Mathematics in Independent Component Analysis

1.6. Applications to biomedical data analysis 45
1 2 3
4 5 6
(a) recovered component maps
1 cc: −0.14 2 cc: −0.13 3 cc: −0.22
4 cc: 0.89 5 cc: 0.12 6 cc: 0.09
(b) time courses
Figure 1.23: Extracted ICA-components of fMRI recordings. (a) shows the spatial and (b)
the corresponding temporal activation patterns, where in (b) the grey bars indicate stimulus
activity. Component 4 contains the (independent) visual task, active in the visual cortex (white
points in (a)). It correlates well with the stimulus activity (b), 4.
with the known stimulus task, see figure 1.24. The absolute corresponding autocorrelations
are 0.84 (stNSS), 0.91 (stSOBI with one-dimensional autocorrelations), 0.58 (stICA applied to
separation provided by stSOBI), 0.53 (stICA) and 0.51 (fastICA). The observation that neither
Stone’s spatiotemporal ICA algorithm (Stone et al., 2002) nor the popular fastICA algorithm
(Hyvärinen and Oja, 1997) could recover the sources showed that spatiotemporal models can
use the additional data structure efficiently in contrast to spatial-only models, and that the
parameter-free joint-diagonalization-based algorithms are robust against convergence issues.
Other analysis models
Before continuing to other biomedical applications, we shortly want to review other recent work
of the author in this field.
In Karvanen and Theis (2004), we proposed the concept of window ICA for the analysis of
fMRI data. The basic idea was to apply, spatial ICA in sliding time windows; this approach
avoided the problems related to the high number of signals and the resulting issues with dimension
reduction methods, and moreover gave some insight into small changes happening during
the experiment, which are otherwise not encoded in changes in the component maps. We demonstrated
the usefulness of the proposed approach in an experiment where a subject listened to
auditory stimuli consisting of sinusoidal sounds (beeps) and words in varying proportions. Here,
the window ICA algorithm was able to find different auditory activations patterns related to the
beeps respectively the words.
An interesting model for activity maps in the brain is given by sparse coding; after all, the
component maps are always implicitly assumed to show only strongly focused regions of activation.
Hence we asked the question whether the sparse models proposed in section 1.4.1 could be