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function [Out1, Out2, Out3] = fastica(mixedsig, varargin)
%FASTICA - Fast Independent Component Analysis
%
% FastICA for Matlab 7.01
% Version 2.3, April 12 2005
% Copyright (c) lucky zhang.
%
% 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
% suplied, 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
% @(#)$Id: fastica.m,v 1.11 2004/07/27 11:46:46 jarmo Exp $
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Check some basic requirements of the data
if nargin == 0,
error ('You must supply the mixed data as input argument.');
end
if length (size (mixedsig)) > 2,
error ('Input data can not have more than two dimensions.');
end
if any (any (isnan (mixedsig))),
error ('Input data contains NaN''s.');
end
if ~isa (mixedsig, 'double')
fprintf ('Warning: converting input data into regular (double) precision.\n');
mixedsig = double (mixedsig);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Remove the mean and check the data
[mixedsig, mixedmean] = remmean(mixedsig);
[Dim, NumOfSampl] = size(mixedsig);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Default values for optional parameters
% All
verbose = 'on';
% Default values for 'pcamat' parameters
firstEig = 1;
lastEig = Dim;
interactivePCA = 'off';
% Default values for 'fpica' parameters
approach = 'defl';
numOfIC = Dim;
g = 'pow3';
finetune = 'off';
a1 = 1;
a2 = 1;
myy = 1;
stabilization = 'off';
epsilon = 0.0001;
maxNumIterations = 1000;
maxFinetune = 5;
initState = 'rand';
guess = 0;
sampleSize = 1;
displayMode = 'off';
displayInterval = 1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Parameters for fastICA - i.e. this file
b_verbose = 1;
jumpPCA = 0;
jumpWhitening = 0;
only = 3;
userNumOfIC = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Read the optional parameters
if (rem(length(varargin),2)==1)
error('Optional parameters should always go by pairs');
else
for i=1:2:(length(varargin)-1)
if ~ischar (varargin{i}),
error (['Unknown type of optional parameter name (parameter' ...
' names must be strings).']);
end
% change the value of parameter
switch lower (varargin{i})
case 'stabilization'
stabilization = lower (varargin{i+1});
case 'maxfinetune'
maxFinetune = varargin{i+1};
case 'samplesize'
sampleSize = varargin{i+1};
case 'verbose'
verbose = lower (varargin{i+1});
% silence this program also
if strcmp (verbose, 'off'), b_verbose = 0; end
case 'firsteig'
firstEig = varargin{i+1};
case 'lasteig'
lastEig = varargin{i+1};
case 'interactivepca'
interactivePCA = lower (varargin{i+1});
case 'approach'
approach = lower (varargin{i+1});
case 'numofic'
numOfIC = varargin{i+1};
% User has suplied new value for numOfIC.
% We'll use this information later on...
userNumOfIC = 1;
case 'g'
g = lower (varargin{i+1});
case 'finetune'
finetune = lower (varargin{i+1});
case 'a1'
a1 = varargin{i+1};
case 'a2'
a2 = varargin{i+1};
case {'mu', 'myy'}
myy = varargin{i+1};
case 'epsilon'
epsilon = varargin{i+1};
case 'maxnumiterations'
maxNumIterations = varargin{i+1};
case 'initguess'
% no use setting 'guess' if the 'initState' is not set
initState = 'guess';
guess = varargin{i+1};
case 'displaymode'
displayMode = lower (varargin{i+1});
case 'displayinterval'
displayInterval = varargin{i+1};
case 'pcae'
% calculate if there are enought parameters to skip PCA
jumpPCA = jumpPCA + 1;
E = varargin{i+1};
case 'pcad'
% calculate if there are enought parameters to skip PCA
jumpPCA = jumpPCA + 1;
D = varargin{i+1};
case 'whitesig'
% calculate if there are enought parameters to skip PCA and whitening
jumpWhitening = jumpWhitening + 1;
whitesig = varargin{i+1};
case 'whitemat'
% calculate if there are enought parameters to skip PCA and whitening
jumpWhitening = jumpWhitening + 1;
whiteningMatrix = varargin{i+1};
case 'dewhitemat'
% calculate if there are enought parameters to skip PCA and whitening
jumpWhitening = jumpWhitening + 1;
dewhiteningMatrix = varargin{i+1};
case 'only'
% if the user only wants to calculate PCA or...
