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We analysed the data set
with artificial activation introduced into baseline FMRI data using
PICA and GLM. The exact activation time courses were used within the
GLM as regressors of interest. This will introduce a small bias in
favour of the GLM analysis which we prefer compared to the alternative
where we would have to artificially encode the more plausible
ignorance that normally exists over the exact shape of the signal
within the data. In order to estimate the consistency of the
probabilistic ICA approach, the analysis was repeated 150
times in order to evaluate the repeatability between runs5. Table 1 summarises the mean correlation between the
estimated and true time courses over all 150 runs while figure
6 shows the ROC curves for both GLM and PICA
Naturally, the estimation accuracy improves with increased signal
level. Note that the ROC curves for the GLM are not monotonically
increasing. This is a direct consequence of the ambiguity built into
the statistical thresholding steps based on Gaussian Random Field
Theory6, where a
-threshold level is combined with a significance level for
cluster heights or size.
In the present case, we evaluated different sets with ranging from
to and ranging from to . For fixed
or fixed , a monotonically increasing ROC curve can be plotted but
for reasons of simplicity, we ordered all results by increasing false
positive rate and in the case of multiple true positive outcomes only
used the best one. In almost all cases, the PICA estimates show an
improved ROC characteristics compared to the GLM results despite the
fact that GLM analysis was carried out under the ideal condition of
perfect knowledge of the regressors of interest.
This is due to the fact that a standard GLM analysis is adversely
affected by the presence of un-modelled structured noise in this data.
The PICA decomposition, on the other hand, estimates sufficiently
strong structured noise as separate components resulting in increased
spatial accuracy for the activation component. Note that in the
case of the GLM a difference in the threshold even within a
commonly-used range of values leads to substantially different quality
of estimation.
Table 1:
Temporal accuracy at different activation levels: correlation
between the extracted time courses and the true signal time courses
over 150 runs.
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Figure 6:
Spatial accuracy at different activation levels: ROC curves
for PICA (solid lines - mean over 150 runs) vs. ROC curves for
statistical maps thresholded using Gaussian Random Field theory at
different and levels. Markers indicate typical threshold
levels: 0.33,0.5 and 0.66 (PICA alternative hypothesis test);
and (GLM null-hypothesis test).
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Next: Accuracy and dimensionality
Up: Results
Previous: Artificial signal in synthetic
Christian F. Beckmann
2003-08-05