Spectral geometric methods in practice

Projektinformationen

SPECGEO

ID Finanzhilfevereinbarung: 802554

DOI 10.3030/802554

EK-Unterschriftsdatum 31 August 2018

Startdatum 1 September 2018

Enddatum 31 August 2024

Finanziert unter

• EXCELLENT SCIENCE - European Research Council (ERC)

Gesamtkosten € 1 434 000,00

EU-Beitrag € 1 434 000,00

Koordiniert durch

UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA
Italy

Ziel

Spectral geometry concerns the study of the geometric properties of data domains, such as surfaces or graphs, via the spectral decomposition of linear operators defined upon them. Due to their valuable properties analogous to Fourier theory, such methods find widespread use in several branches of computer science, ranging from computer vision to machine learning and network analysis.

Despite their pervasive presence, very little efforts have been devoted to the design and application of spectral techniques that deal with corrupted, missing, high-dimensional or abstract data undergoing complex transformations. This lack of focus is mainly motivated by the widespread acceptance, supported in part by theoretical results, that an ε-perturbation to the geometry of the data (as small as the removal of a single point) can induce arbitrary changes in the operator’s eigendecomposition – leading to a limited adoption of spectral models in real-world applications. This project challenges this view, contending that such presumption of instability is primarily due to a suboptimal choice of the analytical tools that are currently being employed, and which only provide part of the picture. In fact, strong evidence largely contradicts the expected behavior on real geometric data. The reason behind this apparent inconsistency lies in the different focus of current methods, which provide crude bounds and are directed toward other kinds of perturbation than those observed in real settings.

The ambitious goal of this project is to develop a novel theoretical and computational framework that will fundamentally change the way spectral techniques are constructed, interpreted, and applied. These tools will enable a range of currently infeasible uses of spectral methods on real data. They will deal with strong incompleteness, corruption and cross-modality, and they will be applied to outstanding problems in geometry processing, computer vision, machine learning, and computational biology.

Wissenschaftliches Gebiet

• social sciences › sociology › social issues › corruption
• natural sciences › computer and information sciences › artificial intelligence › computer vision
• natural sciences › mathematics › pure mathematics › geometry
• natural sciences › computer and information sciences › artificial intelligence › machine learning

Programm/Programme

• H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme

Thema/Themen

• ERC-2018-STG - ERC Starting Grant

Aufforderung zur Vorschlagseinreichung

ERC-2018-STG

Finanzierungsplan

ERC-STG - Starting Grant

Gastgebende Einrichtung

UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA

• Netto-EU-Beitrag: € 1 434 000,00
• Adresse: Piazzale Aldo Moro 5 ; 00185 Roma ; Italien
• Region: Centro (IT) › Lazio › Roma
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: € 1 434 000,00

Begünstigte (1)

UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA

Italien

• Netto-EU-Beitrag: € 1 434 000,00
• Adresse: Piazzale Aldo Moro 5 ; 00185 Roma
• Region: Centro (IT) › Lazio › Roma
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: € 1 434 000,00