[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
original signals
mixed signals
demixed signals
[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
source signals:  
mixed signals:  
separated signals: 
Scalar mixture:  
Goal: Matrix W:  
Global matrix: 
Permutation matrix  
Diagonal matrix 
statistical independence: 
[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
Iteration  batch  online 
Statistics  SOS  HOS 


[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
Section about PCA is better to view in pdf format. Paper is available here.
6. Higher Order Statistics based methods
[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
Methods for BSS can be described by generalized contrast function which is a certain measure of statistical independence/nongaussianity (implies from the Central Limit Theorem). For example:
1. cummulants  kurtosis  
2. negentropy  , 
where  
3. approximation by  tanh(.), exp(x^{2}/2) 
In section Experiments & Presentations are results of various methods based on HOS.
7. Efficient algorithm for ICA: FastICA
[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]
Algorithm is based on approximation of independence measure by contrast function. It is a batch algorithm and uses modified Newton's method for fast separation. The algorithm derivation is available here.
Results of FastICA are also available at Experiments & Presentations.