2014:Discovery of Repeated Themes & Sections Results

Introduction

The task: algorithms take a piece of music as input, and output a list of patterns repeated within that piece. A pattern is defined as a set of ontime-pitch pairs that occurs at least twice (i.e., is repeated at least once) in a piece of music. The second, third, etc. occurrences of the pattern will likely be shifted in time and/or transposed, relative to the first occurrence. Ideally an algorithm will be able to discover all exact and inexact occurrences of a pattern within a piece, so in evaluating this task we are interested in both:

• (1) to what extent an algorithm can discover one occurrence, up to time shift and transposition, and;
• (2) to what extent it can find all occurrences.

The metrics establishment recall, establishment precision and establishment F1 address (1), and the metrics occurrence recall, occurrence precision, and occurrence F1 address (2).

Contribution

Existing approaches to music structure analysis in MIR tend to focus on segmentation (e.g., Weiss & Bello, 2010). The contribution of this task is to afford access to the note content itself (please see the example in Fig. 1A), requiring algorithms to do more than label time windows (e.g., the segmentations in Figs. 1B-D). For instance, a discovery algorithm applied to the piece in Fig. 1A should return a pattern corresponding to the note content of ${\displaystyle P_{1}}$ and ${\displaystyle P_{2}}$, as well as a pattern corresponding to the note content of ${\displaystyle Q_{1}}$. This is because ${\displaystyle Q_{1}}$ occurs again independently of the accompaniment in bars 19-22 (not shown here). The ground truth also contains nested patterns, such as ${\displaystyle P_{1}}$ in Fig. 1A being a subset of the sectional repetition ${\displaystyle S_{1}}$, reflecting the often-hierarchical nature of musical repetition. While we recognise the appealing simplicity of linear segmentation, in the Discovery of Repeated Themes & Sections task we are demanding analysis at a greater level of detail, and have built a ground truth that contains overlapping and nested patterns.

Figure 1. Pattern discovery v segmentation. (A) Bars 1-12 of Mozart’s Piano Sonata in E-flat major K282 mvt.2, showing some ground-truth themes and repeated sections; (B-D) Three linear segmentations. Numbers below the staff in Fig. 1A and below the segmentation in Fig. 1D indicate crotchet beats, from zero for bar 1 beat 1.

For a more detailed introduction to the task, please see 2014:Discovery_of_Repeated_Themes_&_Sections.

Ground Truth and Algorithms

The ground truth, called the Johannes Kepler University Patterns Test Database (JKUPTD-Aug2013), is based on motifs and themes in Barlow and Morgenstern (1953), Schoenberg (1967), and Bruhn (1993). Repeated sections are based on those marked by the composer. These annotations are supplemented with some of our own where necessary. A Development Database (JKUPDD-Aug2013) enabled participants to try out their algorithms. For each piece in the Development and Test Databases, symbolic and synthesised audio versions are crossed with monophonic and polyphonic versions, giving four versions of the task in total: symPoly, symMono, audPoly, and audMono. Algorithms submitted to the task are are shown in Table 1.

Sub code Submission name Abstract Contributors
Task Version symMono
NF1 MotivesExtractor PDF Oriol Nieto, Morwaread Farbood
OL1 PatMinr PDF Olivier Lartillot
VM1 VM1 PDF Gissel Velarde, David Meredith
VM2 VM2 PDF Gissel Velarde, David Meredith
NF1'13 motives_mono PDF Oriol Nieto, Morwaread Farbood
DM10'13 SIATECCompressSegment PDF David Meredith
Task Version symPoly
NF1 MotivesExtractor PDF Oriol Nieto, Morwaread Farbood
NF2'13 motives_poly PDF Oriol Nieto, Morwaread Farbood
DM10'13 SIATECCompressSegment PDF David Meredith
Task Version audMono
NF1 MotivesExtractor PDF Oriol Nieto, Morwaread Farbood
NF3'13 motives_audio_mono PDF Oriol Nieto, Morwaread Farbood
Task Version audPoly
NF1 MotivesExtractor PDF Oriol Nieto, Morwaread Farbood
NF4'13 motives_audio_poly PDF Oriol Nieto, Morwaread Farbood

Table 1. Algorithms submitted to DRTS. Strong-performing algorithms from 2013 (submission codes ending '13) are included for the sake of extra comparisons.

Results in Brief

(For mathematical definitions of the various metrics, please see 2014:Discovery_of_Repeated_Themes_&_Sections#Evaluation_Procedure.)

Nieto and Farbood (2014a) submitted to all four versions of the task (symbolic-monophonic, symbolic-polyphonic, audio-monophonic, audio-polyphonic), as they did last year (Nieto and Farbood, 2013). On the audio-monophonic version of the task, their NF1 algorithm’s ${\displaystyle F_{1}}$ scores were up by an average of .14 (establishing at least one occurrence of each ground truth pattern) and .11 (retrieving all occurrences of a discovered ground truth pattern) compared to last year (see Figs. 30 and 33). There were slighter increases in the audio-polyphonic version of the task. Their work on extracting repetitive structure remains at the forefront of research attempting to cross the audio-symbolic divide (Nieto & Farbood, 2014b; Collins et al., 2014).

