Sparse modelling, tensor decomposition, algorithms and applications

Bernard Mourrain (INRIA)

We will start with the problem of sparse representation of functions, which appear in many applications. As we will see, the tensor decomposition problem is a special case, which we will analyse in details. We will describe algebraic tools and algorithms to compute such a decomposition. This will lead us to the study of duality, apolarity, Hankel operators, solving by eigenvector computation, Artinian Gorenstein algebra, flat extension, orthogonal polynomials. A connection with the Hilbert scheme will be discussed. Several examples of application problems will be presented to illustrate the approach: diffusion tensor decomposition; blind source identification; wave identification; sparse interpolation; …