fastica.m

这是一个关于盲源分离独立成分分析方法（ICA）的软件包

function [Out1, Out2, Out3] = fastica(mixedsig, s1, v1, s2, v2, s3, v3, ...
      s4, v4, s5, v5, s6, v6, s7, v7, s8, v8, ...
      s9, v9, s10, v10, s11, v11, s12, v12, ...
      s13, v13, s14, v14, s15, v15, s16, v16, ...
      s17, v17, s18, v18, s19, v19, s20, v20);

% FASTICA - Fast Independent Component Analysis.
%
% 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 (obtained as
% pseudoinverse of W) as well.
%
% [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.  Ignored if 'approach'='symm'.
%                       Default equals the dimension of data.
%
%======================================================================
% --Choosing the nonlinearity:
%
% 'g'                   (string) Chooses 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)
%                       'gaus'             g(u)=u*exp(-a2*u^2/2)
%
% 'a1'                  (number) Parameter a1 used when g='tanh'.
%                       Default is 1.
% 'a2'                  (number) Parameter a2 used when g='gaus'.
%                       Default is 1.
% 
%======================================================================
% --Controlling convergence:
%
% 'epsilon'             (number) Stopping criterion. Default is 0.0001.
%
% 'maxNumIterations'    (integer) Maximum number of iterations.
%                       Default is 1000.
%
% 'initGuess'           (matrix) Initial guess for A. Default is random.
%
%======================================================================
% --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: 'on' or 'off'. Default 'on'.
%
% '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'.
%
% 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

% 6.4.1998
% Hugo G鋠ert


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Remove the mean and check the data

mixedsig = 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';
a1                = 1;
a2                = 1;
epsilon           = 0.0001;
maxNumIterations  = 1000;
initState         = 'rand';
guess             = 0;
displayMode       = 'on';
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(nargin-1,2)==1)