readme.txt

PearsonICA程序

The Pearson-ICA package is Copyright (c) Helsinki University of Technology,
Signal Processing Laboratory,
Juha Karvanen, Jan Eriksson, and Visa Koivunen.

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

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Version: 1.2
Version date: October 9, 2001

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Description
===========

This package provides the Matlab (5.x) functions needed for the use of the
Pearson-ICA algorithm as described in


  J. Karvanen, J.Eriksson and V. Koivunen:
  "Pearson System Based Method for Blind Separation",
  Proceedings of Second International Workshop on
  Independent Component Analysis and Blind Signal Separation,
  Helsinki 2000, pp. 585--590

  J. Karvanen and V. Koivunen:
  "Blind Separation Methods based on Pearson system and its Extensions"
  Signal Processing, 2002, to appear

The algorithm is proposed to solve  the standard noiseless linear 
ICA problem, i.e. the ICA model is Y=AS, where the number of sources
s_i is equal to the number of observations y_i.

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Installation: Just put all files to a directory along Matlab's search path.
============

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Quick use: Type pearson_ica_demo for a demonstration.
=========

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Use: 
=== 

1) Pearson-ICA algorithm
~~~~~~~~~~~~~~~~~~~~~~~~

Suppose you have the ICA mixture in the matrix `mixedsig', where
the different rows correspond to the different outputs. Then

estimatedsig=pearson_ica(mixedsig)

gives the estimated independent components as the rows of the
matrix `estimatedsig'. The estimated mixing matrix A and
estimated separation matrix W are obtained as

[estimatedsig,A,W]=pearson_ica(mixedsig) 

There are also some optional parameters you can change:
   'epsilon'          Convergence criterion
   'maxNumIterations' Maximum number of iterations
   'borderBase',
   'borderSlope'      The border lines between the Pearson family and the 
                      tanh contrast. I.e. the Pearson is used if  
                      borderBase(1)+borderSlope(1)*skewness^2=<
                      kurtosis=<borderBase(2)+borderSlope(2)*skewness^2,
                      and the contrast tanh is used otherwise.

The default values for the parameters are epsilon=0.0001,
maxNumIterations=200, borderBase=[2.6 4], and borderSlope=[0 1].

Example: 
   estimated_sig=pearson_ica(mixedsig,'epsilon',0.00005,...
                   'maxNumIterations',50,'borderBase',[2.5 4])

2) Use of the functions and the list of files in the package
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

contents.m
  A brief description of all the files in the package.

fasticapearson.m
  Strip down of Hyv剅inen's FastICA algorithm. This is the core function
  used by pearson_ica. Use pearson_ica to call this function.

  Syntax:      [ICs, A, W]=fasticapearson(mixedsig,epsilon,...
			     maxNumIterations,borderBase,borderSlope);

  Dependences: pearson_momentfit, pearson_score

gbd_momentfit.m   (not used in version 1.2)
  Provides the gbd_momentfit function, which estimates the parameters of 
  a distribution from the Generalized Beta Distribution (GBD) using 
  the first four sample moments. Alternatively, the sample minimum and 
  maximum can be used instead of the sample mean and variance.
  
  Syntax:      gbd_momentfit(alpha3,alpha4,samplemin,samplemax,samplen)
               gbd_momentfit(alpha3,alpha4,alpha1,alpha2) 

  Examples:    beta=gbd_momentfit(0.254,2.526,57,580)
               beta=gbd_momentfit(0.254,2.526,-0.68,144,1000)

gbd_score.m (not used in version 1.2)	      
  Provides the gbd_score function, which calculates values of the score 
  function and its derivative of a distribution from the Generalized 
  Beta Distribution (GBD).

  Syntax:      [phi,phi_prime]=gbd_score(x,beta)

  Example:     x=0:0.1:140;
               beta=gbd_momentfit(0.254,2.526,57,580);
               [phi,phi2]=gbd_score(x,beta);
               plot(x,phi);

gpl.txt
  The GNU General Public License

pearson_ica.m
  The main file for the Pearson-ICA algorithm. Look above for instructions
  how to call this function.

pearson_ica_demo.m
  A demonstration of the Pearson-ICA algorithm in work.

pearson_momentfit.m
  Estimates the parameters of the zero mean and unit
  variance Pearson system using the third and forth central moments.  

  Syntax:  pearson_momentfit(alpha3,alpha4)

  Example: [a b]=pearson_momentfit(0,3) 
  gives the parameters of Gaussian distribution

pearson_score.m
  Calculates values for the score function and its derivative of the 
  Pearson  system with parameters given in a=[a(1) a(2)] and b=[b(1) b(2) b(3)].
  
  Syntax:  [phi,phi_prime]=pearson_score(x,B)

  Example: x=-3:0.01:3;
           [a b]=pearson_momentfit(0,3);
           [phi,phi_prime]=pearson_score(x,a,b);
           plot(x,phi);

readme.txt 
  This file.

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