General Signal Processing and Machine Learning Tools for BCI Analysis (Part-1)

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General Signal Processing and Machine Learning
Tools for BCI Analysis (Part-1)

• Md. Zia Uddin
• Bio-Imaging Lab, Department of Biomedical
  Engineering
• Kyung Hee University

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Contents

• Abstract
• Introduction
• Spectral Filtering
• Special Filtering
• Classification

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Abstract

• This presentation is about signal processing and
  machine learning techniques and their
  applications to BCI.
• Overview of general signal processing and
  classification methods as used in single-trial
  EEG analysis is given.
• For further study, original publications are
  encouraged.

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Why ML for BCI

• Subject wise experiments
• Subject to subject result variances for same kind
  of experiments.
• Session wise experiments
• Session to session huge result variability for
  the same person.
• Real time experiments
• The system needs to identify the subjects mental
  state from single trial.
• Much more complexity arises.
• Solution
• A session and user brain signature adaptable
  system is necessary to overcome the subject to
  subject and session to session huge variability.

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Why Preprocessing?

• Relevant information extraction is difficult
  because of large dimensional data (i.e., Curse of
  dimensionality).
• Dimensionality has to be reduced keeping the
  discriminative information and eliminating
  undiscriminative information.
• Most of the classification methods calculate
  covariance matrix of the data for further feature
  analysis. Huge covariance matrix is required in
  the case of large dimensional data.
• Thus, Prepropcessiong steps regarding
  dimensionality reduction is required
• In some cases
• A priory knowledge is used (e.g., spatial Laplace
  filter at predefined scalp locations)
• Automatic methods (e.g., spatial filters
  determined by common spatial pattern analysis)

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Spectral Filter FIR IIR

• Common approach is to use digital frequency
  filter
• To consider desired frequency range
• Two sequences of poles (a) and zeroes (b) with
  length na and nb are necessary that can be
  calculated by Butterworth or elliptic.
• The source signal x is filtered to y as
• a(1)y(t)b(1)x(t) b(2)x(t-1) ...
  b( nb )x(t- nb -1) a(2)y(t-1) -...- a( na )y(t-
  na -1)
• Where a and na are constrained to be 1, is called
  FIR filter (i.e., considering all zeros).
• Advantage of FIR
• Produce steeper slopes in between pass and stop
  band.
• In most of the BCI applications, band pass filter
  is required to consider specific frequency range.

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Spectral Filter Fourier-Based Filter

• A good alternative than FIR and IIR is to use
  temporal Fourier-based filtering in BCI.
• A signal switches from temporal to the spectral
  domain.
• The filtered signal is obtained by choosing
  suitable weighting to the relevant frequency
  components and applying Inverse Fourier
  Transformation (IFT).
• The short time window determines the frequency
  resolution

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Spatial Filter Bipolar Filtering

• EEG channels are measured as voltage potential
  relative to a standard reference (referential
  recording).
• Also, it is possible to record all the channels
  as voltage difference between the electrode
  pairs.
• From referential EEG, bipolar channels can be
  obtained by subtracting the respective channels
• FC4-CP4(FC4-ref) - (CP4-ref)FC4ref -CP4ref
• Reduces the effect of local smearing by computing
  local gradient.
• Focuses on the local activity while contributions
  of more distant sources are attenuated

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Spatial Filter Common Average Reference

• The mean of all EEG channels are subtracted from
  each channel to get the common average reference
  signals.
• Reduces the influence of far field sources but
  may introduce some undesired spatial smearing
• Artifacts of one channel may spread to all other
  channels.

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Spatial Filter Laplace Filtering

• More localize filter can be obtained through
  this.
• Laplace signals are obtained by subtracting the
  average of surrounding electrodes from each
  individual channel.
• C4Lap C4ref- ¼(C2ref C6ref FC4ref CP4ref)
• The choice of surrounding channels determine the
  characteristics of the filter.
• Usually, small Laplacians are used (as example
  given above).
• Large Laplacians use neighbors at 20 distance
  as defined in international 10-20 system.

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Spatial Filter Principle Component Analysis(1)

• Represent multidimensional data with fewer number
  of variables retaining main features of the data.
  
• It is inevitable that by reducing dimensionality
  some features of the data will be lost. It is
  hoped that these lost features are comparable
  with the noise and they do not tell much about
  underlying population.
• The method PCA tries to project multidimensional
  data to a lower dimensional space retaining as
  much as possible variability of the data.
• Its simplicity makes it very popular. But care
  should be taken in applications. First it should
  be analyzed if this technique can be applied.

