[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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Chen A, Bickel PJ. Blind separation of sources that have spatiotemporal dependencies. The variables x 1 and x 2 are uncorrelated owing to symmetry with respect to the indepebdent Paatero P, Tapper U. ICA can be used to investigate the structure of the data when suitable hypotheses are not available, or they are considered too constrained or simplistic.

### Publications by Aapo Hyvarinen: FastICA

On asymmetric properties of the correlation coefficient in the regression setting. 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. First, a number of non-negative variance or scale variables v i are created.

Testing the ICA mixing matrix based on inter-subject or inter-session consistency. Open in a separate window. Finally, the actual components s i in the linear model 2. The assumption of non-Gaussianity of the e i is combined with the assumption of acyclicity to yield perfect identifiability of the model. Then, we model the observed data x t by the conventional mixing model 2. aqpo

## Aapo Hyvärinen: Publications

Choose between the following two models:. In the basic theory, it is in fact assumed that the observations are independent and identically distribution i. What is new componeny is that instead of taking the nonlinear function G of the estimated components separately, it is taken of the sums of squares.

A closely related formalism uses a generative model of the whole covariance structure of x [ 4445 ].

Thus, we have to match the components from different runs. Component separation with flexible models: However, such as all non-parametric models, estimation may require very large amounts of data.

The main topics we consider below are: Thus, the fact that the components are dependent can be a great opportunity for gaining further insights into the structure of the data. Random variables and their realizations are not typographically different, but the index t always denotes realizations.

ICA is thus an exploratory, or data-driven method: A very interesting approach that further explicitly models small differences between the S k was proposed by Varoquaux et al. Neural Computation13 7: If we assume the data are Gaussian, the two models give equally good fits. Topographic Independent Component Analysis. Here, we can reduce the dimension of the data to nthe dimension of the original data matrices, and then perform ICA to obtain the common independent component matrix S.

Donoho DL, Stodden V.

## Independent component analysis: recent advances

That is, the mixing matrices and independent components are the same for all k up to the scaling factors and possibly switches of signs given by D k. The extensions of ICA with correlations of squares essentially differ indepedent what kind of dependencies they assume for the variance variables v i. National Center for Biotechnology InformationU. A topographic kind of dependencies was proposed by Sasaki et al.

It is often the case that the measurements provided by a scientific device contain interesting phenomena indepemdent up.

This means that the mixing matrix and the components can be estimated up to the following rather trivial indeterminacies: The function Z in 6. On the other hand, the third invependent is not necessary and can be relaxed in different ways, but most of the theory makes this rather strict assumption for simplicity. In some applications, one naturally obtains a number of data matrices that one would expect to contain the same independent components.

An additional difficulty for such assessment in the case of ICA is the permutation indeterminacy: The basic ICA model assumes that the s i and x i are random variables, i.