Decomposition of Structured Tensors, Algorithms and Characterization

Project Information

DECONSTRUCT

Grant agreement ID: 252367

Project closed

Start date 8 November 2010

End date 7 November 2012

Funded under

• Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Total cost € 157 945,60

EU contribution € 157 945,60

Coordinated by

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
France

Objective

Tensors play a wide role in numerous application areas as Signal Processing for Telecommunications, Arithmetic Complexity or Data Analysis. In some applications tensors may be completely symmetric, or symmetric only in some modes, or may not be symmetric. In most of these applications, the decomposition of a tensor into a sum of rank-1 terms is relevant, since tensors of interest have a reduced rank. Most of them are structured i.e. they are either symmetric or enjoy some index-invariance. Lastly, they are often real, which raises open problems concerning the existence and calculation of the decompositions. These issues build the basic bricks of the research program we propose. The classes of tensors described above have a geometric translations in terms of classical algebraic varieties: Segre, Veronese, Segre-Veronese varieties and Grassmannians and their secant varieties. A complete description of equations for those secant varieties and their dimensions is still not known (only dimensions of secant varieties to Veronsean are classified), although they have been studied by algebraic and differential geometers and algebraists for a long period up to now. The aim of this research project is: -to attack both the description of the ideal of those secant varieties and their dimensions, starting from low dimensions and low degrees, -to propose algorithms able to compute the rank of structured tensors. Workshops in Palo Alto (CA-USA, 2008) and in Nice (FR, 2009) showed that Italy and France are among the most active in Europe in the field of tensor decompositions. Both the coordinator of this project and the hosting organization have already obtained results in this field regarding equations and algorithms. Hence this program is crucial for the development of those research areas in the European Community, along with the numerous international collaborations already existing. The impact of this project will be visible in both academic and industrial worlds.

Fields of science

• natural sciences › computer and information sciences › data science
• engineering and technology › electrical engineering, electronic engineering, information engineering › electronic engineering › signal processing
• natural sciences › mathematics › pure mathematics › arithmetics
• engineering and technology › electrical engineering, electronic engineering, information engineering › information engineering › telecommunications

Programme(s)

• FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Topic(s)

• FP7-PEOPLE-2009-IEF - Marie Curie Action: "Intra-European Fellowships for Career Development"

Call for proposal

FP7-PEOPLE-2009-IEF
See other projects for this call

Funding Scheme

MC-IEF - Intra-European Fellowships (IEF)

Coordinator

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE

• EU contribution: € 157 945,60
• Address: DOMAINE DE VOLUCEAU ROCQUENCOURT ; 78153 Le Chesnay Cedex ; France
• Region: Ile-de-France › Ile-de-France › Yvelines
• Activity type: Research Organisations
• Administrative Contact: Frédérique Lavirotte (Ms.)
• Total cost: No data