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Spatial Filter Principle Component Analysis(2)

• Orthogonal directions of greatest variance in
  data
• Projections along PC1 discriminate the data most
  along anyone axis
• First principal component is the direction of
  greatest variability (covariance) in the data.
• Second is the next orthogonal (uncorrelated)
  direction of greatest variability
• So first remove all the variability along the
  first component, and then find the next direction
  of greatest variability
• And so on

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Spatial Filter Principle Component Analysis(3)

• We can ignore the components of lesser
  significance.
• We do lose some information, but if the
  eigenvalues are small, we dont lose much
• n dimensions in original data
• calculate n eigenvectors and eigenvalues
• choose only the first p eigenvectors, based on
  their eigenvalues
• final data set has only p dimensions

Basic Steps
Eigenplot
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Visual Evoked Potential Extraction from Single
Trial EEG signals using PCA filtering(1)

• Problem Definition
• Remove the noise to get VEP in the single trial
  29 channels EEG data without ensemble averaging
• Technique adopted to solve the Problem
• Selection of principal components as basis for
  the reconstruction of signal
• Methodology
• Given signal is divided into an ensemble of
  signals, for each channel
• An ensemble average for each channel is obtained
  as a reference
• Apply PCA to find out the orthonormal
  eigenvectors which are used as basis for signal
  approximation
• Selection of Principal components as basis by
  looking at the frequency components present in
  the prototype signal i.e. the averaged signal

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Visual Evoked Potential Extraction from Single
Trial EEG signals using PCA filtering(2)
Original Signal
Single epoch after PCA filtering
Reconstructed epoch stacks
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Spatial Filter Independent Component Analysis(1)

• Basically ICA is applied for Blind Source
  Separation (BSS)
• Assume an observation (signal) is a linear mix of
  unknown independent source signals
• The mixing (not the signals) is stationary
• We have as many observations as unknown sources
• To find sources in observations
• Need to define a suitable measure of independence
• For example - the cocktail party problem
  (sources are speakers) Find Z
• Formal Statement
• N independent sources Zmn ( M xN )
• linear square mixing Ann ( N xN )
• produces a set of observations Xmn ( M xN )
• .. XT AZT

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Spatial Filter Independent Component Analysis(2)

• demix observations XT ( N xM ) into YT WXT
  YT ( N xM ) ? ZT W ( N xN )
  ? A-1
• How do we recover the independent sources?
• (We are trying to estimate W ? A-1 )
• . We require a measure of independence!

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Spatial Filter Independent Component Analysis(3)

• The source signals are mixed by random non
  orthogonal matrix
• JADE algorithm was applied to demix the signals
• After reordering and scaling, the demixed signals
  are very similar to sources.
• PCA would fail here as the mixed signals are not
  orthogonal to each other, which is the key
  assumption of PCA.
• Other ICA algorithms
• Infomax
• FastICA

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Spatial Filter Independent Component
Analysis(4) Applying ICA to single-trial EEG
epochs

• Data Collection
• EEG data were recorded from 31 scalp electrodes
• 29 placed at locations based on a modified
  International 10-20 system
• one placed below the right eye (VEOG),
• one placed at the left outer canthus (HEOG). All
• 31 channels were referred to the right mastoid
  and were digitally sampled for analysis at 256
  Hz with a 0.01- to 100-Hz analog bandpass plus a
  50-Hz lowpass filter.
• Subjects participated in a 2-hour visual spatial
  selective attention task in which they were
  instructed to attend to filled circles flashed
  in random order in five locations.

• Component IC1, generated by blinks
• IC4 generated by temporal muscle activity.

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Spatial Filter Independent Component
Analysis(5) Applying ICA to single-trial EEG
epochs (2)

• The scalp maps and power spectra of the 31
  independent components derived from target
  response epochs from a 32-year-old autistic
  subject.
• Blink and eye movement artifact components (IC1
  and IC9) had a typical strong low frequency
  peak.
• Temporal muscle artifact components (i.e., ICs
  14, 22, 27, and 29) had characteristic focal
  optima at temporal sites and power plateaus at 20
  Hz and higher.

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Conclusion

• Next class
• more classification techniques and some
  practical examples.

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• Thank you