function | fastica

fastica - Fast Independent Component Analysis

FastICA for Matlab 7.x and 6.x

Version 2.5, October 19 2005

Copyright (c) Hugo G�vert, Jarmo Hurri, Jaakko S�rel�, and Aapo Hyv�rinen.

fastica(mixedsig) estimates the independent components from given

multidimensional signals. Each row of matrix mixedsig is one

observed signal. fastica uses Hyvarinen's fixed-point algorithm,

see http://www.cis.hut.fi/projects/ica/fastica/. Output from the

function depends on the number output arguments:

[icasig] = fastica (mixedsig); the rows of icasig contain the

estimated independent components.

[icasig, A, W] = fastica (mixedsig); outputs the estimated separating

matrix W and the corresponding mixing matrix A.

[A, W] = fastica (mixedsig); gives only the estimated mixing matrix

A and the separating matrix W.

Some optional arguments induce other output formats, see below.

A graphical user interface for fastica can be launched by the

command FASTICAG

fastica can be called with numerous optional arguments. Optional

arguments are given in parameter pairs, so that first argument is

the name of the parameter and the next argument is the value for

that parameter. Optional parameter pairs can be given in any order.

OPTIONAL PARAMETERS:

Parameter name Values and description

======================================================================

--Basic parameters in fixed-point algorithm:

'approach' (string) The decorrelation approach used. Can be

symmetric ('symm'), i.e. estimate all the

independent component in parallel, or

deflation ('defl'), i.e. estimate independent

component one-by-one like in projection pursuit.

Default is 'defl'.

'numOfIC' (integer) Number of independent components to

be estimated. Default equals the dimension of data.

======================================================================

--Choosing the nonlinearity:

'g' (string) Chooses the nonlinearity g used in

the fixed-point algorithm. Possible values:

                    Value of 'g':      Nonlinearity used:
                    'pow3' (default)   g(u)=u^3
                    'tanh'             g(u)=tanh(a1*u)
                    'gauss             g(u)=u*exp(-a2*u^2/2)
                    'skew'             g(u)=u^2

'finetune' (string) Chooses the nonlinearity g used when

fine-tuning. In addition to same values

as for 'g', the possible value 'finetune' is:

'off' fine-tuning is disabled.

'a1' (number) Parameter a1 used when g='tanh'.

Default is 1.

'a2' (number) Parameter a2 used when g='gaus'.

Default is 1.

'mu' (number) Step size. Default is 1.

If the value of mu is other than 1, then the

program will use the stabilized version of the

algorithm (see also parameter 'stabilization').

'stabilization' (string) Values 'on' or 'off'. Default 'off'.

This parameter controls wether the program uses

the stabilized version of the algorithm or

not. If the stabilization is on, then the value

of mu can momentarily be halved if the program

senses that the algorithm is stuck between two

points (this is called a stroke). Also if there

is no convergence before half of the maximum

number of iterations has been reached then mu

will be halved for the rest of the rounds.

======================================================================

--Controlling convergence:

'epsilon' (number) Stopping criterion. Default is 0.0001.

'maxNumIterations' (integer) Maximum number of iterations.

Default is 1000.

'maxFinetune' (integer) Maximum number of iterations in

fine-tuning. Default 100.

'sampleSize' (number) [0 - 1] Percentage of samples used in

one iteration. Samples are chosen in random.

Default is 1 (all samples).

'initGuess' (matrix) Initial guess for A. Default is random.

You can now do a "one more" like this:

[ica, A, W] = fastica(mix, 'numOfIC',3);

[ica2, A2, W2] = fastica(mix, 'initGuess', A, 'numOfIC', 4);

======================================================================

--Graphics and text output:

'verbose' (string) Either 'on' or 'off'. Default is

'on': report progress of algorithm in text format.

'displayMode' (string) Plot running estimates of independent

components: 'signals', 'basis', 'filters' or

'off'. Default is 'off'.

'displayInterval' Number of iterations between plots.

Default is 1 (plot after every iteration).

======================================================================

--Controlling reduction of dimension and whitening:

Reduction of dimension is controlled by 'firstEig' and 'lastEig', or

alternatively by 'interactivePCA'.

'firstEig' (integer) This and 'lastEig' specify the range for

eigenvalues that are retained, 'firstEig' is

the index of largest eigenvalue to be

retained. Default is 1.

'lastEig' (integer) This is the index of the last (smallest)

eigenvalue to be retained. Default equals the

dimension of data.

'interactivePCA' (string) Either 'on' or 'off'. When set 'on', the

eigenvalues are shown to the user and the

range can be specified interactively. Default

is 'off'. Can also be set to 'gui'. Then the user

can use the same GUI that's in FASTICAG.

If you already know the eigenvalue decomposition of the covariance

matrix, you can avoid computing it again by giving it with the

following options:

'pcaE' (matrix) Eigenvectors

'pcaD' (matrix) Eigenvalues

If you already know the whitened data, you can give it directly to

the algorithm using the following options:

'whiteSig' (matrix) Whitened signal

'whiteMat' (matrix) Whitening matrix

'dewhiteMat' (matrix) dewhitening matrix

If values for all the 'whiteSig', 'whiteSig' and 'dewhiteMat' are

supplied, they will be used in computing the ICA. PCA and whitening

are not performed. Though 'mixedsig' is not used in the main

algorithm it still must be entered - some values are still

calculated from it.

Performing preprocessing only is possible by the option:

'only' (string) Compute only PCA i.e. reduction of

dimension ('pca') or only PCA plus whitening

('white'). Default is 'all': do ICA estimation

as well. This option changes the output

format accordingly. For example:

                    [whitesig, WM, DWM] = fastica(mixedsig,
                    'only', 'white')
                    returns the whitened signals, the whitening matrix
                    (WM) and the dewhitening matrix (DWM). (See also
                    WHITENV.) In FastICA the whitening matrix performs
                    whitening and the reduction of dimension. Dewhitening
                    matrix is the pseudoinverse of whitening matrix.

                    [E, D] = fastica(mixedsig, 'only', 'pca')
                    returns the eigenvector (E) and diagonal
                    eigenvalue (D) matrices  containing the
                    selected subspaces.

======================================================================

EXAMPLES

    [icasig] = fastica (mixedsig, 'approach', 'symm', 'g', 'tanh');
            Do ICA with tanh nonlinearity and in parallel (like
            maximum likelihood estimation for supergaussian data).

    [icasig] = fastica (mixedsig, 'lastEig', 10, 'numOfIC', 3);
            Reduce dimension to 10, and estimate only 3
            independent components.

    [icasig] = fastica (mixedsig, 'verbose', 'off', 'displayMode', 'off');
            Don't output convergence reports and don't plot
            independent components.

A graphical user interface for fastica can be launched by the

command FASTICAG

See also fasticag