Applied Statistics Using SPSS, STATISTICA, MATLAB and R

Exercises 269
6.2 Repeat the previous exercise for the three classes of the Cork Stoppers’ dataset,
using features N, PRM and ARTG.
6.3 Consider the problem of classifying cardiotocograms (CTG dataset) into three classes:
N (normal), S (suspect) and P (pathological).
a) Determine which features are most discriminative and appropriate for a
Mahalanobis classifier approach for this problem.
b) Design the classifier and estimate its performance using a partition method for the
test set error estimation.
6.4 Repeat the previous exercise using the Rocks’ dataset and two classes: {granites} vs.
{limestones, marbles}.
6.5 A physician would like to have a very simple rule available for screening out
carcinoma situations from all other situations using the same diagnostic means and
measurements as in the Breast Tissue dataset.
a) Using the Breast Tissue dataset, find a linear Bayesian classifier with only
one feature for the discrimination of carcinoma versus all other cases (relax the
normality and equal variance requirements). Use forward and backward search
and estimate the priors from the training set sizes of the classes.
b) Obtain training set and test set error estimates of this classifier, and 95%
confidence intervals.
c) Using the SC Size program, assess the deviation of the error estimate from the
true Bayesian error, assuming that the normality and equal variance requirements
were satisfied.
d) Suppose that the risk of missing a carcinoma is three times higher than the risk of
misclassifying a non-carcinoma. How should the classifying rule be reformulated
in order to reflect these risks, and what is the performance of the new rule?
6.6 Design a linear discriminant classifier for the three classes of the Clays’ dataset and
evaluate its performance.
6.7 Explain why all ROC curves start at (0,0) and finish at (1,1) by analysing what kind of
situations these points correspond to.
6.8 Consider the Breast Tissue dataset. Use the ROC curve approach to determine
single features that will discriminate carcinoma cases from all other cases. Compare the
alternative methods using the ROC curve areas.
6.9 Repeat the ROC curve experiments illustrated in Figure 6.20 for the FHR Apgar
dataset, using combinations of features.
6.10 Increase the amplitude of the signal impulses by 20% in the Signal & Noise
dataset. Consider the following impulse detection rule:
2
An impulse is detected at time n when s(n) is bigger than α ∑ ( s(
n − i)
+ s(
n + i)
) .
i=
1
Determine the ROC curve corresponding to several α values, and determine the best α
for the impulse/noise discrimination. How does this method compare with the
amplitude threshold method described in section 6.4?