Mathematics in Independent Component Analysis

1.6. Applications to biomedical data analysis 47
(a) training data set (b) directional normalization (c) classification result
Figure 1.25: Directional neural networks: As training data set, a few labeled A’s from a test
image have been used (a). (b) then shows five rotated A’s together with their image patches
normalized using main principal component direction below. This small-scale classificator reproduces
the A-locations in a test image sufficiently well (c), even though the training data set
was small and different fonts, noise etc. had been added.
(Gruber et al., 2007), a Matlab toolbox for data-driven analysis of biomedical data, which may
also be used as SPM plugin. Its main focus lies on the analysis of functional Nuclear Magnetic
Resonance Imaging (fMRI) data sets with various model-free or data-driven techniques. The
toolbox includes BSS algorithms based on various source models including ICA, spatiotemporal
ICA, autodecorrelation and NMF. They can all be easily combined with higher-level analysis
methods such as reliability analysis using projective clustering of the components, sliding time
window analysis or hierarchical decomposition.
1.6.2 Image segmentation and cell counting
A supervised interpretation of the initial data analysis model from section 1.1 leads to a classification
problem: given a set of input-output samples, find a map that interpolate these samples,
hopefully generalizing well to new input samples. Such a map thus serves as classifier if the
output consists of discrete labels. Classification based on support vector machines (Boser et al.,
1992, Burges, 1998, Schölkopf and Smola, 2002) or neural networks (Haykin, 1994) has prominent
applications in biomedical data analysis. Here we review an application to biomedical
image processing from Theis et al. (2004c), see chapter 21.
While many different tissues of the mammalian organism are capable of renewing themselves
after damage, it was believed for long that the nervous system is not able to regenerate at all.
Nevertheless, the first data showing that the generation of new nerve cells in the adult brain
could happen were presented in the 1960s (Altman and Das, 1965) showing new neurons in
the brain of adult rats. In order to quantify neurogenesis in animals, newborn cells are labeled
with specific markers such as BrdU; in brain sections these can later be analyzed and counted
through the use of a confocal microscope. However so far, this counting process had been
performed manually.
In Theis et al. (2004b,c), we proposed an algorithm called ZANE to automatically identify cell