ROYER , Jean-Philip

In this manuscript, we focus on the minimal polyadic decomposition of third order tensors, which is often referred to: "Canonical Polyadic" (CP), "CanDecomp", or "Parafac". This decomposition is useful in a very wide panel of applications. However, here, we only address the problem of fluorescence spectroscopy applied to environment data...

This paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with matrix exponentials. Gradient components are then...

Computing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the...

This paper deals with the minimal polyadic decomposition (also known as canonical decomposition or Parafac) of a 3-way array, assuming each entry is positive. In this case, the low-rank approximation problem becomes well-posed. The suggested approach consists of taking into account the nonnegative nature of the loading matrices directly in the...

In tensor factorization approaches to blind separation of multidimensional sources, two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the...

In tensor factorization approaches to blind separation of multidimensional sources, two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the...

Raw data are collected in five measurement locations along the Var river. It is assumed that some locations interact with each other, whereas others do not. In such a context, we are interested in determining the contribution of each location and in better understanding the water exchanges that are involved. Organic components can also be...