[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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Neurocomputing 81— However, ICA is able to find the underlying components and sources mixed in the observed data in many cases where the classical methods fail. 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 [ 25analyais ].

## Aapo Hyvärinen: Publications

Thus, the ICA model holds forwith the common mixing matrix A. Nature— Typically, the literature uses the formalism where the index t is dropped, and the x i and the s i are considered random variables.

In fact, empirical results tend to show that ICA estimation compoment to be rather robust against some violations of the independence assumption.

Thus, it should be useful to develop methods that use both the autocorrelations and non-Gaussianity. The assumption of acyclicity is quite typical in the theory of Bayesian networks: Independent component analysis is a probabilistic method for learning a linear transform of a random vector.

Source adaptive blind source separation: A multi-layer sparse coding network learns contour coding from natural indelendent. In fact, if we consider a real dataset, it seems quite idealistic to assume that it could be a linear superposition of strictly independent components. Efficient independent component analysis. A closely related formalism uses a generative model of the whole covariance structure of x [ 44compnoent ].

The basic ICA model assumes that the s i and x i are random variables, i. The goal is to find components that are maximally independent and non-Gaussian componetn. NeuroImage 22— In the case of actual time series x i t and s i tdependencies between the components which would usually be called source signals can obviously have a temporal aspect as well.

## Independent component analysis: recent advances

The idea is to consider a generative model similar to the one in 6. Finally, the actual components s i in the linear model 2. This changes the statistical characteristics because are zero-mean while the v i are non-negative.

Nonlinear Independent Component Analysis: While the components are assumed to be independent in the model, the model does not have enough parameters to actually make the components independent for any given random vector x.

In the general SEM, we model the observed data vector x as. In fact, this is just a special case of the general problem of estimating a linear Bayesian network, or an SEM.

In other words, there should be many observations very close to zero. Separating interesting components from time-series. Basically, preprocess the data by short-time Fourier transforms and then do ICA.

### Publications by Aapo Hyvärinen: ICA

Fast and robust fixed-point algorithms for independent component analysis. The residuals e 1e 2 infependent assumed to be independent of the regressors x 1 and x 2respectively. Considering the vector of short-time Fourier transforms of the observed data vector, we simply take the sum of the log-moduli over each window and component, obtaining. However, such methods based on autocorrelations alone have the serious disadvantage that they only work if the independent independsnt have different autocorrelation structures, i.

An adaptive method for subband decomposition ICA. The applications have become very widespread, and it would hardly be possible to give a comprehensive list anymore.

In fact, the s i are then linearly correlated. This gives a statistically rigorous method for assessing the reliability of the components. The s i are the independent components, whereas the coefficients a ij are called the hyvzrinen coefficients.