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The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which(More)
Glossary x vector of components x p , 1 ≤ p ≤ P s, x, y sources, observations, separator outputs N number of sources P number of sensors T number of observed samples convolution A matrix with components A ij A, B mixing and separation matrices G, W, Q global, whitening, and separating unitary matriceš g Fourier transform of g s estimate of quantity s p x(More)
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors. Any symmetric tensor can be decomposed into a linear combination of(More)
For about two decades, many fourth order (FO) array processing methods have been developed for both direction finding and blind identification of non-Gaussian signals. One of the main interests in using FO cumulants only instead of second-order (SO) ones in array processing applications relies on the increase of both the effective aperture and the number of(More)
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referred to as RobustICA, is put forward in(More)
Though it arouses more and more curiosity, the HJ iterative algorithm has never been derived in mathematical terms to date. We attempt in this paper to describe it from a statistical point of view. For instance the updat ing term of the synaptic efficacies matrix cannot be the gradient of a single C a functional contrary to what is sometimes understood. In(More)
The ALS algorithm, used to fit the Parafac model, sometimes needs a large number of iterations before converging. The slowness in convergence can be due to the large size of the data, or to the presence of degeneracies, etc. Several methods have been proposed to speed up the algorithm, some of which are compression [3], and Line Search [2]. In this paper,(More)
We present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric tensors of dimension 2. We exploit the known fact that every symmetric tensor is equivalently represented by a homogeneous polynomial in n variables of total degree(More)
This work was originally motivated by a classification of tensors proposed by Richard Harshman. In particular, we focus on simple and multiple “bottlenecks”, and on “swamps”. Existing theoretical results are surveyed, some numerical algorithms are described in details, and their numerical complexity is calculated. In particular, the interest in using the(More)