SORENSEN , Mikael

The computation of the model parameters of a Canonical Polyadic Decomposition (CPD), also known as the parallel factor (PARAFAC) or canonical decomposition (CANDECOMP) or CP decomposition, is typically done by resorting to iterative algorithms, e.g. either iterative alternating least squares type or descent methods. In many practical problems...

Tensor decompositions permit to estimate in a deterministic way the parameters in a multi-linear model. Applications have been already pointed out in antenna array processing and digital communications, among others, and are extremely attractive provided some diversity at the receiver is available. As opposed to the widely used ALS algorithm,...

Approximate Joint Diagonalization (AJD) of a set of symmetric matrices by an orthogonal transform is a popular problem in Blind Source Separation (BSS). In this paper we propose a gradient based algorithm which maximizes the sum of squares of diagonal entries of all the transformed symmetric matrices. Our main contribution is to transform the...

Space-Time Block Codes can be represented by tensors, like for example the Kathri-Rao Space Time codes introduced by Sidiropoulos. In this paper, we introduce a Parallel Factor Analysis 2 (PARAFAC2) model for Orthogonal Space-Time Block Codes (OSTBC). This model, along with tensor diagonalisation designed for orthogonal tensors, leads us to...

Multilinear techniques are increasingly used in Signal Processing and Factor Analysis. In particular, it is often of interest to transform a tensor into another that is as diagonal as possible or to simultaneously transform a set matrices into a set of matrices that are close to diagonal. In this paper we propose a parameterization of the...

Canonical Polyadic Decomposition (CPD) of a higher-order tensor is an important tool in mathematical engineering. In many applications at least one of the matrix factors is constrained to be column-wise orthonormal. We first derive a relaxed condition that guarantees uniqueness of the CPD under this constraint. Second, we give a simple proof of...