## Section: Other Grants and Activities

### National actions

#### ANR DECOTES, Tensorial decomposition and applications

Years: 2006–2009.

Partners: I3S, CNRS; LTSI, INSERM; GALAAD, INRIA; SBP, Thales communications.

The problem of decomposition of a symmetric or non-symmetric tensor in minimal way is an important problem, which has applications in many domains. It is essential in the process of Blind Identification of Under-Determined Mixtures (UDM), i.e., linear mixtures with more inputs than observable outputs and appear in many application areas, including speech, mobile communications, machine learning, factor analysis with k -way arrays (MWA), biomedical engineering, psychometrics, and chemometrics. The aim of the project DECOTES is to study the key theoretical problems of such decompositions and to devise numerical algorithms dedicated to some selected applications.

With Elias Tsigaridas, within the framework of a post-doctoral position, we are investigating algebraic methods to compute such a decomposition in order to extend the Sylvester's approach for binary forms to polynomials with more variables.