[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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Joint estimation of linear non-Gaussian acyclic models. Another interesting feature of the objective function in 2. Some nonlinearities have to be taken between different layers. Clmponent overcomplete independent component bases for image windows.

Doing ICA on is typically quite straightforward. Zhang K, Chan L. A different framework of dependent components in time series was proposed by Lahat et al. Interestingly, this objective function depends only on the yhvarinen densities of the estimated independent components. This is because statistical independence is a very strong property with potentially an infinite number of degrees of freedom.

The ensuing objective function is usually formulated in terms hyvarineh the inverse ofwhose rows are denoted byas. 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.

Blind separation of sources that have spatiotemporal variance dependencies. The residuals e 1e 2 are assumed to be independent of the regressors x 1 and x 2respectively. If the independent components are similar enough in the different datasets, one can assume that hyvaginen correspond to something real.

It is probably fair to say incependent in the last 10 years, ICA has become a standard tool in machine learning and signal processing. Choose between the following two models: In the earliest work, the v i were divided into groups or subspaces such that the variables in the same group are positively correlated, while the variables in different groups are independent [ 39 ].

### Publications by Aapo Hyvärinen: ICA

In an intuitive sense, such methods would more fully exploit the structure present in the data, leading to smaller estimation errors e. In most of the widely used ICA algorithms, the non-quadratic functions G i are fixed; possibly just their signs are adapted, as is implicitly done in FastICA [ 77 ].

A unifying model for blind separation of independent sources. A very interesting approach that further explicitly models small differences between the S k was proposed by Varoquaux et al.

Indrpendent likelihood is to be maximized for orthogonal or unitary W for whitened data. Non-Gaussianity also gives a new meaning to independence: Second-order methods based on color. It is often the case that the measurements provided by a scientific device contain interesting phenomena mixed up.

In fact, if we assume the variables x 1 and x 2 are standardized to unit variance, the regression coefficients are equal, i. Independent component analysis is a probabilistic method for learning a linear transform of hgvarinen random vector.

Emergence of complex cell properties by learning to generalize in natural scenes. 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.

Separating interesting components from time-series. Non-linear neurons in the low noise jyvarinen One way to assess the reliability of the results is to perform some randomization of the data or the algorithm, and see whether the results change a lot [ 2524 ].

## Independent component analysis: recent advances

A microphone measures sounds coming hyvarnen different sources in the environment. Dodge Y, Rousson V. Estimation of non-normalized statistical models using score matching. An information-maximization approach to blind separation and blind deconvolution. Here, a sum of the squares of two Fourier coefficients is implicitly computed by taking the modulus ofwhich is complex valued.

### Publications by Aapo Hyvarinen: FastICA

E 70 Blind source separation by sparse decomposition in a signal dictionary. In the case of neuroimaging, for example, one typically measures brain activities of many subjects, and tries to find components that the subjects have in common [ 27 ].

Eriksson J, Koivunen V. On the other hand, independence is now being seen as a useful approximation that is hardly ever strictly true.

Thus, we have to match the components from different runs. This is an additional source of randomness and errors in the results [ 24 ]. When does non-negative matrix factorization give a correct decomposition into parts?

This equation suggests that to find a transformation that is guaranteed to give independent components, we need an infinite number of parameters, i. Neurocomputing50 C: In those early models, the dependency structure of the v i is fixed a priori but see the extension compoment Gruber et al.

The basic idea of ICA.

However, we can make some progress in this extremely important question by postulating that one of the variables has to be the cause and the other one the effect.

Finally, we will review methods for more efficient estimation of the basic linear mixing model independenr. A physical interpretation of independence is also sometimes possible: This changes the statistical characteristics because are zero-mean while the v i are non-negative.

Xnalysis resampling approach to estimate the stability of one-dimensional or multidimensional independent components. In the general SEM, we model the observed data vector x as. Three-way structure is related to a powerful approach to ICA based on joint diagonalization of covariance matrices. Thus, more sophisticated methods are needed to infer the correct ordering, for example, based on acyclicity [ 1618 ].