Lartillot (2014a, 2014b) submitted an incremental pattern mining algorithm to the symbolic-monophonic version of the task this year. The musical dimensions represented (e.g., chromatic pitch, diatonic pitch) are able to vary throughout the course of a pattern occurrence. The ability to vary representation within an occurrence should mean that Lartillot’s OL1 algorithm is well prepared for retrieving both exact and inexact occurrences of motifs and themes. This does seem to be the case, with OL1 the strongest performer on the occurrence ${\displaystyle F_{1}}$ metric (Fig. 9).

Velarde and Meredith (2014) submitted a wavelet-based method to the symbolic-monophonic version of the task this year. This algorithm, VM1, tested significantly stronger according to Friedman's test than NF1 (${\displaystyle \chi ^{2}(1)=25,\ p<.001}$, Bonferroni-corrected) and OL1 (${\displaystyle \chi ^{2}(1)=17.86,\ p<.001}$, Bonferroni-corrected) at discovering at least one occurrence of each ground truth pattern (Fig. 2). While VM1 also seems to find lots of occurrences of each ground truth pattern (with high occurrence recall in Fig. 7, and in Fig. 3 on a per-pattern basis), it may also find quite a few false-positive occurrences (with lower occurrence precision in Fig. 8). (To avoid a bias toward the more numerous submissions of Velarde and Meredith (2014), VM1 was preselected for comparison with Nieto and Farbood's (2014a) and Lartillot's (2014a) submissions, based on performance for the Development Database.)

Discussion

Last year it was observed that the discovery of repeated sections was addressed well by the submissions, but that the discovery of themes and motifs required more attention in future iterations of this task. There has been some improvement in this regard: VM1 scores better on establishment recall (Fig. 2) than last year's algorithms, for pattern occurrences in pieces 1-3 that contain 7, 9, 5, and 4 notes.

It was pleasing to see Nieto and Farbood’s (2014a) results improve by 10-15% compared with last year on the audio-monophonic version of the task. This improvement underlines the importance of the Discovery of Repeated Themes and Sections task in helping researchers to push the boundaries of music informatics research.

It was exciting to see more participants than last year converge on one particular task version, from which Lartillot (2014a) emerged with the strongest results for retrieving exact and inexact occurrences of already-discovered patterns, and Velarde and Meredith (2014) emerged with an impressively strong algorithm for discovering at least one occurrence of each ground truth pattern.

Next year it would be great to see yet more researchers with relevant algorithms engaging in the task (Conklin & Bergeron, 2008; Giraud et al., in press; Müller & Jiang, 2012; Peters & Deruty, 2009). I have already made (and am happy to make) amendments/additions to the databases in order to encourage participation. A renewed effort to tackle the polyphonic versions of this task would also be most welcome, as these are inherently harder but perhaps more interesting for that reason. These polyphonic scenarios have more immediate applications in the support of other MIR tasks (e.g., beat tracking and/or expressive rendering might be improved by knowledge of motif/theme/section locations), so it would also be great to see some research developing in this direction too.

Tom Collins, Leicester, 2014

Results in Detail

symMono

(Submission OL1 did not complete on piece 5. The task captain took the decision to assign the mean of the evaluation metrics for OL1 calculated across the remaining pieces.)

Figure 2. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 3. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 4. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 5. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?

Figure 6. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.

Figure 7. Occurrence recall (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 8. Occurrence precision (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?

Figure 9. Occurrence F1 (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.

Figure 10. Three-layer recall averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment recall), three-layer recall uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 11. Three-layer precision averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment precision), three-layer precision uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 12. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.

Figure 13. Log runtime of the algorithm for each piece/movement.

symPoly

Figure 14. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 15. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 16. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 17. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?

Figure 18. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.

Figure 19. Occurrence recall (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 20. Occurrence precision (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?

Figure 21. Occurrence F1 (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.

Figure 22. Three-layer recall averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment recall), three-layer recall uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 23. Three-layer precision averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment precision), three-layer precision uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 24. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.

Figure 25. Log runtime of the algorithm for each piece/movement.

audMono

Figure 26. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 27. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 28. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 29. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?

Figure 30. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.

Figure 31. Occurrence recall (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 32. Occurrence precision (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?

Figure 33. Occurrence F1 (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.

Figure 34. Three-layer recall averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment recall), three-layer recall uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 35. Three-layer precision averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment precision), three-layer precision uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 36. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.

Figure 37. Log runtime of the algorithm for each piece/movement.

audPoly

Figure 38. Establishment recall on a per-pattern basis. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 39. Occurrence recall on a per-pattern basis. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 40. Establishment recall averaged over each piece/movement. Establishment recall answers the following question. On average, how similar is the most similar algorithm-output pattern to a ground-truth pattern prototype?

Figure 41. Establishment precision averaged over each piece/movement. Establishment precision answers the following question. On average, how similar is the most similar ground-truth pattern prototype to an algorithm-output pattern?

