Egon Valentini

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ICA-applications II

• Egon Valentini
• TU-GRAZ
• WS 2001/02

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Contents

• Preface
• BSS
• EEG MEG
• Financial Applications

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Applicationfields of ICA

• BSS
• Feature extraction
• Telecommunication
• EEG - MEG
• Finance
• Text document analysis
• Radio-communication
• Seismic monitoring

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BSS contents

• Short repetition
• Online-JAVA-applet
• Online BSS with Mathlab

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Cocktail-Party-Problem
Concrete application person is talking to a
mobile-phone in a noisy car
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2 Speaker, speaking simultaneously
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2 Microphones in different locations
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ICA-Model
x1(t) a11s1 a12s2 x2(t) a12s1 a22s2
aij ... depending on the distances of the
microphones from the speakers
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Get the original signals out of the recorded ones
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Online-ICA-demos
ICA by nonlinear Decorrelation and Nonlinear PCA
http//www.lis.inpg.fr/demos/sep_sourc/ICAdemo
H?rald-Jutten algorithm (A.Hyvärinen, Juha
Karhunen, Erkki Oja Independent Component
Analysis, John Wiley Sons 2001, P.242) Mutual
Information minimization using online estimation
of density derivates (A.Hyvärinen, Juha Karhunen,
Erkki Oja Independent Component Analysis, John
Wiley Sons 2001, P221ff.)
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H?drault-Jutten
ICA-Model x As Feedback-circuit Initial
output are fed back to system, output
recomputed, until an equilibrium is reached
x1(t) a11s1 a12s2 x2(t) a12s1 a22s2
y1 x1 -m12yy2 y2 x2 -m21yy1
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H?drault-Jutten
y x - My y (IM)-1 x Note ICA s
A-1x If IMA then ys H?rault-Jutten
adapt m12 and m21 so that y1 and y2 become
independent For indipendence, HJ used the
criterion of nonlinear correlation.
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H?drault-Jutten
Learning rules
Dm12 µf(y1)g(y2) Dm21 µf(y2)g(y1) f(y)
y3 g(y) arctan(y)
http//www.lis.inpg.fr/demos/sep_sourc/ICAdemo
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BSS with Matlab

• using FastICA
• using EcoBliSS (Extended Convolutive BSS)
• (see http//www.esp.ele.tue.nl/onderzoek/daniel
  s/BSS.html)

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Brain Imaging Applications

• EEGrecords electric
• MEGrecords magnetic fields of signals from
  neural currents in brain

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Neurons potentials

• Human brain 1010 to 1011 neurons
• Signals between neurons are transmitted by means
  of action potentials, short burts of electricity
  activity.Action potential is transformed in
  receiving neuron to postsynaptic potential
  (longer duration)
• Neurons with strong postsynaptic potentials tent
  to cluster. Total electric current produced in
  this cluster may be detected.

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EEG MEG

• EEG measures potential distribution on scalp by
  placing electrodes
• MEG measuers magnetic fields associate with
  current (more sophisticated)

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EEG MEG

• EEG Used for measuring spontaneous activity and
  for study of evoked potentials (triggerd by a
  stimulus, e.g. Auditory or somatosensory)
• MEG Use for cognitive brain research

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Application of EEG MEG

• Articacts (signals not generated by brain
  activity, but some external disturbans
  (muscles,...))
• 122 - sensonr scalp magnetometer.
• Test-person should blink, make horizontal
  saccades, bite for 20s
• Other artifact digital watch 1m away from
  magnetometer.

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Activation of 2 diff. Muscels sets
Horizontal eye movement
Heart beating, digital watch

Breathing, bumps caused by overlearning
Faulty sensor
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ICA on other measure techniques

• Functional Magnetic resonance images
• Removing artifacts from cardiographic (heart)
  signals

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Where does ICA not work?

• ? maybe ask Mr. Vicario

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Good news
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ICA in Financial Application

• Finding hidden factors in financial data

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ICA reveals hidden factors

• Exp Try to find the fundamental factors common
  to all stores affecting cashflow (cashflow of
  some stores of same retail chain)
• ICA-Model
• xi(t)... financial time series

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ICs in time series

• Seasonal variation due to holidays
• Other factors having effect on purchasing power
  of customers (e.g. Price-changes of
  commodities) Depending on advertisment, effect
  of this factors on cashflow are diff.

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Using ICA...

• Data first prewhitened using PCA
• Problem no knowledge about number of independent
  components.(approx. using eigenvalue spectrum
  of data covarianz matrix)
• Here FastICA with 4 ind. Components

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Demos

• Demos-Download-Sitehttp//sig.enst.fr/cardoso/i
  cacentral/algos.html
• Online-Demohttp//www.lis.inpg.fr/demos/sep_sour
  c/ICAdemo
• Homepage von Aapo Hyvärinen http//www.cis.hut.fi
  /aapo/

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Literatur-Referencies

• Independent Component Analysis Aapo Hyvärinen,
  Juha Karhunen, Erkki Oja John Wiley Sons, Inc.
• Vicardo Nuno Vigário, Dr. Techhttp//www.cis.hut.
  fi/rvigario
• Applying independent component analysis (ICA) and
  time/frequency analysis to collections of
  single-trial EEG (or MEG) data, or to collections
  of averaged event-related potential (ERP) or
  field (ERF) epochs.http//www.cnl.salk.edu/scott
  /PNAS.html
• ICA-CNL Overviewhttp//www.cnl.salk.edu/tewon/i
  ca_cnl.html

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Literatur-Referencies

• ICA and Clinical EEG, ICA and functional
  MRihttp//www.cnl.salk.edu/martin/index.html

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Thanks
Merry X-mas and happy new year