switch lower (varargin{i+1})
case 'pca'
only = 1;
case 'white'
only = 2;
case 'all'
only = 3;
end
otherwise
% Hmmm, something wrong with the parameter string
error(['Unrecognized parameter: ''' varargin{i} '''']);
end;
end;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% print information about data
if b_verbose
fprintf('Number of signals: %d\n', Dim);
fprintf('Number of samples: %d\n', NumOfSampl);
end
% Check if the data has been entered the wrong way,
% but warn only... it may be on purpose
if Dim > NumOfSampl
if b_verbose
fprintf('Warning: ');
fprintf('The signal matrix may be oriented in the wrong way.\n');
fprintf('In that case transpose the matrix.\n\n');
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculating PCA
% We need the results of PCA for whitening, but if we don't
% need to do whitening... then we dont need PCA...
if jumpWhitening == 3
if b_verbose,
fprintf ('Whitened signal and corresponding matrises suplied.\n');
fprintf ('PCA calculations not needed.\n');
end;
else
% OK, so first we need to calculate PCA
% Check to see if we already have the PCA data
if jumpPCA == 2,
if b_verbose,
fprintf ('Values for PCA calculations suplied.\n');
fprintf ('PCA calculations not needed.\n');
end;
else
% display notice if the user entered one, but not both, of E and D.
if (jumpPCA > 0) & (b_verbose),
fprintf ('You must suply all of these in order to jump PCA:\n');
fprintf ('''pcaE'', ''pcaD''.\n');
end;
% Calculate PCA
[E, D]=pcamat(mixedsig, firstEig, lastEig, interactivePCA, verbose);
end
end
% skip the rest if user only wanted PCA
if only > 1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Whitening the data
% Check to see if the whitening is needed...
if jumpWhitening == 3,
if b_verbose,
fprintf ('Whitening not needed.\n');
end;
else
% Whitening is needed
% display notice if the user entered some of the whitening info, but not all.
if (jumpWhitening > 0) & (b_verbose),
fprintf ('You must suply all of these in order to jump whitening:\n');
fprintf ('''whiteSig'', ''whiteMat'', ''dewhiteMat''.\n');
end;
% Calculate the whitening
[whitesig, whiteningMatrix, dewhiteningMatrix] = whitenv ...
(mixedsig, E, D, verbose);
end
end % if only > 1
% skip the rest if user only wanted PCA and whitening
if only > 2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculating the ICA
% Check some parameters
% The dimension of the data may have been reduced during PCA calculations.
% The original dimension is calculated from the data by default, and the
% number of IC is by default set to equal that dimension.
Dim = size(whitesig, 1);
% The number of IC's must be less or equal to the dimension of data
if numOfIC > Dim
numOfIC = Dim;
% Show warning only if verbose = 'on' and user suplied a value for 'numOfIC'
if (b_verbose & userNumOfIC)
fprintf('Warning: estimating only %d independent components\n', numOfIC);
fprintf('(Can''t estimate more independent components than dimension of data)\n');
end
end
% Calculate the ICA with fixed point algorithm.
[A, W] = fpica (whitesig, whiteningMatrix, dewhiteningMatrix, approach, ...
numOfIC, g, finetune, a1, a2, myy, stabilization, epsilon, ...
maxNumIterations, maxFinetune, initState, guess, sampleSize, ...
displayMode, displayInterval, verbose);
% Check for valid return
if ~isempty(W)
% Add the mean back in.
if b_verbose
fprintf('Adding the mean back to the data.\n');
end
icasig = W * mixedsig + (W * mixedmean) * ones(1, NumOfSampl);
%icasig = W * mixedsig;
if b_verbose & ...
(max(abs(W * mixedmean)) > 1e-9) & ...
(strcmp(displayMode,'signals') | strcmp(displayMode,'on'))
fprintf('Note that the plots don''t have the mean added.\n');
end
else
icasig = [];
end
end % if only > 2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The output depends on the number of output parameters
% and the 'only' parameter.
if only == 1 % only PCA
Out1 = E;
Out2 = D;
elseif only == 2 % only PCA & whitening
if nargout == 2
Out1 = whiteningMatrix;
Out2 = dewhiteningMatrix;
else
Out1 = whitesig;
Out2 = whiteningMatrix;
Out3 = dewhiteningMatrix;
end
else % ICA
if nargout == 2
Out1 = A;
Out2 = W;
else
Out1 = icasig;
Out2 = A;
Out3 = W;
end
end