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High-fuzziness ICA mixtures
100
30
80
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60
10
40
0.8
0
0
1
0.6
0
0.8
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0.6
0.5
0.4
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0.2
1
outliers
supervision
0
1
0
outliers
supervision
(a) Classification
(b) Training
Low-fuzziness ICA mixtures
100
50
40
90
30
80
20
70
10
60
0
0
0.8
0
0.6
1
0.8
0.5
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0.2
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1
outliers
supervision
0.2
supervision
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outliers
(c) Classification
(d) Training
Fig. 3.9
Semi-supervised results in classification and training. a, c Classification; b, d training
where X is the set of available mixture data and S the respective source vectors. w
denote all the unknown parameters of the mixture data model; p ð S ; w = X Þ denote
the posterior pdf for the reference model, and q ð S ; w = X Þ denote the posterior pdf
for the estimated model.
The mean results of the performance of semi-supervised learning are shown in
Fig. 3.9 for the simulated datasets divided into high-fuzziness and low-fuzziness
ICA mixtures. Since the simulations consisted of ICA mixtures of three classes,
the highest value of fuzziness possible was 1-1/3, so we set 0.14 (21 % of the
highest fuzziness) as the threshold between high and low fuzziness.
The evolution of the values of classification success in Fig. 3.9 a shows that
small increments in supervision rapidly increase the percentage of classification
accuracy. They also increase the similarity, which is measured by the KL-distance
between the reference models and the semi-supervised training models as shown in
Fig. 3.9 b. The results for low-fuzziness ICA mixtures (Fig. 3.9 c, d) show a
behaviour similar to that for high-fuzziness ICA mixtures. However, classification
accuracy is improved with smaller increments of supervision, and the effect of
outliers in worsening semi-supervised training models is higher. The data of low-
fuzziness mixtures are more separated from each others, and they have a high
probability of belonging to different classes. Therefore, clusters of low-fuzziness
mixtures are better defined than data of high-fuzziness mixtures. Due to the low
values of posterior probability in the data of high-fuzziness ICA mixtures, the
 
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