Page 27 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

16 DETECTION AND CLASSIFICATION

The shapes of scrap objects are difficult to predict. Therefore, their
measurements are scattered all over the space.
In this example the measurements are more or less clustered accord-
ing to their true class. Therefore, a new object is likely to have
measurements that are close to the cluster of the class to which the
object belongs. Hence, the assignment of a class boils down to decid-
ing to which cluster the measurements of the object belong. This can
be done by dividing the 2D measurement space into four different
partitions; one for each class. A new object is classified according to
the partitioning to which its measurement vector points.
Unfortunately, some clusters are in each other’s vicinity, or even
overlapping. In these regions the choice of the partitioning is critical.

This chapter addresses the problem of how to design a pattern classifier.
This is done within a Bayesian-theoretic framework. Section 2.1
discusses the general case. In Sections 2.1.1 and 2.1.2 two particular
cases are dealt with. The so-called ‘reject option’ is introduced in Section
2.2. Finally, the two-class case, often called ‘detection’, is covered by
Section 2.3.

2.1 BAYESIAN CLASSIFICATION

Probability theory is a solid base for pattern classification design. In this
approach the pattern-generating mechanism is represented within a
probabilistic framework. Figure 2.3 shows such a framework. The start-
ing point is a stochastic experiment (Appendix C.1) defined by a set
O ¼f! 1 , .. . ,! K g of K classes. We assume that the classes are mutually
exclusive. The probability P(! k ) of having a class ! k is called the prior

measurement data not available (prior) measurement data available (posterior)

measurement assigned
class sensory vector class
experiment object pattern
ω ∈Ω system z classification y(z)

Ω = {ω 1 ,...,ω k }
P (ω )
k
Figure 2.3 Statistical pattern classification