Figure 42. Establishment F1 averaged over each piece/movement. Establishment F1 is an average of establishment precision and establishment recall.

Figure 43. Occurrence recall (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence recall answers the following question. On average, how similar is the most similar set of algorithm-output pattern occurrences to a discovered ground-truth occurrence set?

Figure 44. Occurrence precision (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence precision answers the following question. On average, how similar is the most similar discovered ground-truth occurrence set to a set of algorithm-output pattern occurrences?

Figure 45. Occurrence F1 (${\displaystyle c=.75}$) averaged over each piece/movement. Occurrence F1 is an average of occurrence precision and occurrence recall.

Figure 46. Three-layer recall averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment recall), three-layer recall uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 47. Three-layer precision averaged over each piece/movement. Rather than using ${\displaystyle |P\cap Q|/\max\{|P|,|Q|\}}$ as a similarity measure (which is the default for establishment precision), three-layer precision uses ${\displaystyle 2|P\cap Q|/(|P|+|Q|)}$, which is a kind of F1 measure.

Figure 48. Three-layer F1 (TLF) averaged over each piece/movement. TLF is an average of three-layer precision and three-layer recall.

Figure 49. Log runtime of the algorithm for each piece/movement.

Tabular Versions of Plots

symMono

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF'1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 NF1 piece1 5 15.000 0.450 0.435 0.442 0.670 0.218 0.329 0.204 0.218 0.211 466.000 0.000 0.403 0.219 0.370 0.175 0.238 0.000 0.000 0.000
1 NF1 piece2 5 48.000 0.316 0.707 0.437 0.798 0.581 0.673 0.147 0.483 0.226 1432.000 0.000 0.264 0.383 0.611 0.244 0.348 0.000 0.000 0.000
1 NF1 piece3 10.000 11.000 0.615 0.442 0.514 0.791 0.264 0.395 0.493 0.367 0.421 53.000 0.000 0.289 0.511 0.614 0.385 0.474 0.000 0.000 0.000
1 NF1 piece4 8 26.000 0.685 0.806 0.741 0.727 0.581 0.646 0.429 0.584 0.494 104.000 0.000 0.504 0.587 0.595 0.534 0.563 0.077 0.250 0.118
1 NF1 piece5 13.000 13.000 0.437 0.331 0.377 0.000 0.000 0.000 0.334 0.294 0.312 349.000 0.000 0.280 0.400 0.559 0.332 0.417 0.000 0.000 0.000
2 OL1 piece1 5 114.000 0.660 0.635 0.647 0.827 0.509 0.630 0.295 0.498 0.370 14013.284 0.000 0.368 0.389 0.723 0.559 0.630 0.009 0.200 0.017
2 OL1 piece2 5 98.000 0.117 0.737 0.202 0.842 0.868 0.855 0.148 0.611 0.238 126065.856 0.000 0.277 0.440 0.750 0.709 0.729 0.020 0.400 0.039
2 OL1 piece3 10.000 9 0.739 0.467 0.573 0.897 0.695 0.783 0.625 0.466 0.534 1751.959 0.000 0.348 0.622 0.728 0.608 0.663 0.111 0.100 0.105
2 OL1 piece4 8 4 0.950 0.405 0.568 0.950 0.967 0.958 0.974 0.400 0.567 204.197 0.000 0.405 0.974 0.950 0.967 0.958 0.500 0.250 0.333
