Mathematics in Independent Component Analysis

1.6. Applications to biomedical data analysis 43
#1
#2
#n
mixing
matrix A
component maps observations
Figure 1.21: Visualization of the spatial fMRI separation model. The n-dimensional source
vector is represented as component maps, which in turn are interpreted to contribute linearly in
different concentrations to the fMRI observations at the various time points t ∈ {1, . . . , m}.
and the decoding of auditory speech stimuli. One- and two-syllable words were divided into
several frequency-bands and then rearranged randomly to obtain a set of auditory stimuli. Only
a single band was perceivable as words. During the functional imaging session these stimuli were
presented pseudo-randomized to 5 subjects, according to the rules of a stochastic event-related
paradigm. The task of the subjects was to press a button as soon as they were sure that they
had just recognized a word in the sound presented. It was expected that in case of the single
perceptive frequency-band, these four types of stimuli activate different areas of the auditory
system as well as the superior temporal sulcus in the left hemisphere (Specht and Reul, 2003).
The regression-based analysis using a general linear model was performed using SPM2. This
was compared with components extracted using ICA, namely fastICA (Hyvärinen and Oja,
1997). The results are illustrated in figure 1.22, see Keck et al. (2004). Indeed, one independent
component represented a network of three simultaneously active areas in the inferior frontal
gyrus, which was previously proposed to be a center for the perception of speech (Specht and
Reul, 2003). Altogether, we were able to show that ICA detects hidden or suspected links and
activity in the brain that cannot be found using the classical, model-based approach.
Spatial and spatiotemporal separation
As short example of spatial and spatiotemporal BSS, we present the analysis of an experiment
using visual stimuli. fMRI data were recorded from 10 healthy subjects performing a visual
task. 100 scans each were acquired with 5 periods of rest and 5 photic stimulation periods,
t=1
t=2
t=m