SPM course - 2002 The Multivariate ToolBox (F. Kherif, JBP et al.)

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SPM course - 2002The Multivariate ToolBox (F.
Kherif, JBP et al.)
T and F tests (orthogonal projections)
Hammering a Linear Model
The RFT
Multivariate tools (PCA, PLS, MLM ...)
Use for Normalisation
Jean-Baptiste Poline Orsay SHFJ-CEA www.madic.org
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From Ferath Kherif MADIC-UNAF-CEA
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SVD the basic concept

A time-series of 1D images 128 scans of 40
voxels Expression of 1st 3 eigenimages Eigen
values and spatial modes The time-series
reconstituted
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Eigenimages and SVD
V1
V2
V3
voxels
APPROX. OF Y
U1
APPROX. OF Y
APPROX. OF Y
U2
U3
s2
s3
s1

...
Y (DATA)
time
Y USVT s1U1V1T s2U2V2T
...
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Linear model recall ...
voxels
parameterestimates


?
residuals
design matrix
data matrix
scans
Variance(e)
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SVD of Y (corresponds to PCA...)
V1
V2
U1
U2
voxels
APPROX. OF Y
APPROX. OF Y
s2
s1

...

Y
scans
U S V SVD (Y)
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SVD of ? (corresponds to PLS...)
V1
V2
U1
U2
APPROX. OF Y
APPROX. OF Y
parameterestimates
s2
s1

...

U S V SVD (XY)
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SVD of residuals a tool for model checking
V1
V2
voxels
U1
U2
APPROX. OF Y
APPROX. OF Y
E
s2
scans
s1

...

/
E / std normalised residuals
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Normalised residuals first component
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Normalised residuals first component of a
language study
Temporal pattern difficult to interpret
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SVD of normalised ? (MLM ...)
V1
V2
parameterestimates
U1
U2
APPROX. OF Y
APPROX. OF Y

...
(X V X)-1/2 X
s1
s2

U S V SVD ((X C X)-1/2 XY )
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MLM some good points

• Takes into account the temporal and spatial
  structure without withening
• Provides a test
• sum of q last eigenvalues Si for q n, n-1, ...,
  1
• find a distribution for this sum under the null
  hypothesis (Worsley et al)
• Temporal and spatial responses
• Yt Y V Temporal OBSERVED response
• Xt X(XX)-1 (X C X)1/2 US Temporal
  PREDICTED response
• Sp (X C X)-1/2 XY U S-1 Spatial response

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MLM first component p lt 0.0001
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MLM more general and computations improved ...

• From XY to XGYG
• XG X - G(GG)GX
• YG Y - G(GG)GY
• X and XG used to need to be of full rank
• not any more
• G is chosen through an  F-contrast  that
  defines a space of interest

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MLM implementation

• Computation through betas
• Several subjects
• IN
• An SPM analysis directory (the model has been
  estimated) IN GENERAL, GET A FLEXIBLE MODEL FOR
  MLM
• A CONTRAST defining a space of interest or of no
  interest (here G) IN GENERAL, GET A FLEXIBLE
  CONTRAST FOR MLM
• Output directory
• names for eigenimages
• OUT eigenimages, MLM.mat (stat, ) observed and
  predicted temporal responses YY

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Re-inforcement in space ...
V1
V2
voxels
U1
U2
Subjet 1
Subjet 2
APPROX. OF Y
APPROX. OF Y
Y
s2

...

s1
Subjet n
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... or time
V1
Subjet 1
U1
Subjet n
voxels
Subjet 2
APPROX. OF Y
s1

Y
V2
U2
...

APPROX. OF Y
s2
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SVD implementation

• Choose or not to divide by the sd of residual
  fields (ResMS)
• removes components due to large blood vessels
• Choose or not to apply a temporal filter (stored
  in xX)
• Choose a projector that can be either  in  X or
  in a space orthogonal to it
• study the residual field by choosing a contrast
  that define the all space
• study the data themselves by choosing a null
  contrast (we need to generalise spm_conman a
  little)
• to detect non modeled sources of variance that
  may lead to non valid or non optimal data
  analyses.
• to rank the different source of variance with
  decreasing importance.
• Possibility of several subjects

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SVD implementation

• Computation through the svd(PYYP) v s v
• compute Y Y once, reuse it for an other
  projector
• Y can be filtered or not divided by the res or
  not
• to get the spatial signal, reread the data and
  compute Yvs-1
• TAKES A LONG TIME
• possibility of several subjects (in that case,
  sums the individual YY)
• (near) future implementation use the betas when
  P projects in the space of X

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SVD implementation

• IN
• Liste of images (possibly several  subjects )
• Input SPM directory (this is not always
  theoretically necessary but it is in the current
  implementation)
• A CONTRAST defining a space of interest or of no
  interest
• in the residual space of that contrast or not ?
• Output directory (general, per subject )
• names for eigenimages
• OUT eigenimages, SVD.mat, observed temporal
  responses YY

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Multivariate Toolbox An application for model
specification in neuroimaging(F. Kherif et al.,
NeuroImage 2002 )
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From Ferath Kherif MADIC-UNAF-CEA
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From Ferath Kherif MAD-UNAF-CEA
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RESULTS
MODEL SELECTION
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Z1M-1/2 XY1 Z2M-1/2 XY2 ZkM-1/2 XYk
W1Z1 Z1 W2 Z2 Z2 Wk Z2 Z2
Similarity measure
Distance matrix
Subjects classification (multi-dimensionnal
scaling)
Group Homogeneity Analysis