[This is probably the most widely used algorithm for performing independent component analysis, a recently developed variant of factor analysis that is. Independent Component Analysis [Aapo Hyvärinen, Juha Karhunen, Erkki Oja] on *FREE* shipping on qualifying offers. A comprehensive. Aapo Hyvärinen and Erkki Oja. Helsinki University of with the title “Independent Component Analysis: Algorithms and Applications”. April 1 Motivation.

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Efficient source adaptivity in independent component analysis. A more efficient way of choosing between the models can be based on likelihood ratios of the two models [ 1314 ].

Open in a separate window. This estimation problem is also called blind source separation.

Neurocomputing50 C: Comparing this with 2. In some applications, one naturally obtains a number of data gyvarinen that one would expect to contain the same independent components.

It was shown that the weights needed to best approximate the derivative of G i can be obtained by a rather simple procedure. Neural Computation11 7: Hvarinen connection between ICA and deep learning models is a very interesting topic for future research. Random variables and their realizations are not typographically different, but the index t always denotes realizations. This article has been cited by other articles in PMC.

### Independent Component Analysis: A Tutorial

The classical validation of estimation results is statistical significance also called reliabilitywhich assesses if it is componeent that the results could be obtained by chance. Mutual information is an information-theoretically motivated measure of dependence; so its minimization is simply motivated by the goal of finding components that are as independent as possible.

Neural Computing Surveys 2: Existence and Uniqueness results.

Its fundamental difference to classical multi-variate statistical methods is in the assumption of non-Gaussianity, which enables the identification of original, underlying components, in contrast to classical methods. However, the conditions are not often fullfilled, and in practice, the performance of the methods can be poor.

Alternatively, we can assume that the components s i t are independent in a certain frequency band only. Interestingly, this objective function depends only on the marginal densities of the estimated independent components.

The generality and potential usefulness of the model were never in question, but in the early days of ICA, there was some doubt about the adequacy of the assumptions of non-Gaussianity and independence.

## Independent Component Analysis: A Tutorial

That is why it has been proposed to combine non-negativity with non-Gaussianity, in particular the widespread form of non-Gaussianity called sparseness [ 91 ]. Tensorial extensions of independent component analysis for group fMRI data analysis.

Thus, from an algorithmic viewpoint, the fundamental utility hyarinen using 7. Zoran D, Weiss Y. Survey on Independent Component Analysis. Such NMF with sparseness constraints can be seen analysiss a version of the ICA model where the mixing matrix is constrained to be non-negative, and the independent components are modelled by a distribution that is non-negative and sparse such as the exponential distribution. ICA yyvarinen to find the original components or sources by some simple assumptions of their statistical properties.

If we can make even stronger assumptions on the similarities of the data matrices for different kwe can use methods developed for analysis of such three-way in the context of classical Gaussian multi-variate statistics.

On the identifiability of the post-nonlinear causal model. An information-maximization approach to blind separation and blind deconvolution. We hyvrinen the review of recent developments by considering a rather unexpected application of the theory of ICA found in causal analysis.

## Aapo Hyvärinen: Publications

It has been realized that non-Gaussianity is in fact quite widespread in any applications dealing with scientific measurement devices as opposed to, for example, data in the social and human sciences. In an intuitive sense, such methods would more compknent exploit the structure present in the data, leading to smaller estimation errors e.

It is also possible to estimate nonlinear models, in which case non-Gaussianity may no longer be necessary [ 2223 ]. Paatero P, Tapper U.

As a trivial example, consider two-dimensional data that are concentrated on four points: Author information Copyright and Ihdependent information Disclaimer. In the context of ICA, we would like to be able to say if a component could be obtained, for example, by inputting just pure noise to an ICA algorithm. Imposing sparsity on the mixing matrix in independent component analysis.

Indeterminacy and identifiability of blind identification. The assumption of non-Gaussianity of the e i is combined with the assumption of acyclicity to yield perfect identifiability of the model.