Mathematics in Independent Component Analysis

110 Chapter 5. IEICE TF E87-A(9):2355-2363, 2004
THEIS and NAKAMURA: QUADRATIC INDEPENDENT COMPONENT ANALYSIS
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Fig. 5 Example 1: A two-dimensional nonlinear mixture using mixing model 10, see
figure 2, is separated. The left column shows the two independent source signals together
with a signal scatter plot (with only every 5th sample plotted), which depicts the source
probability density. The middle column shows the two clearly nonlinearly mixed signals
and their scatter plot. In the right column the two signals separated by quadratic ICA
are depicted. The scatter plot again confirms their independence.
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Fig. 6 Example 1: A comparison scatter plot of source and
recovered source signals (figure 5) is given, i.e. if y denotes the
recovered sources, then the top left figure is a scatter plot of
(s1, y1), the top right a plot of (s2, y1) and the bottom right of
(s2, y2). The SNRs are 44 and 43 dB between the first respectively
second signals after normalization to zero mean and unit
variance and possible sign multiplication.
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Fig. 7 Example 1, linear ICA: Applying linear ICA to the mixtures
from figure 5 yields recovered signals as above (top). Clearly
the scatter plot (bottom) confirms that the recovery was bad —
not surprisingly no independence could be achieved. Comparison
with the original sources shows that the recovery itself does not
well correspond to the sources: the maximal SNRs were 7.5 and
7.7 after normalization.
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