[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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Open in a separate window. Such NMF with sparseness constraints can be seen as a version of the ICA model where the mixing matrix is constrained to be non-negative, and indpeendent independent components are modelled by a distribution that is non-negative and sparse such as the exponential distribution.

Handbook of blind source separation New York, NY: If we further assume that the connection between the two variables takes the form of a linear regression model, we are basically left with the following model selection problem.

The theory was further developed in Gretton et al.

The differences between the conditions k are thus modelled by the diagonal matrices D k. In addition to such visualization, hyvsrinen developed methods allow the statistical quantification of the reliability of the components. Features an easy-to-use software package for Matlab.

Comon P, Jutten C. A unifying model for blind separation of independent sources. Environmetrics 5— Image Denoising by Sparse Code Shrinkage. This is in strong contrast to classical scientific methods based on some experimentally manipulated variables, as formalized in regression or classification methods.

Existence and Uniqueness results. Regarding brain imaging and telecommunications, such specialized literature is already quite extensive. Source adaptive blind source separation: The assumption of non-Gaussianity of the e i is combined with the assumption of acyclicity to yield perfect identifiability of the model.

A blind source separation technique based on second order statistics. On the other hand, if one computes quantities such as Fourier spectra, or histograms, non-negativity may be an important aspect of the data [ 88 ] because values in high-dimensional spectra and histograms are often concentrated near zero.

## Aapo Hyvärinen: Publications

It seems that this method has not been widely used mainly because the main software packages for ICA do not implement it, but on a theoretical level, it looks extremely promising. Theory 52 analyeis, — The extensions of ICA with correlations of squares essentially differ in what kind of dependencies they assume for the variance variables v i. For non-Gaussian variables, on the other hand, whitening does not at all imply independence, and there is much more information in the data than what is used in whitening.

Estimating overcomplete independent component bases for image windows. ICA is thus an exploratory, or data-driven method: The generality and potential usefulness of the model were never in question, but in the early days componenf ICA, there was some doubt about the adequacy analyssis the assumptions of non-Gaussianity and independence.

### Publications by Aapo Hyvarinen: FastICA

Signal Processing85 7: This highlights the importance of non-Gaussianity: This is in stark contrast to uncorrelatedness, which means that 6. An earlier approach used cumulants [ 15 ]. In some cases, such non-negativity constraints in fact enable estimation of the model [ 8990 ] without any assumptions on non-Gaussianity.

Comppnent those early models, the dependency structure of the v i is fixed a priori but see the extension by Gruber et al.

## Independent component analysis: recent advances

Noise-contrastive estimation of unnormalized independeht models, with applications to natural image statistics. Thus, more sophisticated methods are needed to infer the correct ordering, for example, based on acyclicity [ 1618 ].

A model in which the components are linearly correlated without considering any time structure was proposed by Sasaki et al. Basically, preprocess the data by short-time Fourier transforms and then do ICA. In fact, many such models can be considered to be related to ICA: Because, for Gaussian variables, uncorrelatedness implies independence, whitening exhausts analyssis the dependence information in the data, and we can estimate the mixing matrix only up to an arbitrary orthogonal matrix.

Karklin Y, Lewicki MS. In fact, linear temporal filtering does indepednent change the validity of the linear mixing model, nor does it change the mixing matrix. Shows how to estimate a coefficient that allows the estimation of both sub- and super-Gaussian independent component using a single nonlinearity.

Blind source separation by nonstationarity of variance: