Page 27 - Introduction to Statistical Pattern Recognition

1 Introduction 9

Once the structure of the data is thoroughly understood, the data dictates
which classifier must be adopted. Our choice is normally either a linear, qua-
dratic, or piecewise classifier, and rarely a nonparametric classifier. Non-
parametric techniques are necessary in off-line analyses to carry out many
important operations such as the estimation of the Bayes error and data struc-
ture analysis. However, they are not so popular for any on-line operation,
because of their complexity.
After a classifier is designed, the classifier must be evaluated by the pro-
cedures discussed in Chapter 5. The resulting error is compared with the
Bayes error in the feature space. The difference between these two errors indi-
cates how much the error is increased by adopting the classifier. If the differ-
ence is unacceptably high, we must reevaluate the design of the classifier.
At last, the classifier is tested in the field. If the classifier does not
perform as was expected, the data base used for designing the classifier is dif-
ferent from the test data in the field. Therefore, we must expand the data base
and design a new classifier.

Notation

n Dimensionality
L Number of classes

N Number of total samples

N, Number of class i samples
Class i
Oi
A priori probability of 0,

Vector
Random vector

Conditional density function of O,
Mixture density function
A poster-iori probability of w,
given X
M, =E(XI w, I Expected vector of o,