Page 253 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

234 6 Statistical Classification

vectors, x and y , of integer classification labels. The classification matrix of Table
6.3 can be obtained as follows, assuming the cork data frame has been attached
with columns ND , PRT and CL corresponding to variables N, PRT and CLASS,
respectively:

> y <- cbind(ND[1:100],PRT[1:100]/10)
> co <- classify(y,y,CL[1:100])
> classmatrix(CL[1:100],co)

The meanings of MATLAB’s classify arguments are the same as in R.
MATLAB does not provide a function for obtaining the classification matrix. We
include in the book CD the classmatrix function for this purpose, working in
the same way as in R.
We didn t obtain the same values in MATLAB as we did with the other software
’
products. The reason may be attributed to the fact that MATLAB apparently does
not use pooled covariances (therefore, is not providing linear discriminants).

6.3 Bayesian Classification

In the previous sections, we presented linear classifiers based solely on the notion
of distance to class means. We did not assume anything specific regarding the data
distributions. In this section, we will take into account the specific probability
distributions of the cases in each class, thereby being able to adjust the classifier to
the specific risks of a classification.

6.3.1 Bayes Rule for Minimum Risk
Let us again consider the cork stopper problem and imagine that factory production
was restricted to the two classes we have been considering, denoted as: ω 1 = Super
and ω 2 = Average. Let us assume further that the factory had a record of production
stocks for a reasonably long period, summarised as:

Number of produced cork stoppers of class ω 1: n 1 = 901 420
Number of produced cork stoppers of class ω 2: n 2 = 1 352 130
Total number of produced cork stoppers: n = 2 253 550

With this information, we can readily obtain good estimates of the probabilities
of producing a cork stopper from either of the two classes, the so-called prior
probabilities or prevalences:

P(ω 1) = n 1/n = 0.4; P(ω 2) = n 2/n = 0.6. 6.14