Figure 10.5 (left), shows the theoretical AR model log likelihood on the Xaxis and the theoretical MFCC log likelihood on the Yaxis for 100 samples each of MFCC data (circles) and AR data (dots). For perfect performance, the data from each class should remain on the correct side of the X=Y line. A few errors can be seen. The Optimal classification error probability was determined to be 1.68% using 80,000 test samples.
Figure 10.5 (right) shows the experiment repeated using the projected PDFs using AR and MFCC features. It is difficult to see a difference between the two plots. To obtain a more quantitative result, we need to measure error probability in trials.

Next, we reran the experiment using a variety of training sample sizes, measuring classification performance. We compared the method with (a) NeymanPearson (optimal) classifier, (b) additive combination of the AR and MFCC feature loglikelihood functions, sometimes called ``stacking", and (c) feature concatenation in which the union of the AR and MFCC features was formed. The same feature PDF estimation approach was used as for the feature density in PDF projection. We ran the experiments using both MFCC and MFCCML features. The results are shown in Figure 10.6 which shows the classification error probability in percent. For the left graph we used MFCC features, and for the right graph MFCCML features. After the optimal NeymanPearson classifier, PDF projection was best overall, with MFCCML slightly better than MFCC. For MFCC features, feature concatenation showed about 35% more errors than PDF projection. For MFCCML, that ratio went up to about 50%. Likelihood stacking did much worse than feature concatenation, indicating that feature concatenation took advantage of the statistical dependence between the ML and AR features.

Baggenstoss 20170519