A decomposition for three-way arrays
SIAM Journal on Matrix Analysis and Applications
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
High-order contrasts for independent component analysis
Neural Computation
Blind source separation via the second characteristic function
Signal Processing
Learning Overcomplete Representations
Neural Computation
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
Blind identification and source separation in 2×3 under-determined mixtures
IEEE Transactions on Signal Processing
Blind identification of MISO-FIR channels
Signal Processing
Blind underdetermined mixture identification by joint canonical decomposition of HO cumulants
IEEE Transactions on Signal Processing
Computing symmetric rank for symmetric tensors
Journal of Symbolic Computation
Multihomogeneous polynomial decomposition using moment matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
General tensor decomposition, moment matrices and applications
Journal of Symbolic Computation
| Hi-index | 0.00 |
Linear mixtures of independent random variables (the so-called sources) are sometimes referred to as under-determined mixtures (UDM) when the number of sources exceeds the dimension of the observation space. The algorithms proposed are able to identify algebraically a UDM using the second characteristic function (c.f.) of the observations, without any need of sparsity assumption on sources. In fact, by taking higher order derivatives of the multivariate c.f. core equation, the blind identification problem is shown to reduce to a tensor decomposition. With only two sensors, the first algorithm only needs a SVD. With a larger number of sensors, the second algorithm executes an alternating least squares (ALS) algorithm. The joint use of statistics of different orders is possible, and a LS solution can be computed. Identifiability conditions are stated in each of the two cases. Computer simulations eventually demonstrate performances in the absence of sparsity, and emphasize the interest in using jointly derivatives of different orders.