2 OL1 piece5 13.000 56.250 0.617 0.561 0.498 0.879 0.760 0.807 0.510 0.494 0.427 35508.820 0.000 0.350 0.606 0.788 0.711 0.745 0.160 0.237 0.124
3 VM1 piece1 5 7 0.557 0.849 0.673 0.360 0.777 0.492 0.344 0.362 0.353 61.442 0.000 0.849 0.482 0.372 0.777 0.503 0.000 0.000 0.000
3 VM1 piece2 5 7 0.412 0.817 0.548 0.486 0.805 0.606 0.320 0.430 0.367 310.739 0.000 0.472 0.074 0.399 0.764 0.524 0.286 0.400 0.333
3 VM1 piece3 10.000 7 0.773 0.738 0.755 0.442 0.823 0.575 0.627 0.521 0.569 13.439 0.000 0.628 0.557 0.533 0.703 0.606 0.000 0.000 0.000
3 VM1 piece4 8 7 0.932 0.920 0.926 0.644 0.869 0.740 0.749 0.620 0.679 66.057 0.000 0.812 0.735 0.526 0.855 0.651 0.286 0.250 0.267
3 VM1 piece5 13.000 7 0.819 0.684 0.745 0.512 0.755 0.610 0.675 0.400 0.503 52.330 0.000 0.566 0.549 0.414 0.656 0.507 0.286 0.154 0.200
4 VM2 piece1 5 5 0.540 0.570 0.555 0.000 0.000 0.000 0.286 0.207 0.240 18.906 0.000 0.570 0.286 0.291 0.490 0.365 0.000 0.000 0.000
4 VM2 piece2 5 7 0.446 0.761 0.562 0.649 0.863 0.741 0.357 0.488 0.413 34.308 0.000 0.419 0.128 0.427 0.630 0.509 0.143 0.200 0.167
4 VM2 piece3 10.000 7 0.690 0.521 0.594 0.865 0.441 0.584 0.609 0.471 0.531 3.570 0.000 0.393 0.541 0.662 0.561 0.607 0.000 0.000 0.000
4 VM2 piece4 8 6 0.842 0.765 0.802 0.579 0.837 0.684 0.732 0.504 0.597 5.942 0.000 0.721 0.711 0.410 0.732 0.525 0.167 0.125 0.143
4 VM2 piece5 13.000 7 0.739 0.540 0.624 0.910 0.781 0.841 0.677 0.434 0.529 38.698 0.000 0.420 0.554 0.517 0.636 0.570 0.000 0.000 0.000
5 NF1'13 piece1 5 16.000 0.608 0.430 0.504 0.528 0.154 0.238 0.200 0.205 0.203 92.000 0.000 0.420 0.207 0.521 0.154 0.237 0.000 0.000 0.000
5 NF1'13 piece2 5 8 0.029 0.023 0.026 0.000 0.000 0.000 0.015 0.014 0.015 326.000 0.000 0.023 0.022 0.000 0.000 0.000 0.000 0.000 0.000
5 NF1'13 piece3 10.000 12.000 0.618 0.454 0.524 0.754 0.408 0.530 0.455 0.374 0.411 19.000 0.000 0.344 0.453 0.576 0.335 0.424 0.000 0.000 0.000
5 NF1'13 piece4 8 26.000 0.602 0.781 0.680 0.693 0.498 0.580 0.401 0.598 0.480 20.000 0.000 0.429 0.444 0.601 0.449 0.514 0.038 0.125 0.059
5 NF1'13 piece5 13.000 14.000 0.505 0.423 0.460 0.969 0.969 0.969 0.448 0.381 0.412 78.000 0.000 0.191 0.421 0.681 0.439 0.534 0.000 0.000 0.000
6 DM10'13 piece1 5 35.000 0.423 0.642 0.510 0.507 0.717 0.594 0.295 0.530 0.379 87.000 0.000 0.436 0.617 0.453 0.749 0.564 0.000 0.000 0.000
6 DM10'13 piece2 5 37.000 0.514 0.683 0.587 0.620 0.868 0.723 0.446 0.554 0.494 249.000 0.000 0.523 0.474 0.527 0.872 0.657 0.000 0.000 0.000
6 DM10'13 piece3 10.000 12.000 0.646 0.616 0.631 0.722 0.452 0.556 0.527 0.470 0.497 6.000 0.000 0.384 0.548 0.538 0.529 0.534 0.083 0.100 0.091
6 DM10'13 piece4 8 20.000 0.397 0.671 0.499 0.398 0.804 0.532 0.269 0.390 0.319 4.000 0.000 0.671 0.505 0.309 0.713 0.431 0.050 0.125 0.071
6 DM10'13 piece5 13.000 54.000 0.634 0.431 0.513 0.588 0.916 0.716 0.610 0.389 0.475 461.000 0.000 0.304 0.803 0.533 0.869 0.661 0.000 0.000 0.000

