We develop a super-fast kernel density estimation algorithm (FastKDE) and based on this a fast kernel independent component analysis algorithm (KDICA). FastKDE calculates the kernel density estimator exactly and its computation only requires sorting n numbers plus roughly 2n evaluations of the exponential function, where n is the sample size. KDICA converges as quickly as parametric ICA algorit...

This paper presents an introduction to independent component analysis (ICA). Unlike principal component analysis, which is based on the assumptions of uncorrelatedness and normality, ICA is rooted in the assumption of statistical independence. Foundations and basic knowledge necessary to understand the technique are provided hereafter. Also included is a short tutorial illustrating the implemen...

In this paper, we derive new xed-point algorithms for the blind separation of complex-valued mixtures of independent, possibly non-circularly-symmetric, and non-Gaussian source signals. Leveraging recent results in complex independent component analysis, we construct iterative procedures for complex signal mixtures whose evolutionary characteristics are identical to those of the real-valued Fa...

In this paper, a prototype of novel algorithm for blind separation of convolutive mixtures of audio sources is proposed. The method works in time-domain, and it is based on the recently very successful algorithm EFICA for Independent Component Analysis, which is an enhanced version of more famous FastICA. Performance of the new algorithm is very promising, at least, comparable to other (mostly ...

An improved method for independent component analysis based on the diagonalization of cumulant tensors is proposed. It is based on Comon’s algorithm [1] but it takes thirdand fourth-order cumulant tensors into account simultaneously. The underlying contrast function is also mathematically much simpler and has a more intuitive interpretation. It is therefore easier to optimize and approximate. A...

We address independent component analysis (ICA) of piecewise stationary and nonGaussian signals and propose a novel ICA algorithm called Block EFICA that is based on this generalized model of signals. The method is a further extension of the popular nonGaussianity-based FastICA algorithm and of its recently optimized variant called EFICA. In contrast to these methods, Block EFICA is developed t...

A major problem in application of independent component analysis (ICA) is that the reliability of the estimated independent components is not known. Firstly, the finite sample size induces statistical errors in the estimation. Secondly, as real data never exactly follows the ICA model, the contrast function used in the estimation may have many local minima which are all equally good, or the pra...

Independent component analysis (ICA) is a modern factor analysis tool developed in the last two decades. Given p-dimensional data, we search for that linear combination of data which creates (almost) independent components. Here copulae are used to model the p-dimensional data and then independent components are found by optimizing the copula parameters. Based on this idea, we propose the COPIC...

The FastICA algorithm is a popular procedure for independent component analysis and blind source separation. In this paper, we analyze the average convergence behavior of the single-unit FastICA algorithm with kurtosis contrast for general m-source noiseless mixtures. We prove that this algorithm causes the average inter-channel interference (ICI) to converge exponentially with a rate of (1/3) ...