Mathematics in Independent Component Analysis

120 Chapter 6. LNCS 3195:726-733, 2004
1 2 3
4 5 6
7 8
(a) component maps
SOBI based on multi-dimensional autocovariances 7
1 cc: −0.08 2 cc: 0.19 3 cc: −0.11
4 cc: −0.21 5 cc: −0.43 6 cc: −0.21
7 cc: −0.16 8 cc: −0.86
(b) time courses
Fig. 4. mdSOBI fMRI analysis. The data was reduced to the first 8 principal components.
(a) shows the recovered component maps (white points indicate values stronger
than 3 standard deviations), and (b) their time courses. mdSOBI was performed with
K = 32. Component 5 represents inner ventricles, component 6 the frontal eye fields.
Component 8 is the desired stimulus component, which is mainly active in the visual
cortex; its time-course closely follows the on-off stimulus (indicated by the gray boxes)
— their crosscorrelation lies at cc = −0.86 — with a delay of roughly 2 seconds induced
by the BOLD effect.
photic simulation periods with rest. Simulation and rest periods comprised 10
repetitions each, i.e. 30s. Resolution was 3 × 3 × 4 mm. The slices were oriented
parallel to the calcarine fissure. Photic stimulation was performed using
an 8 Hz alternating checkerboard stimulus with a central fixation point and a
dark background with a central fixation point during the control periods. The
first scans were discarded for remaining saturation effects. Motion artifacts were
compensated by automatic image alignment (AIR, [11]).
BSS, mainly based on ICA, nowadays is a quite common tool in fMRI analysis
(see for example [12]). Here, we analyze the fMRI data set using spatial decorrelation
as separation criterion. Figure 4 shows the performance of mdSOBI; see figure
text for interpretation. Using only the first 8 principal components, mdSOBI
could recover the stimulus component as well as detect additional components.
When applying SOBI to the data set, it could not properly detect the stimulus
component but found two components with crosscorrelations cc = −0.81 and
−0.84 with the stimulus time course.
5 Conclusion
We have proposed an extension called mdSOBI of SOBI for data sets with multidimensional
parametrizations, such as images. Our main contribution lies in