Table 2. Tabular version of Figures 4-13.

AlgIdx AlgStub Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
1 NF1 piece1 5
0.435 0.794 0.538 0.000 0.405
0.00000 0.218 0.000 0.000 0.000
0.00000 0.218 0.000 0.000 0.000
1 NF1 piece2 5
0.571 0.875 0.250 0.906 0.934
0.00000 0.109 0.000 0.876 0.934
0.00000 0.109 0.000 0.876 0.934
1 NF1 piece3 10.000
0.389 0.662 0.808 0.217 0.553 0.579 0.182 0.737 0.184 0.105
0.00000 0.000 0.264 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.264 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 NF1 piece4 8
1.00000 0.700 0.000 1.000 0.933 1.000 0.818 1.000
0.357 0.000 0.000 0.208 0.750 0.850 0.690 1.000
0.357 0.000 0.000 0.208 0.750 0.850 0.690 1.000
1 NF1 piece5 13.000
0.263 0.184 0.683 0.709 0.110 0.110 0.028 0.041 0.043 0.500 0.552 0.692 0.387
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 OL1 piece1 5
1.00000 0.964 0.137 0.140 0.933
0.688 0.226 0.000 0.000 0.578
0.688 0.226 0.000 0.000 0.578
2 OL1 piece2 5
0.727 0.812 0.273 0.936 0.934
0.00000 0.734 0.000 0.936 0.934
0.00000 0.734 0.000 0.936 0.934
2 OL1 piece3 10.000
0.632 0.735 0.929 0.263 0.579 0.289 0.053 0.645 0.350 0.200
0.00000 0.000 0.695 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.695 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 OL1 piece4 8
0.00000 0.000 0.000 0.308 0.933 1.000 0.000 1.000
0.00000 0.000 0.000 0.000 0.933 1.000 0.000 1.000
0.00000 0.000 0.000 0.000 0.933 1.000 0.000 1.000
2 OL1 piece5 13.000
0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528 0.528
0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276
0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276 0.276
3 VM1 piece1 5
0.944 1.000 1.000 0.364 0.938
0.775 0.771 0.784 0.000 0.782
0.775 0.771 0.784 0.000 0.782
3 VM1 piece2 5
0.800 0.812 0.600 0.936 0.934
0.614 0.734 0.000 0.936 0.934
0.614 0.734 0.000 0.936 0.934
3 VM1 piece3 10.000
0.647 0.752 0.846 1.000 0.579 0.314 0.500 0.742 1.000 1.000
0.00000 0.752 0.724 0.831 0.000 0.000 0.000 0.000 0.905 1.000
0.00000 0.752 0.724 0.831 0.000 0.000 0.000 0.000 0.905 1.000
3 VM1 piece4 8
1.00000 0.857 0.600 1.000 1.000 1.000 0.900 1.000
0.860 0.429 0.000 1.000 1.000 0.912 0.750 1.000
0.860 0.429 0.000 1.000 1.000 0.912 0.750 1.000
3 VM1 piece5 13.000
0.857 0.714 0.989 0.993 0.968 0.400 0.125 0.529 0.500 0.771 0.800 0.668 0.573
0.857 0.000 0.989 0.993 0.968 0.000 0.000 0.000 0.000 0.366 0.746 0.000 0.000
0.857 0.000 0.989 0.993 0.968 0.000 0.000 0.000 0.000 0.366 0.746 0.000 0.000
4 VM2 piece1 5
0.727 0.719 0.625 0.111 0.667
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
4 VM2 piece2 5
0.538 0.812 0.600 0.920 0.934
0.00000 0.734 0.000 0.920 0.934
0.00000 0.734 0.000 0.920 0.934
4 VM2 piece3 10.000
0.786 0.744 0.962 0.278 0.395 0.360 0.250 0.677 0.571 0.190
0.384 0.000 0.498 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.384 0.000 0.498 0.000 0.000 0.000 0.000 0.000 0.000 0.000
4 VM2 piece4 8
0.667 0.571 0.600 1.000 1.000 0.714 0.800 0.769
0.00000 0.000 0.000 0.911 1.000 0.000 0.733 0.769
0.00000 0.000 0.000 0.911 1.000 0.000 0.733 0.769
4 VM2 piece5 13.000
0.609 0.087 0.974 0.982 0.633 0.600 0.333 0.111 0.084 0.800 0.667 0.652 0.488
0.00000 0.000 0.974 0.982 0.000 0.000 0.000 0.000 0.000 0.388 0.000 0.000 0.000
0.00000 0.000 0.974 0.982 0.000 0.000 0.000 0.000 0.000 0.388 0.000 0.000 0.000
5 NF1'13 piece1 5
0.235 0.900 0.600 0.000 0.417
0.00000 0.154 0.000 0.000 0.000
0.00000 0.154 0.000 0.000 0.000
5 NF1'13 piece2 5
0.111 0.000 0.000 0.004 0.002
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
5 NF1'13 piece3 10.000
0.533 0.512 0.778 0.500 0.500 0.526 0.200 0.667 0.226 0.103
0.00000 0.000 0.408 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.408 0.000 0.000 0.000 0.000 0.000 0.000 0.000
5 NF1'13 piece4 8
0.857 0.556 0.500 1.000 0.867 0.571 0.900 1.000
0.321 0.000 0.000 0.219 0.433 0.000 0.771 1.000
0.321 0.000 0.000 0.219 0.433 0.000 0.771 1.000
5 NF1'13 piece5 13.000
0.318 0.256 0.375 0.969 0.316 0.426 0.170 0.044 0.054 0.637 0.565 0.706 0.665
0.00000 0.000 0.000 0.969 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.969 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
6 DM10'13 piece1 5
0.882 0.857 0.333 0.273 0.867
0.866 0.613 0.000 0.000 0.778
0.866 0.613 0.000 0.000 0.778
6 DM10'13 piece2 5
0.778 0.438 0.400 0.872 0.929
0.544 0.000 0.000 0.872 0.908
0.544 0.000 0.000 0.872 0.908
6 DM10'13 piece3 10.000
0.600 0.674 0.821 1.000 0.500 0.275 0.050 0.575 1.000 0.667
0.00000 0.000 0.498 0.190 0.000 0.000 0.000 0.000 0.667 0.000
0.00000 0.000 0.498 0.190 0.000 0.000 0.000 0.000 0.667 0.000
6 DM10'13 piece4 8
1.00000 0.857 0.200 0.364 0.875 0.619 0.600 0.857
0.750 0.643 0.000 0.000 0.867 0.000 0.000 0.846
0.750 0.643 0.000 0.000 0.867 0.000 0.000 0.846
6 DM10'13 piece5 13.000
0.086 0.080 0.934 0.985 0.283 0.206 0.082 0.075 0.083 0.835 0.292 0.914 0.742
0.00000 0.000 0.934 0.983 0.000 0.000 0.000 0.000 0.000 0.504 0.000 0.914 0.000
0.00000 0.000 0.934 0.983 0.000 0.000 0.000 0.000 0.000 0.504 0.000 0.914 0.000

