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8 1 Basic Notions

1.2.3 Description Tasks
In both classification and regression tasks similarity is a distance and therefore
evaluated as a numeric quantity. Another type of similarity is related to the feature
structure of the objects. Let us assume that we are presented with tracings of foetal
heart rate during some period of time. These tracings register the instantaneous
frequency of the foetus' heart beat (between 50 and 200 b.p.m.) and are used by
obstetricians to assess foetal well-being. One such tracing is shown in Figure 1.6.
These tracings show ups and downs relative to a certain baseline corresponding
to the foetus'basal rhythm of the heart (around 150 b.p.m. in Figure 1.6a). Some of
these ups and downs are idiosyncrasies of the heart rate to be interpreted by the
obstetrician. Others, such as the vertical downward strokes in Figure 1.6, are
artefacts introduced by the measuring equipment. These artefacts or spikes are to
be removed. The question is: when is an up or a down wave a spike?
In order to answer this question we may start by describing each tracing as a
sequence of segments connecting successive heart beats as shown in Figure 1.6b.
These segments could then be classified in the tracing elements or primitives listed
in Table 1.1.

Figure 1.6. (a) Foetal heart rate tracing with the vertical scale in b.p.m. (b) A detail
of the first prominent downward wave is shown with its primitives.

Table 1.1 Primitives of foetal heart rate tracings.

Primitive Name Symbol Description
Horizontal h A segment of constant value
Up slope u An upward segment with slope < A
Down slope d A downward segment with slope > - A
Strong up slope U An upward segment with slope 2 A
Strong down slope D A downward segment with slope I - A
A is a minimum slope value specified beforehand