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I .3 Classes, Patterns and Features 11

- From each pattern we can extract information characterizing it, the features. In
the ECG case the features are related to wave measurements of amplitudes and
durations. A feature can be, for instance, the ratio between the amplitudes of the
Q and R waves, Q/R ratio.

In order to solve a PR problem we must have clear definitions of the class,
pattern and feature spaces. In the present case these spaces are represented in
Figure 1.10.

classes Patterns Features
(heart condition) (ECGs) (amplitudes, durations, ...)
Figure 1.10. PR spaces for the heart condition classification using ECG features.

A PR system emulating the cardiologist abilities, when presented with a feature
vector, would have to infer the heart condition (diagnostic class) from the feature
vector. The problem is that, as we see from Figure 1.10, there are annoying
overlaps: the same Q/R ratio can be obtained from ECGs corresponding to classes
N and LVH; the same ECG can be obtained from classes MI and RVH. The first
type of overlap can be remedied using additional features; the second type of
overlap is intrinsic to the method and, as a matter of fact, the best experts in
electrocardiography have an upper limit to their performance (about 23% overall
classification error when using the standard " 12-lead ECG system" composed of 12
ECG signals). Therefore, a PR system frequently has a non-zero performance error,
independent of whatever approach is used, and usually one is satisfied if it
compares equally or favourably with what human experts can achieve.
Sun~marizing some notions:

Classes
Classes are states of "nature" or crrtegorirs of objects associated with concepts or
prototyyrs.
In what follows we assume c classes denoted (0, E Q , (i = 1,. . . . c), where R is
the set of all classes, known as the itllerpretutiotz spuce. The interpretation space
has cmcept-drivetz properties such as unions, intersections and hierarchical trees of
classes.