Table 3. Tabular version of Figures 2 and 3.

symPoly

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF_1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 NF1 piece1 5 15.000 0.308 0.319 0.313 0.205 0.075 0.109 0.077 0.100 0.087 61.000 0.000 0.312 0.160 0.214 0.120 0.154 0.000 0.000 0.000
1 NF1 piece2 5 48.000 0.166 0.409 0.236 0.000 0.000 0.000 0.093 0.333 0.145 1660.000 0.000 0.169 0.265 0.520 0.130 0.208 0.000 0.000 0.000
1 NF1 piece3 10.000 11.000 0.291 0.240 0.263 0.000 0.000 0.000 0.263 0.224 0.242 62.000 0.000 0.200 0.289 0.000 0.000 0.000 0.000 0.000 0.000
1 NF1 piece4 5 26.000 0.126 0.444 0.197 0.333 0.083 0.133 0.062 0.207 0.096 11.000 0.000 0.378 0.262 0.333 0.083 0.133 0.038 0.200 0.065
1 NF1 piece5 13.000 13.000 0.287 0.245 0.264 0.000 0.000 0.000 0.248 0.230 0.239 356.000 0.000 0.213 0.307 0.000 0.000 0.000 0.000 0.000 0.000
2 NF2'13 piece1 5 5 0.240 0.222 0.231 0.000 0.000 0.000 0.143 0.142 0.142 15.000 0.000 0.222 0.143 0.000 0.000 0.000 0.000 0.000 0.000
2 NF2'13 piece2 5 27.000 0.264 0.416 0.323 0.778 0.778 0.778 0.077 0.245 0.118 1221.000 0.000 0.314 0.229 0.778 0.778 0.778 0.000 0.000 0.000
2 NF2'13 piece3 10.000 20.000 0.695 0.584 0.635 0.703 0.320 0.440 0.473 0.439 0.455 34.000 0.000 0.355 0.473 0.603 0.373 0.461 0.000 0.000 0.000
2 NF2'13 piece4 5 2 0.667 0.272 0.386 0.885 0.885 0.885 0.609 0.240 0.344 3.000 0.000 0.272 0.609 0.885 0.885 0.885 0.000 0.000 0.000
2 NF2'13 piece5 13.000 18.000 0.564 0.334 0.419 0.690 0.393 0.501 0.417 0.345 0.377 153.000 0.000 0.245 0.549 0.601 0.488 0.539 0.000 0.000 0.000
3 DM10'13 piece1 5 37.000 0.395 0.535 0.454 0.406 0.439 0.422 0.281 0.422 0.337 53.000 0.000 0.498 0.485 0.384 0.515 0.440 0.000 0.000 0.000
3 DM10'13 piece2 5 67.000 0.601 0.693 0.644 0.565 0.954 0.710 0.527 0.595 0.559 1287.000 0.000 0.256 0.303 0.511 0.925 0.658 0.000 0.000 0.000
3 DM10'13 piece3 10.000 20.000 0.648 0.546 0.592 0.586 0.825 0.685 0.622 0.461 0.530 89.000 0.000 0.321 0.720 0.514 0.782 0.620 0.000 0.000 0.000
3 DM10'13 piece4 5 21.000 0.503 0.508 0.505 0.472 0.941 0.628 0.368 0.326 0.346 3.000 0.000 0.415 0.556 0.306 0.726 0.430 0.000 0.000 0.000
3 DM10'13 piece5 13.000 69.000 0.662 0.509 0.576 0.629 0.947 0.756 0.626 0.443 0.519 3108.000 0.000 0.205 0.643 0.564 0.881 0.688 0.000 0.000 0.000

Table 4. Tabular version of Figures 16-25.

