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Fig. 3.6 SIR versus number
of observation vectors used
for density estimation. Sr
supervision ratio
percentage of supervision is added. For instance, in the case of 500 observation
vectors the SIR gain is 9.16 dB from sr = 0tosr= 0.5 and 25.04 dB from
sr = 0.7 to sr = 1.
3.4.4 Classification of ICA Mixtures with Nonlinear
Dependencies
Several simulations were performed using ICA mixtures with nonlinear data. We
used multi-layer perceptron (MLP) networks to model the nonlinear mixing
mapping g ðÞ from source signals to observations, x ¼ g ð s Þ , where X is the
observed m-dimensional data vector, g is a m-component mixing function, and s is
a
n-vector
of
independent
components.
MLP
networks
have
the
universal
approximation property [ 23 ] for smooth continuous mappings [ 24 - 26 ].
ICA mixture data were generated for two classes from uniform sources. The
generative data model for one of the classes included only linear dependencies,
while the other class was modelled using nonlinearities. For this latter class, the
data were generated through a nonlinear mapping which was obtained by using a
randomly initialized MLP network having 20 hidden neurons with the output
neurons being equal to the number of sources. A total of 800 Monte Carlo
experiments were performed with the following parameters: (i) Number of classes
in the ICA mixture K ¼ 2 : (ii) Number of observation vectors per class N ¼ 400.
(iii) Number of sources = 2,3,4,5. (iv) Supervision ratio = 0.5. (v) Number of
training observation vectors = 0.7N.
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