Typical DA Results Illustrated with an Extended Example

3 Typical DA Results Illustrated with an Extended Example 

In this example let us stress again the interlaboratory experiment results first introduced in Section 5.3.5. In some variables we have added a digit in the 5th decimal place for a few objects only in order to avoid numerical problems as a result of identical values. 

If we calculate the four nonelementary discriminant functions df we find the following fractions of data variance explained 77.3% (by one function), 98.8% (by two functions), and 99.9% (by three discriminant functions). Hence we do not expect severe biased projections of our data on to the plane. In Fig. 5-23 we find some overlapping laboratories, however. In the 3D-plot of Fig. 5-24 a good, separated display of all laboratories data is indicated. So far, the data projection is satisfactory. 

Another aspect is how good the discriminant functions are for classification. With all seven original features we do not have any misclassification. Now a laboratory expert may ask if it is really necessary to use all the measurement information, in other words, if it is possible to reach equally good reclassification with fewer than seven features. 

In Tab. 5-13 we report the results of both mentioned strategies for the selection process. In both procedures the WILKS lambda varies monotonously and each set has a significant meaning. We may, therefore, stop the selection process following the misclassification rate. In the forward strategy the first zero error rate appears with the feature set Ti, Mg, Ca in step 3 (Fig. 5-25) whereas in the backward strategy the zero error rate is obtained with the remaining elements Si, Ca, Al, Mg in step 3. Now it is up to the expert to decide which feature set to retain in the future. 

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