md. zia uddin bio-imaging lab, department of biomedical engineering kyung hee university
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Md. Zia Uddin Bio-Imaging Lab, Department of Biomedical Engineering
Kyung Hee University
Abstract
Introduction
Spectral Filtering
Special Filtering
Classification
ContentsContents
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.
AbstractAbstract
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.
Why ML for BCIWhy ML for BCI
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)
Why Preprocessing?Why Preprocessing?
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.
Spectral Filter: FIR & IIRSpectral Filter: FIR & IIR
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
Spectral Filter: Fourier-Based FilterSpectral Filter: Fourier-Based Filter
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
Spatial Filter: Bipolar FilteringSpatial Filter: Bipolar Filtering
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.
Spatial Filter: Common Average ReferenceSpatial Filter: Common Average Reference
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.
Spatial Filter: Laplace FilteringSpatial Filter: Laplace Filtering
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.
Spatial Filter: Principle Component Analysis(1)Spatial Filter: Principle Component Analysis(1)
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 …
Spatial Filter: Principle Component Analysis(2)Spatial Filter: Principle Component Analysis(2)
Original Variable A
Ori
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rigin
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BB
PC 1PC 2
Spatial Filter: Principle Component Analysis(3)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
don’t 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
Subtract the mean
Calculate the covariance matrix
Calculate the eigenvectors and
eigenvalues of the covariance matrix
Get data Choosing top components and forming a feature
vector
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PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10
Varia
nce
(%)
Basic StepsEigenplot
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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60Channel # 9 signal
Original Signal
Single epoch after PCA filtering Reconstructed epoch stacks0 100 200 300 400 500
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Filtered signalOriginal signalTemplate signal
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
Spatial Filter: Spatial Filter: Independent Component Analysis(1)Independent Component Analysis(1)
Spatial Filter: Spatial Filter: Independent Component Analysis(2)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!
Spatial Filter: Spatial Filter: Independent Component Analysis(3)Independent Component Analysis(3)
Spatial Filter: Spatial Filter: Independent Component Analysis(4)Independent Component Analysis(4)Applying ICA to single-trial EEG epochsApplying ICA to single-trial EEG epochs
Data CollectionEEG data were recorded from 31 scalp electrodes29 placed at locations based on a modified International 10-20 systemone placed below the right eye (VEOG),one placed at the left outer canthus (HEOG). All31 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 blinksIC4 generated by temporal muscle activity.
Spatial Filter: Spatial Filter: Independent Component Analysis(5)Independent Component Analysis(5)Applying ICA to single-trial EEG epochs (2)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.
Next class more classification techniques and some practical examples.
ConclusionConclusion
Thank you
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