomedicine, remote sensing for earth observation and conservation, or scans of historical documents from cultural heritage. The key issues to be addressed in this project are basic processing of data (e.g., reconstruction, filtering, denoising, or inpainting) as well as methods that extract advanced information from the data, like clustering or decomposition. These goals are to be achieved using a merely data-driven approach trying to exploit ephemeral patterns and self-similarity at larger distances hidden in the data, which are called ‘nonlocal methods’ and are often realized on weighted graphs. The latter are an active field of research in mathematics and computer science with a strong overlap to modern machine learning, in particular several current deep learning architectures. For this sake, NoMADS builds on a large multidisciplinary network of universities and companies, bringing together a strong international group of leading researchers from mathematics (applied and computational analysis, statistics, and optimisation), computer vision, and data mining. A major objective is to significantly increase understanding and applicability of nonlocal methods in a wide range of applications that covers a variety of different data sources. The overall objectives of this project are the theoretical understanding of nonlocal relationships of data and associated mathematical operators, the efficient implementation of numerical algorithms for nonlocal problems, and their application to real-world problems in industry and society. During the implementation of this project our research network has discovered fundamental mathematical principles for the characterization of nonlocal operators both in a discrete setting as well as in continuous mathematics and has established important relationships between these two worlds. Furthermore, we were able to develop new efficient algorithms, that exploit the geometry of given data and consequently boost the performance of software implementations using these methods. Finally, many interesting approaches and ideas have been investigated on real-world problems that allowed to bridge the gap between theory of nonlocal operators and their future use in industrial applications.

Data: CORDIS, © European Union

Project objective

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 convolutionalneural 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-independentproperties 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 wellwith 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.

Original text from CORDIS.

Participants

  • FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN-NUERNBERG · ErlangenCoordinatorGermany
  • ASTRAZENECA UK LIMITED · CAMBRIDGEUnited Kingdom
  • CAMELOT BIOMEDICAL SYSTEMS SRL · GenovaItaly
  • CARNEGIE MELLON UNIVERSITY · PittsburghUnited States
  • CLINICAL SCIENCE SYSTEMS · LeidenNetherlands
  • CLK GMBH · ALTENBERGEGermany
  • DATEXIM · CaenFrance
  • ECOLE NATIONALE SUPERIEURE D'INGENIEURS DE CAEN · CaenFrance
  • ECOLE POLYTECHNIQUE · PALAISEAU CEDEXFrance
  • INSTITUTO SUPERIOR TECNICO · LisboaPortugal
  • MEDIGUIDE LTD · HaifaCity levelIsrael
  • POLITECNICO DI MILANO · MilanoItaly
  • TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY · HaifaIsrael
  • TECHNISCHE UNIVERSITEIT DELFT · DelftNetherlands
  • THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE · CAMBRIDGEUnited Kingdom
  • THE MATHWORKS LIMITED · Cambridge CambsUnited Kingdom
  • THE REGENTS OF THE UNIVERSITY OF CALIFORNIA · OaklandUnited States
  • THE UNIVERSITY OF MANCHESTER · ManchesterUnited Kingdom
  • THE UNIVERSITY OF NOTTINGHAM · NottinghamUnited Kingdom
  • UNIVERSIDAD POMPEU FABRA · BarcelonaSpain
  • UNIVERSITA DEGLI STUDI DI GENOVA · GENOVAItaly
  • UNIVERSITAET MUENSTER · MuensterGermany
  • UNIVERSITE COTE D'AZUR · NiceFrance
  • UNIVERSITE DE BORDEAUX · BordeauxFrance
  • UNIVERSITE DE CAEN NORMANDIE · Caen Cedex 5France
  • UNIVERSITE LYON 1 CLAUDE BERNARD · Villeurbanne CedexFrance
  • UNIVERSITEIT TWENTE · EnschedeNetherlands

Links

Data: CORDIS, © European Union