Unsupervised Recursive Sequence Processing - Institute of ...

Fig. 10. Symbols a, b, c which are embedded in R 2 as a = (0, 0) + µ, b = (1, 0) + µ, and
c = (0, 1) + µ, subject to noise µ with different variances: noise level are 0.1, 0.3, and 0.4.
The latter two noise levels show considerable overlap of the classes which represent the
symbol.
x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
P (a|ab) 0 0.01 0 0.01 0 0.04 0 0.04 0.01
P (b|ab) 0 0.08 0.3 0.31 0.38 0.55 0.68 0.66 0.78
P (c|ab) 1 0.91 0.7 0.68 0.62 0.41 0.32 0.3 0.21
P (a|ac) 0 0 0 0 0 0.01 0.01 0 0.01
P (b|ac) 1 0.81 0.8 0.66 0.52 0.55 0.32 0.31 0.24
P (c|ac) 0 0.19 0.2 0.34 0.48 0.44 0.67 0.69 0.75
Table 2
Transition probabilities extracted from the trained map. The noise level was fixed to 0.1
and different generating transition probabilities x were used.
noise 0.1 0.2 0.3 0.4 0.5 true
P (a|ab) 0.01 0 0 0.1 0.98 0
P (b|ab) 0.42 0.49 0.4 0.24 0.02 0.4
P (c|ab) 0.57 0.51 0.6 0.66 0.02 0.6
P (a|ac) 0.01 0 0 0.09 0 0
P (b|ac) 0.59 0.6 0.44 0.39 0 0.6
P (c|ac) 0.4 0.4 0.56 0.52 0 0.4
Table 3
Probabilities extracted from the trained map with fixed input transition probabilities and
different noise levels. For a noise level of 0.5, the extraction mechanism breaks down and
the symbol a becomes most dominant. For smaller noise levels, extraction of the symbols
can still be done also for overlapping clusters because of temporal differentiation of the
clusters in recursive models.
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