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12 1 Basic Notions

Patterns
Patterns are "physical" represenkitions of the objects. Usually signals, images or
simple tables of values. Often we will refer to patterns as objects, cases or samples.
In what follows we will use the letter n to indicate the total number of available
patterns for the purpose of designing a PR system, the so-called training or design
set.

Features

Features are measurements, attributes or primitives derived from the patterns, that
may be useful for their characterization.
We mentioned previously that an initial choice of adequate features is often
more an art than a science. By simplicity reasons (and for other compelling reasons
to be discussed later) we would like to use only a limited number of features.
Frequently there is previous knowledge guiding this choice. In the case of the
ECGs a 10s tracing sampled at a convenient 500 Hz would result in 5000 signal
samples. However it would be a disastrous choice to use these 5000 signal samples
as features! Fortunately there is previous medical knowledge guiding us in the
choice of a quite reduced set of features. The same type of problem arises when we
want to classify images in digitised form. For a greyscale 256x256 pixels image we
have a set of 65536 values (light intensities). To use these values as features in a
PR system is unthinkable! However, frequently a quite reduced set of image
measurements is sufficient as feature vector.
Table 1.2 presents a list of common types of features used for signal and image
recognition. These can be obtained by signal and image processing techniques
described in many textbooks (see e.g. Duda and Hart, 1973 and Schalkoff, 1992).

Table 1.2. Common types of signal and image features.
Signal Features Image Features

Wave amplitudes, durations Region size
Histogram measurements Region colour components
Wave moments (e.g. standard Region average light inlensity
deviation) Image moments
Wave morphology (e.g. symmetry) Histogram measurements
Zero crossings Spectral peaks (Fourier transform)
Autocorrelation peaks Topological features (e.g. region connectivity)
Spectral peaks (Fourier transform) Mathematical morphology features