Digital Signal Processing Reference
In-Depth Information
who elaborated upon the Infomax principle first advocated by Linsker
[157] [158].
In the calculations we used the well-known and well-studied FastICA
algorithm [124] of Hyvarinen and Oja, which separates the signals
using negentropy, and therefore non-Gaussianity, as a measure of the
separation signal quality.
Results
We used only 29 of the 39 samples because the number of missing pa-
rameters was too high in the other samples. As preprocessing, we applied
PCA in order to whiten the data and to project the 16-dimensional data
vector to the five dimensions of highest eigenvalues.
Figure 6.19 gives a plot of the linearly separated signals together
with the comparison patient diagnosis - the first 14 samples were CB
(diagnosis 0) and the last 15 were ILD (diagnosis 1). Since we were
trying to associate immunological parameters with a given diagnosis in
our data set, we calculated the correlation of the separated signals with
this diagnosis signal. In figure 6.18, the signal with the highest diagnosis
correlation is signal 5, with a correlation of 0
.
43 (which is still quite low).
The rows of the inverse mixing matrix contain the information on
how to construct the corresponding independent components from the
sample data. After normalization to unit signal variance, ICA signal 5
is constructed by multiplication of
w
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with the signal data. We see that parameter 1 (RANTES), parameter
2 (IP10), parameter 4 (CD8), parameter 8 (CXCR3CD4), and param-
eter 9 (CXCR3+CD8) are those with the highest absolute values. This
indicates that those parameters have the greatest influence on the clas-
sification of the patients into one of the two diagnostic groups. The
perceptron learning results from the next section will confirm that high
values of RANTESZZ (which is positively correlated with RANTES re-
lated to lymphocytes in BALF (RANBALLY), which is analyzed using
the neural network) and CX3CD8 are indicators for CB; of course this
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