Objective 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. Fields of science social sciencessociologysocial issuescorruptionnatural sciencescomputer and information sciencesartificial intelligencecomputer visionnatural sciencesmathematicspure mathematicsgeometrynatural sciencescomputer and information sciencesartificial intelligencemachine learning Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2018-STG - ERC Starting Grant Call for proposal ERC-2018-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Coordinator UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA Net EU contribution € 1 434 000,00 Address Piazzale aldo moro 5 00185 Roma Italy See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA Italy Net EU contribution € 1 434 000,00 Address Piazzale aldo moro 5 00185 Roma See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