AlgIdx AlgStub Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
1 NF1 piece1 5
0.286 0.771 0.538 0.000 0.000
0.00000 0.075 0.000 0.000 0.000
0.00000 0.075 0.000 0.000 0.000
1 NF1 piece2 5
0.571 0.319 0.250 0.468 0.438
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
1 NF1 piece3 10.000
0.311 0.271 0.397 0.217 0.242 0.250 0.182 0.239 0.184 0.105
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 NF1 piece4 5
0.462 0.467 0.000 1.000 0.294
0.00000 0.000 0.000 0.083 0.000
0.00000 0.000 0.000 0.083 0.000
1 NF1 piece5 13.000
0.289 0.184 0.423 0.418 0.110 0.110 0.028 0.041 0.043 0.337 0.381 0.431 0.387
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 NF2'13 piece1 5
0.266 0.422 0.109 0.074 0.238
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
2 NF2'13 piece2 5
0.444 0.319 0.429 0.790 0.099
0.00000 0.000 0.000 0.778 0.000
0.00000 0.000 0.000 0.778 0.000
2 NF2'13 piece3 10.000
0.951 0.628 0.987 0.486 0.407 0.787 0.235 0.641 0.446 0.271
0.170 0.000 0.305 0.000 0.000 0.390 0.000 0.000 0.000 0.000
0.170 0.000 0.305 0.000 0.000 0.390 0.000 0.000 0.000 0.000
2 NF2'13 piece4 5
0.276 0.000 0.000 0.182 0.902
0.00000 0.000 0.000 0.000 0.885
0.00000 0.000 0.000 0.000 0.885
2 NF2'13 piece5 13.000
0.372 0.173 0.759 0.634 0.072 0.071 0.020 0.026 0.025 0.805 0.321 0.578 0.481
0.00000 0.000 0.380 0.000 0.000 0.000 0.000 0.000 0.000 0.396 0.000 0.000 0.000
0.00000 0.000 0.380 0.000 0.000 0.000 0.000 0.000 0.000 0.396 0.000 0.000 0.000
3 DM10'13 piece1 5
0.941 0.619 0.286 0.217 0.611
0.439 0.000 0.000 0.000 0.000
0.439 0.000 0.000 0.000 0.000
3 DM10'13 piece2 5
0.700 0.516 0.333 0.963 0.952
0.00000 0.000 0.000 0.963 0.944
0.00000 0.000 0.000 0.963 0.944
3 DM10'13 piece3 10.000
0.851 0.875 0.852 0.500 0.595 0.310 0.063 0.821 0.366 0.225
0.847 0.759 0.843 0.000 0.000 0.000 0.000 0.821 0.000 0.000
0.847 0.759 0.843 0.000 0.000 0.000 0.000 0.821 0.000 0.000
3 DM10'13 piece4 5
0.556 0.429 0.364 0.250 0.941
0.00000 0.000 0.000 0.000 0.941
0.00000 0.000 0.000 0.000 0.941
3 DM10'13 piece5 13.000
0.619 0.368 0.934 0.964 0.213 0.209 0.069 0.275 0.047 0.918 0.300 0.958 0.747
0.00000 0.000 0.934 0.956 0.000 0.000 0.000 0.000 0.000 0.912 0.000 0.951 0.000
0.00000 0.000 0.934 0.956 0.000 0.000 0.000 0.000 0.000 0.912 0.000 0.951 0.000

Table 5. Tabular version of Figures 14 and 15.

audMono

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF_1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 NF1 piece1 5 5 0.710 0.433 0.538 0.375 0.124 0.186 0.150 0.114 0.129 536.000 0.000 0.433 0.150 0.344 0.130 0.189 0.000 0.000 0.000
1 NF1 piece2 5 12.000 0.459 0.602 0.520 0.423 0.423 0.423 0.163 0.242 0.195 71.000 0.000 0.351 0.171 0.457 0.187 0.266 0.000 0.000 0.000
1 NF1 piece3 10.000 17.000 0.676 0.564 0.615 0.590 0.268 0.368 0.325 0.325 0.325 77.000 0.000 0.429 0.376 0.428 0.260 0.323 0.000 0.000 0.000
1 NF1 piece4 8 13.000 0.695 0.723 0.709 0.770 0.328 0.460 0.492 0.519 0.505 238.000 0.000 0.330 0.398 0.664 0.379 0.482 0.077 0.125 0.095
1 NF1 piece5 13.000 23.000 0.387 0.352 0.369 0.000 0.000 0.000 0.196 0.203 0.199 1598.000 0.000 0.258 0.218 0.365 0.147 0.210 0.000 0.000 0.000
2 NF3'13 piece1 5 41.000 0.506 0.586 0.543 0.384 0.119 0.182 0.124 0.219 0.158 135.000 0.000 0.428 0.154 0.362 0.122 0.182 0.000 0.000 0.000
2 NF3'13 piece2 5 19.000 0.344 0.422 0.379 0.406 0.109 0.172 0.097 0.110 0.103 21.000 0.000 0.274 0.104 0.392 0.088 0.143 0.000 0.000 0.000
2 NF3'13 piece3 10.000 7 0.637 0.437 0.519 0.482 0.167 0.248 0.275 0.220 0.244 7.000 0.000 0.314 0.263 0.440 0.138 0.210 0.000 0.000 0.000
2 NF3'13 piece4 8 10.000 0.523 0.375 0.437 0.767 0.167 0.274 0.579 0.386 0.463 20.000 0.000 0.238 0.594 0.601 0.360 0.451 0.000 0.000 0.000
2 NF3'13 piece5 13.000 1 0.432 0.102 0.165 0.000 0.000 0.000 0.148 0.045 0.069 122.000 0.000 0.102 0.148 0.000 0.000 0.000 0.000 0.000 0.000

Table 6. Taublar version of Figures 28-37.

