independent component analysis from pca to ica bell sejnowski algorithm kurtosis method...
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Independent Component Analysis
From PCA to ICABell Sejnowski algorithmKurtosis methodDemonstrations
Bell and Sejnowski 1995
Consider y=g(x)+noise with f depending on w
I(y;x)=H(y)- H(y|x)
H(y|x)=E_x E_y|x [-log P(y|x)]
ICA based on KurtosisOja and Hyvarinen
Independent Component Analysis
Perform “blind separation” of signals recorded at multiple sensors
Use minimal assumptions about the characteristics of the signal sources.
An overview of applications of ICA to biological data and general data mining,Computational Neurobiology Laboratory Salk Institute, La Jolla CA (April, 1999).
Enter [Enter] to advance, [up-arrow] to rewind.
Principle: Maximize Information
• Q:Q: How to extract maximum
information from multiple visual
channels?
Set of 144 ICA filters
• AA: ICA does this -- it maximizes
joint entropy & minimizes
mutual information between output
channels (Bell & Sejnowski, 1995).• ICA produces brain-like visual filters
for natural images.
ICA versus PCA
• Independent Component Analysis (ICA) finds directions of maximal independence in non-Gaussian data (higher-order statistics).
• Principal Component Analysis (PCA) finds directions of maximal variance in Gaussian data (second-order statistics).
Example: Audio decomposition
Play Mixtures Play Components
Perform ICA
Mic 1
Mic 2
Mic 3
Mic 4
Terry Scott
Te-Won Tzyy-Ping
Electroencephalography (EEG)
• ICA separates
brain signals from
artifacts.
Artifacts
Brainsignals
• Allows monitoring
of multiple brain
processes.
• Permits study of
brain activity in
noisy conditions.
Functional Brain Imaging
• Functional magnetic
resonance imaging (fMRI)
data are noisy and
complex.
I C A C o m p o n e n t T y p e s
S u s t a i n e d t a s k - r e l a t e d
( a )
T r a n s i e n t l yt a s k - r e l a t e d
( b )
S l o w l y - v a r y i n g
( c )
Q u a s i - p e r i o d i c
( d )
A b r u p t h e a dm o v e m e n t
( e )
A c t i v a t e dS u p p r e s s e d
S l o w h e a dm o v e m e n t
( f )
• ICA identifies concurrent
hemodynamic processes.
• Does not require a priori
knowledge of time courses
or spatial distributions.
Data Mining
• ICA was applied to Armed Forces Vocation Aptitude Battery (ASVAB) test scores and Navy Fire Control School grades.
• ICA may suggest more efficient and balanced selection criteria.
• Two ICA components contributed to final school
grade.
This presentation by
• Scott Makeig, Naval Health Research Center, San Diego
• Tzyy-Ping Jung, Institute for Neural Computation,
UCSD, La Jolla CA
• Te-Won Lee, Salk Institute, La Jolla CA
• Sigurd Enghoff, Salk Institute
• Terrence J. Sejnowski, Salk Institute & UCSD
From Barak Pearlmutter Contextual ICA The first demo applies the Contextual ICA blind source
separation algorithm. Lucas Parra and I digitally extracted ten five-second clips from ten audio CDs. These were digitally mixed, without time delays or echos, and with random gains, to form the output of a synthetic microphone. Ten such microphone outputs were synthesized. These synthetic microphone outputs formed the input to the Bell-Sejnowski Independent Components Analysis algorithm. The sources are somewhat separated in the output of the Bell-Sejnowski ICA algorithm, but not fully.
The same synthetic microphone outputs were then used as input to our new cICA algorithm (see my publications page for technical details). The sources are almost fully separated in the output of cICA.