Page 278 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

6.7 Tree Classifiers 259

A: Table 6.12 shows the leave-one-out results, obtained with SPSS, in the
classification of the three cork-stopper classes, using the four features selected by
dynamic search in Example 6.13. The training set error is 10.7%; the test set error
estimate is 12%. Therefore, we still have a reliable error estimate of about (10.7 +
12)/2 = 11.4% for this classifier, which is not surprising since the dimensionality
ratio is high (n/d = 12.5). For the estimate Pe = 11.4% the 95% confidence interval
corresponds to an error tolerance of 5%.

Table 6.12. Listing of the classification matrices obtained with SPSS, using the
leave-one-out method in the classification of the three classes of the cork-stopper
data with four features.
Predicted Group Membership Total
C 1 2 3
Original Count 1 43 7 0 50
2 5 45 0 50
3 0 4 46 50
% 1 86.0 14.0 0.0 100
2 10.0 90.0 .0 100
3 0.0 8.0 92.0 100
Cross-validated Count 1 43 7 0 50
2 5 44 1 50
3 0 5 45 50
% 1 86.0 14.0 0.0 100
2 10.0 88.0 2.0 100
3 0.0 10.0 90.0 100

6.7 Tree Classifiers

In multi-group classification, one is often confronted with the problem that
reasonable performances can only be achieved using a large number of features.
This requires a very large design set for proper training, probably much larger than
what we have available. Also, the feature subset that is the most discriminating set
for some classes can perform rather poorly for other classes. In an attempt to
overcome these difficulties, a “divide and conquer” principle using multistage
classification can be employed. This is the approach of decision tree classifiers,
also known as hierarchical classifiers, in which an unknown case is classified into
a class using decision functions in successive stages.