AlgIdx AlgStub Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
1 NF1 piece1 5
0.895 0.844 0.123 0.000 0.306
0.075 0.148 0.000 0.000 0.000
0.075 0.148 0.000 0.000 0.000
1 NF1 piece2 5
0.727 0.625 0.300 0.846 0.509
0.00000 0.000 0.000 0.423 0.000
0.00000 0.000 0.000 0.423 0.000
1 NF1 piece3 10.000
0.929 0.721 0.808 0.545 0.421 0.579 0.222 0.645 0.500 0.267
0.231 0.000 0.322 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.231 0.000 0.322 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 NF1 piece4 8
1.00000 0.857 0.000 1.000 1.000 0.571 0.667 0.692
0.250 0.214 0.000 0.167 0.917 0.000 0.000 0.000
0.250 0.214 0.000 0.167 0.917 0.000 0.000 0.000
1 NF1 piece5 13.000
0.400 0.250 0.194 0.195 0.421 0.485 0.121 0.176 0.321 0.557 0.457 0.615 0.385
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 NF3'13 piece1 5
0.850 0.862 0.312 0.500 0.405
0.097 0.133 0.000 0.000 0.000
0.097 0.133 0.000 0.000 0.000
2 NF3'13 piece2 5
0.727 0.875 0.333 0.124 0.049
0.00000 0.109 0.000 0.000 0.000
0.00000 0.109 0.000 0.000 0.000
2 NF3'13 piece3 10.000
0.929 0.109 0.519 0.545 0.289 0.579 0.250 0.484 0.467 0.200
0.167 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.167 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 NF3'13 piece4 8
0.00000 0.000 0.000 0.800 0.533 0.571 0.556 0.538
0.00000 0.000 0.000 0.167 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.167 0.000 0.000 0.000 0.000
2 NF3'13 piece5 13.000
0.00000 0.000 0.077 0.000 0.381 0.432 0.108 0.000 0.000 0.000 0.000 0.225 0.100
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Table 7. Tabular version of Figures 26 and 27.

audPoly

AlgIdx AlgStub Piece n_P n_Q P_est R_est F1_est P_occ(c=.75) R_occ(c=.75) F_1occ(c=.75) P_3 R_3 TLF_1 runtime FRT FFTP_est FFP P_occ(c=.5) R_occ(c=.5) F_1occ(c=.5) P R F_1
1 NF1 piece1 5 5 0.252 0.238 0.245 0.197 0.072 0.105 0.043 0.052 0.047 118.000 0.000 0.238 0.043 0.197 0.072 0.105 0.000 0.000 0.000
1 NF1 piece2 5 12.000 0.357 0.387 0.372 0.000 0.000 0.000 0.113 0.159 0.133 80.000 0.000 0.293 0.115 0.504 0.080 0.137 0.000 0.000 0.000
1 NF1 piece3 10.000 17.000 0.291 0.269 0.279 0.000 0.000 0.000 0.157 0.176 0.166 122.000 0.000 0.208 0.190 0.000 0.000 0.000 0.000 0.000 0.000
1 NF1 piece4 5 13.000 0.063 0.212 0.097 0.000 0.000 0.000 0.066 0.208 0.100 31.000 0.000 0.212 0.172 0.500 0.250 0.333 0.077 0.200 0.111
1 NF1 piece5 13.000 23.000 0.324 0.288 0.305 0.000 0.000 0.000 0.142 0.154 0.148 1096.000 0.000 0.225 0.158 0.000 0.000 0.000 0.000 0.000 0.000
2 NF4'13 piece1 5 1 0.323 0.126 0.181 0.000 0.000 0.000 0.100 0.032 0.048 7.000 0.000 0.126 0.100 0.000 0.000 0.000 0.000 0.000 0.000
2 NF4'13 piece2 5 105.000 0.241 0.304 0.269 0.333 0.050 0.087 0.058 0.103 0.074 29.000 0.000 0.222 0.090 0.337 0.082 0.132 0.000 0.000 0.000
2 NF4'13 piece3 10.000 23.000 0.277 0.262 0.269 0.000 0.000 0.000 0.148 0.172 0.159 10.000 0.000 0.203 0.218 0.000 0.000 0.000 0.000 0.000 0.000
2 NF4'13 piece4 5 1 0.294 0.112 0.162 0.000 0.000 0.000 0.442 0.127 0.197 2.000 0.000 0.112 0.442 0.000 0.000 0.000 0.000 0.000 0.000
2 NF4'13 piece5 13.000 24.000 0.288 0.304 0.296 0.000 0.000 0.000 0.130 0.159 0.143 135.000 0.000 0.227 0.163 0.000 0.000 0.000 0.000 0.000 0.000

Table 8. Tabular version of Figures 40-49.

AlgId TaskVersion Piece n_P R_est R_occ(c=.75) R_occ(c=.5)
NF4 audPoly piece1 5
0.323 0.000 0.308 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
NF4 audPoly piece2 5
0.800 0.277 0.333 0.084 0.026
0.050 0.000 0.000 0.000 0.000
0.050 0.000 0.000 0.000 0.000
NF4 audPoly piece3 10.000
0.341 0.205 0.333 0.273 0.242 0.250 0.200 0.230 0.292 0.250
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
NF4 audPoly piece4 5
0.00000 0.000 0.000 0.267 0.294
0.00000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000
NF4 audPoly piece5 13.000
0.379 0.242 0.271 0.280 0.314 0.429 0.121 0.188 0.333 0.375 0.381 0.351 0.290
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Table 9. Tabular version of Figures 38 and 39.

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