Analyzing Quantitative EEG Using Machine Learning and Information Theoretic Techniques

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Analyzing Quantitative EEG Using Machine Learning
and Information Theoretic Techniques
Pedja Neskovic

Booz Allen Hamilton Arlington, VA Institute
for Brain and Neural Systems Brown University,
Providence, RI
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• Objective
• Classify EEG signals into different tasks
  (learning, memory, etc) within and across
  subjects decoding brain signals

• Methods
• To extract informative characteristics use
  information theory and to learn/detect patterns
  in EEG use machine learning

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n-back task

• The n-back task requires subjects to decide
  whether a currently present stimulus matches one
  presented n trials previously

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• Challenges
• Low signal to noise ratio the noise level is
  typically about 20 , and the signal of
  interest about 5
• Signal is contaminated by artifacts (eye
  movements/blinks, muscle contr.)
• Processing large amounts of data in real time
• Design a method for extracting most
  discriminative features

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Representing EEG signals

• Representation what characteristics/features to
  use?
• Most widely used features are power spectrum
  (PS), coherence analysis, linear correlation
  (LC), auto regression (AR) analysis, PCA, etc.
• - Main drawbacks capture only linear
  dependences and 2nd order statistics

• Introduce new features Entropy (H) and Mutual
  Information (MI)
• In contrast to power spectrum which is based on
  second order statistics,
• H encompasses higher order statistics
• In contrast to linear approaches (e.g
  correlation, coherence, partial coherence
  analysis, linear Granger causality and Directed
  Transfer Function (DTF)), MI captures both linear
  and nonlinear dependences

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Definitions

• Entropy measures the uncertainty of a discrete
  random variable X
• If H0 it means that every measurement occurs
  with probability 1 or 0
• Mutual information is the reduction in the
  uncertainty of X due to the knowledge of Y
• MI0 iff X and Y are statistically independent
• (in contrast with Pearson correlation which
  quantifies only linear dependencies)

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Calculating p(x)

• Standard approach use histograms to estimate p

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Stochastic process

• Shortcoming of using H and MI ignored temporal
  dependences
• Model outputs as a Markov stochastic process
  represent outputs of one electrode as a sequence
  of random variables

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Capturing temporal dependences

• Conditional entropy
• Conditional MI - capture both spatial and
  temporal dependences

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How to estimate entropy?

• Histogram approach is not good if we have to
  estimate joint probabilities of many variables
• Some of the bins will have zero counts
  sometimes there are more bins than data points
• To calculate expected Entropy use Bayesian
  approach

- vector of true (unknown) probabilities
- vector of counts
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Entropy estimation

• Likelihood multinomial distribution
• Dirichlet prior
• - reflects the prior knowledge of the number
  of points in each bin

- Digamma function
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Classification task subject

• Goal Associate a given EEG segment with
  both the subject and the class
• Classifiers Naïve Bayes (NB) and SVM
• Features 62 for H, and 1,891 for MI
• 24 classes 6 subject and 4 tasks

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Dependence on prior parameters
Single trial classification rates with SVM
Five trial classification rates with SVM
 

• EF N
• prior parameter becomes less important as more
  observations become available

- effective number of points
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SVM classification rates 64 features
Five trial long segments
Single trial long segments

• PS Power Spectra
• H Entropy, H(X)
• CH Conditional Entropy, H(XX), captures
  temporal dependences within a single electrode

• Band A 1-20Hz
• Band B 20-40Hz
• Band C 40-60Hz

 
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SVM classification rates 1,891 features
Five trial long segments
Single trial long segments

• LC Linear Correlation
• MI(2) MI between two electrodes, MII(X,Y) -
  captures "spatial" dependences
• MI(3) MI between two electrodes (using 3 random
  variables), MI(3) (XYX) - captures spatial
  and temporal dependences
• MI(4) MI using 4 random variables, MI(4)
  (XYX,Y)

 
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Classifying EEG across subjects

• Using all the features classification is around
  chance!

• Problems too many features e.g., 6262 for MI
  features and not all are important (noisy
  features, irrelevant features, etc.)

• Solution reduce the number of features by
  measuring the statistical dependence between
  features and a class variable (e.g. MI)

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Classifying EEG across subjects

• Problem have to calculate joint probability
  that involves many features and a class variable

• Solution select features sequentially, treat
  one feature at a time and calculate MI between
  every feature and a class variable.
• Maximize the dependence between a feature and
  the class variable and minimize the redundancy
  among features

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Classification across subjects
Goal Associate a given EEG segment with the
task across subjects (test on a subject that
has not been used for training)

• Classifiers
• Naïve Bayes (Bayes)
• Support Vector Machine (SVM)
• Nearest Neighbor (NN)

• Features
• For MI, start with 1,891 and use only 40 highly
  discriminative features
• Use 6 subjects 5 for training and 1 for
  testing

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Results
Power Spectra
Conditional Entropy
Conditional MI
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Conclusions

• Information-theoretic features (H, CH and MI(i))
  outperform conventional features (power spectrum,
  lin. correlation)
• Although H and MI features capture non-linear
  dependences, they assume that the signal is
  stationary
• To capture temporal dependences, treat electrode
  outputs as a stochastic process and introduce
  conditional entropy and conditional mutual
  information features
• To detect more difficult patterns (classify
  across subjects from single trials) necessary to
  reduce dimensionality of the feature space

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Collaborators

• Liang Wu and Leon Cooper
• Physics Department
• Institute for Brain and Neural Systems
• Brown University, Providence, RI
• Bill Heindel and Elena Festa
• Department of Psychology
• Brown University, Providence, RI