1. Information Theoretic Blind Source Separation with ANFIS and Wavelet Analysis 03 February 2006 서경호

2. Research Process

3. Blind Source Separation
Cocktail Party Problem
Imagine that you are in a cocktail party. Many people are speaking simultaneously. Maybe, you can concentrate on a person in spite of other sounds around you. Similarly, if you have many microphones at different locations, you can get the time signals from them and they will be very useful if we separate the voice of each person from the mixed signals. This kind of problems are known as ‘Cocktail Party Problem’.

4. Outline of Blind Source Separation
The mixing situation in the cocktail party problem can occur not only in the time signals, but also in the space signals. For example, when we try to obtain EEG signals or functional MRI signals, we will get the mixed signals at best because the sensors are too close unavoidably, or the signals are too weak compared to the noises. The separation of sources can be applied to the processing such data.
In most cases like above examples, we must find the original sources under the situation that we have no information about the original sources and also we do not know the environments that represent how the signals mixed. We know only the mixed input signals. From this blindness about the environments and sources, we call this class of separation problems as the Blind Source Separation ( BSS ).

5. Independent Component Analysis(ICA)
In general, we overcome the blindness by assuming the statistical independence between the original sources. In this point of view, the BSS problem is nothing but finding independent sources that compose the mixed sources, and this can be thought as the Independent Component Analysis ( ICA ).

6. Formulations
Assume that there are n sources s1(t)~sn(t) and the mixing system accepts the sources as its input and mixed signals as its output,x1(t)~xn(t).
The BSS problem is finding the signals y1(t)~yn(t) when we know only x1(t)~xn(t).

7. Information Theoretic Algorithms
Minimum Mutual Information ( MMI )
MMI algorithm separates signals by minimizing the mutual information between the outputs of separate system.
Mutual Information I(X)
- We can interpret the mutual information as the degree of independence!
Mutual Information is always greater than or equal to zero.
- By minimizing mutual information we can find independent components!

8. Information Theoretic Algorithms
Maximum Entropy
- By maximizing mutual information between input signals and output signals, sources can be separated independently.
- The maximization of mutual information is equivalent to the maximizing entropy of output signals.

9. ICA of EEG Data
EEG recordings of brain electrical activity measure changes in potential difference between pairs of points on the human scalp. Scalp recordings also include artifacts such as line noise, eye movements, blinks and cardiac signals ( ECG ) which can present serious problems for analyzing and interpreting EEG recordings.
The information theoretic ICA algorithm is very effective for performing source separation in domains where,
(1) the mixing medium is linear and propagation delays are negligible,
(2) the time courses of the sources are independent,
(3) the number of sources is greater or equal the number of sources. ( if N sensors are used the ICA algorithm can separate a maximum of N sources )

10. Limitations
The algorithm requires the number of sensors to be the same or greater than the number of sources
Nonlinear mixing phenomena
Sources may not be stationary, i.e. sources may appear and disappear and move ( speaker moving in a room )
Sensor noise may influence separation and should be included

11. ICA of EEG Data
When the ICA algorithm is applied to EEG analysis, the analysis can be more meaningful if it considers individual environment.
( gold tooth, bodily habit during analysis, body size…)
This process can be realized effectively by artificial neural network because individual training is possible.
Selection of the neural network inputs is very important component of designing the neural network – raw EEG signal input is not effective.

12. ANFIS

13. Fourier Transform
If the signal properties do not change much over time, Fourier analysis is very useful. However, most interesting signals contain numerous non-stationary or transitory characteristics : drift, trends, abrupt changes, and beginnings and ends of events. These characteristics are often the most important part of the signal, and Fourier analysis is not suited to detecting them.

14. Limitation of Fourier Analysis
Raw EEG signal has many sharp peaks. Therefore Fourier analysis may have poor analysis result.

15. Wavelet Transform
A wavelet is a waveform of effectively limited duration that has an average value zero.

16. Continuous Wavelet Transform

17. ANFIS

18. Research Process