Modeling and Nonlinear Analysis in fMRI via Statistical Learning - Advance Image Processing in Magnetic Resonance Imaging - page 561

multiply all t i by a coefficient W-scale and all m ( t i ) by a coefficient W-model . The
notion of scaling different components of the input vector is critical to an under-
standing of the potential utility of SVR. The scaling can balance the relative
explanatory power of the different components. Scaling has this effect because
of the projection of the input to a higher-dimensional space using nonlinear kernel
functions. It is this nonlinearity that renders the regression sensitive to scaling.
In linear models, the scaling is irrelevant because the different components of
the input vector do not interact. However, in SVR the scale of each explanatory
variable can have a profound effect on the interactions.
The effect of temporal scale can be adjusted by varying W-scale , the
coefficient for the time indices. Varying W-scale is equivalent to examining
the temporal data at different scales and, therefore, achieves multiresolution
signal analysis. A larger W-scale corresponds to a finer temporal resolution.
We can restore the time courses at multiple resolutions and extract different
frequency components by changing W-scale . Many voxel time series in fMRI
exhibit low-frequency trend components that may be due to aliased high-
frequency physiological components or drifts in the scanner. These trends can
be removed in a variety of ways. In addition to using a simple high-pass filter
in the temporal domain, a running-lines smoother has been proposed (28).
However, most existing methods only aim to handle linear trends. In the
spatiotemporal nonlinear SVR, with appropriate W-scale (usually relatively
small), low-frequency noise can be extracted and removed and thus achieve
nonlinear detrending.
The optimal W-scale for a specific frequency component is expected to be
related to the total number of time points, the period of the stimulation, and the
data noise level, whose value is currently determined empirically. A more rigorous
formulation of W-scale determination is one of our future directions, which might
be achieved in the frequency domain through spectrum analysis, etc.
For the data generated in Section 18.4.2 (shown in Figure 18.4 ), the ST-SVR
window size used is 3

72. Figure 18.5 demonstrates the effects of W-
scale by showing the recovered time courses for an activated pixel (Figure 18.5
left) and for a nonactivated pixel (Figure 18.5 right) of the simulated noisy data
(Figure 18.4c) without model fitting ( W-model

× 3 × 3 ×

0, data driven). As W-scale
increases, higher-frequency temporal components are extracted. When W-scale

=

=
5 (Figure 18.5a and Figure 18.5d), the restored signal captures the low-frequency
component, which can be interpreted as a nonlinear trend.

18.4.4 M ERGING M ODEL -D RIVEN WITH

D ATA -D RIVEN M ETHODS

The coefficient associated with the model index, W-model , determines the degree of
influence of the temporal-model term and the degree to which the approach is model-
driven. A higher W-model ( W-model 1) is used when reliable temporal models are

available. Otherwise, a lower or zero W-model is used, and the approach becomes
more data driven. W-model can be interpreted as a model confidence or fitness

=