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Independent Component Analysis (ICA) is a technique for unsupervised exploration of multichannel data that is widely used in observational sciences. In its classic form, ICA relies on modeling the data as linear mixtures of nonGaussian independent sources. The maximization of the corresponding likelihood is a challenging problem if it has to be completed quickly and accurately on large sets of real data. This problem has been addressed by resorting to quasi-Newton methods, which rely on sparse approximations of the Hessian of the log-likelihood. However, those approximations are not accurate when the ICA model does not hold exactly, as is often the case for real datasets. We propose a new algorithm, dubbed Picard, which makes use of sparse approximate Hessians only as a preconditioner to the L-BFGS algorithm, refining the Hessian approximation from a memory of the past iterates. Extensive numerical comparisons to several algorithms of the same class demonstrate the superior performance of the proposed technique, especially on real data. [ABSTRACT FROM AUTHOR]

Abstract: This paper works on joint approximate diagonalization of simplified fourth order cumulant matrices for very fast and large scale blind separation of instantaneous mixing model sources. The JADE algorithm is widely accepted but only limited to small scale separation tasks. The SHIBBS algorithm calculates a fraction of the fourth order cumulant set and avoids eigenmatrix decomposition to reduce calculation cost. However, it was seen to be slower than JADE at the time of its first publication and is hence less known. On the other hand, the SJAD algorithm using the same approach is shown to be very fast. This paper studies the iteration convergence criterion and proposes to use a signal to noise ratio based iteration stopping threshold approach. The improved SHIBBS/SJAD algorithm is very fast, and capable of large scale separation. Experimental separation comparisons between the SHIBBS/SJAD and FastICA are presented. [Copyright &y& Elsevier]