Mathematics in Independent Component Analysis

48 Chapter 1. Statistical machine learning of biomedical data
components in digitized section images. First, a so-called cell classifier was trained with cell and
non-cell patches using single- and multi-layer perceptrons as well as unsupervised independent
component analysis with correlation comparison. In order to account for a larger variety of cell
shapes, a directional normalization approach is proposed. The cell classifier can then be used in
an arbitrary number of sections by scanning the section and choosing maxima of this classifier
as cell center locations. This is illustrated using a toy example in figure 1.25. A flow-chart with
the basic segmentation setup is shown in figure 1.26.
ZANE was successfully applied to measure neurogenesis in adult rodent brain sections, where
we showed that the proliferation of neurons is substantially stronger (340%) in the dentate gyrus
of an epileptic mouse than in a control group. When comparing the counting result with manual
counts, the mean ZANE classification rate is 90% of all (manually detected) cells; this was within
the error bounds of a perfect count, since manual counts by different experts varied by roughly
10% themselves (Theis et al., 2004b).
1.6.3 Surface electromyograms
In sections 1.2 and 1.4, we presented blind
data factorization models based on statistical
independence, explicit sparseness and nonnegativity.
It is known that all three approaches
tend to induce a more meaningful,
often more sparse representation of the multivariate
data set. However, developing explicit
applications and more so performing meaningful
comparisons of such methods is still of considerable
interest.
In Theis and García (2006), see chapter
20, we analyzed and compared the above
models, but not from a theoretical point of
view but rather based on a real-world example,
namely the analysis of surface electromyogram
(sEMG) data sets. An electromyogram
(EMG) denotes the electric signal generated
by a contracting muscle (Basmajian and Luca,
1985). In general, EMG measurements make
use of invasive, painful needle electrodes. An
alternative is to use sEMG, which is measured
using non-invasive, painless surface electrodes.
However, in this case the signals are rather
more difficult to interpret due to noise and Figure 1.26: ZANE image segmentation.
the overlap of several source signals. Direct
application of the ICA model to real-world noisy sEMG turns out to problematic (García et al.,
2004), and it is yet unknown if the assumption of independent sources holds well in the setting
of sEMG.