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RSA Overview
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in this video I'm going to provide a
brief overview of the application of
representational similarity analysis or
RSA to ERP data RSA is widely used in
fMRI but it can also be used with ERP is
to generate some amazing results it's a
general-purpose method for assessing
links among different kinds of neural
measures computational models and
behavior each of these sources of data
has a different format which makes them
difficult to compare directly for
example we have bold activation across
the set of voxels in fMRI voltage over
time at a bunch of electrodes in EEG and
a pattern of activation across the units
of a neural network model how can we
compare these different data formats RSA
solves this problem by converting each
source of data into a representational
similarity matrix or RSM we can then
look at how well the are SMS from the
different data sources are correlated
with each other
okay let's unpack all of this to get a
representational similarity matrix you
need to look at the pattern of activity
produced by several different inputs for
example imagine that we showed
participants a set of twenty scenes and
for each scene we obtain the pattern of
bold activation across visual cortex we
could then ask how similar to the
pattern of activation is for scene one
versus scene two there are many ways of
quantifying similarity but we could
simply calculate the Pearson R
correlation coefficient between the two
patterns of bold activation we might get
a correlation of 0.84 between the fMRI
patterns for scene 1 and scene 2 and we
might find a correlation of 0.09 between
the fMRI pattern for scene 1 and the
fMRI pattern for scene 3 we have a total
of 20 scenes so we'd end up with a 20 by
20 matrix of correlations the result is
called a representational similarity
matrix or RSM because it expresses the
pattern of similarity in the neural
representations of the 20 scenes we'd
get a separate RSM for each subject the
correlation between a given scene and
itself is always 1 so we ignore the
diagonal and the upper and lower
triangles are mirror images so we ignore
the upper triangle
some researchers prefer to use a
representational dissimilarity matrix
which is just one minus the correlation
in the end you get exactly the same
results either way we could also get a
representational similarity matrix for a
neural network model that's trained on
scene recognition we could feed each of
the 20 scenes into the network and note
the pattern of activation across the
units for each scene we could then
examine the correlation between the
active pattern for each pair of scenes
this would give us a 20 by 20
representational similarity matrix for
the neural network we could then ask
whether the RSM for the model is similar
to the RSM for the fMRI data we would do
this by just looking at the correlation
between the lower triangles of the two
representational similarity matrices we
use a rank order correlation because we
don't want to assume anything about the
scaling of these two matrices if the
matrices are correlated with each other
this indicates that the representational
geometry of the model is predictive of
the representational geometry of the
fMRI data and vice-versa we could also
have subjects view these twenty scenes
while we record the EEG we could then
make an average ERP for each scene and
calculate the similarity between each
pair of scenes in terms of the ERP data
to take advantage of the millisecond
level temporal resolution of the ERP
data we could do this separately for
each time point that is for each time
point in an average we can compute a
scalp distribution we can then get a 20
by 20 representational similarity matrix
for that time point by computing the
correlation between the scalp
distributions for each pair of scenes we
actually have a separate scalp
distribution for each time point in the
ERP waveform so we have a separate RSM
for each time point for example if we
have a sampling rate of 250 Hertz one
sample every 4 milliseconds we'd get
something like this you have an RSM at
time 0 which is the onset of the
stimulus then we have 1 at 4
milliseconds after stimulus onset 8
milliseconds after stimulus onset etc
this would go on for several hundred
milliseconds depending on the length of
the epoch that was used during averaging
of course the RSM stirring the period
immediately following stimulus onset
will be noise because information about
the stimulus hasn't reached the cortex
yet for a visual stimulus the RSM will
start being structured around
50 to 70 milliseconds after stimulus
onset remember each cell in these our
SMS is just the correlation between the
ERP scalp distributions for a pair of
scenes at that time point we can then
correlate the RSM at each time point
with the RSM for the fMRI data or the
neural network model this is just the
rank order correlation between the our
SMS we'd expect pretty low correlations
at time zero because the ERP RSM should
just be noise at that time we then
compute the correlation between the ERP
RSM at four milliseconds with the fMRI
and model our SMS and then we'd repeat
this for every time point in the ERP
waveform each Spearman Rho correlation
value indicates the representational
similarity between the ERP data at a
given time and either the fMRI data or
the pattern of activation in the model
we can plot these values as waveforms
much the way we plot ERP waveforms
except now the y-axis is the correlation
between the ERP RSM at a given time
point and either the fMRI RSM or the
model RSM so by abstracting away from
the original units of measure and
creating representational similarity
matrices we can quantify the extent to
which the representational geometry of
one source of data matches the
representational geometry of the other
sources up to this point I've been
showing artificial data but here's a
real study they used event related
magnetic fields rather than ERPs but the
principle is the same you tend to get
stronger effects with M eg than with EEG
but given how much cheaper EEG is I'm
not tempted to move to M eg subjects in
this study viewed a sequence of natural
images and performed an orthogonal
vigilant's task to keep them alert and
attentive each subject was tested in
separate M eg and fMRI sessions with the
same images the goal was to link the
temporal resolution of the event related
magnetic fields with the neuroanatomical
specificity of the ERP data to
accomplish this they calculated a
representational dissimilarity matrix
for the M eg data at each time point and
a representational dissimilarity matrix
for the fMRI data for each brain area
remember a representational
dissimilarity matrix is just one - the
representational similarity matrix
the next step was to calculate the
spearmen row rank order correlation
between the m EG matrix at each time
point with the fmri matrix for each
region this resulted in one Spearman row
correlation value for each combination
of M eg time point and fMRI brain region
here's what they found the intensity at
each voxel is the representational
similarity between that brain region in
the fMRI data and the magnetic field
distribution at a given time point in
the m EG data this is completely
different from most source localization
methods there making no assumptions
about the physics of EEG e or m EG
instead these results are obtained by
using a variety of visual stimuli to
probe the brain and comparing the
representational geometries of the fMRI
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