Figure: Selected rules produced by TClass in the CBF
task and some instances of each class.
Figure: Selected rules produced by TClass and the
corresponding definitions from the Auslan Dictionary [Johnston, 1989].
The artificial cylinder-bell-funnel task was originally proposed by Saito [Saito, 1994], and further worked on by Manganaris [Manganaris, 1997]. The task is to classify a stream as one of three classes, cylinder (c), bell (b) or funnel (f). Samples are generated as follows:
where 
and 
are drawn from a standard normal
distribution N(0,1), a is an integer drawn uniformly from
[16,32] and 
is an integer drawn uniformly from [32, 96].
See figure 2 (right hand side) for some
instances of each class. The cylinder class is characterised
by a plateau from time a to b, the bell class by a
gradual increase from a to b followed by a sudden decline and the
funnel class by a sudden increase at a and a gradual
decrease until b. Although univariate (i.e., only has one channel)
and of a fixed length (128 frames), the CBF task attempts to
characterise some of the typical properties of temporal domains.
Firstly, there is random amplitude variation as a result of the
in the equation. Secondly, there is random noise (represented by the
). Thirdly, there is significant temporal variation in
both the start of events (since a can vary from 16 to 32) and the
duration of events (since can vary from 32 to 96).
The left-hand side of figure 2 shows the rules generated by our system and discussed in the rest of this paper.
