## 3 Onset Detection
The test set for each classifier consisted in 3000 piano audio files of chords and single notes extracted from the MAPS database [56], corresponding to almost 5 min of music:

Figure 11: Results of 5-fold cross-validation for ten classifiers, using 500 cases dataset, half positive half negative. Precision (\(\mu=0.91,\sigma=0.027\)), recall (\(\mu=0.95,\sigma=0.025\)), and F-measure (\(\mu=0.93\), \(\sigma=0.025\)). Figure 12: Results of the overall training stage for 61 classifiers. Precision (\(\mu=0.92,\sigma=0.029\)), recall (\(\mu=0.97,\sigma=0.026\)), and F-measure (\(\mu=0.93,\sigma=0.024\)). 3000 random pitched chords and single notes between C2 (65.406 Hz) to C7 (2093.0 Hz), with polyphony levels ranging from 1 to 6. For each sound, a single 93 ms frame located after the onset time was extracted. The test results are illustrated in Figure 13.

We accomplished a final F-measure value of 0.76 (76%). As expected, these are slightly lower results when compared to the values obtained during the training stage. However, they are very competitive in the MPE context. We also calculated the accuracy using F-measure for each polyphony from 1 to 6 during the test process. Our system returns F-measures in percentages of 77%, 79%, 77%, 73%, 69%, and 66% for polyphony (Polyphony 0 corresponds to silence, easily detected by an analytic power spectrum analysis.) 1, 2, 3, 4, 5, and 6, respectively (Figure 14). Our CGP system presents higher F-measure values for polyphony 2 and 3, and then, it decreases until polyphony 6, with a 13% gap between the top and bottom polyphony F-measure values. The entire database includes sounds from seven different pianos. Analysing the results by piano, we have about 4% standard deviation. This means that our system accuracy does not significantly depend on piano differences, recording conditions, or whether a real piano or a software-based one is used, which suggests robustness for varying production conditions. Our final results are expressed in Figure 13. These are the results obtained for each of the improvements we applied. Previous versions and several improvements were made since we initially proposed our toolbox for CGP [48] until this last version called CGP-harmonic mask (HM)-DA. All the previous published results are shown in Figure 15. Our first F-measure result was 62.7% using CGP-1 [46,48]. We improved our system using a

Figure 14: Polyphony test results from polyphony 1 (monophonic) to polyphony 6 for precision, recall, and F-measure. Figure 13: Results of the overall testing stage for 61 classifiers. Precision (\(\mu=0.72,\sigma=0.08\)), recall (\(\mu=0.82,\sigma=0.036\)), and F-measure (\(\mu=0.764,\sigma=0.06\)). harmonic mask, CGP-HM, in [49]; later, some functions were added to the function set and minor improvements were made, CGP-HM2 [60], resulting in a better F-measure, 73%. Finally, we were able to extend the training set using a artificial data augmentation process, CGP-HM-DA, producing our best results described in this article, reaching F-measure values over 76%. Our training stage consumes a lot of time: to train 10 runs with 10,000 generations using a multi-core (4 core) processor, it takes more than a day. Nevertheless, for some classifiers, we performed additional tests increasing the number of generations to 20,000. Unfortunately, we did not have the necessary time or the computer resources to completely train with 20,000 generations for all the classifiers. Our preliminary results show a mean increase in F-measure of 1.2%. ### White-Box Optimization

Many machine learning algorithms were proven to successfully accomplish their tasks. However, some of them featured \"opacity\": they do not provide information about how they do it in an analytic way and were thus labelled as _black box_. Our CPG multi-classifier system is completely transparent. It is known that each classifier is composed by a graph of nodes, where each node is essentially a mathematical function from a defined function set.