2016:Discovery of Repeated Themes & Sections Results

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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 $P_{1}$ and $P_{2}$, as well as a pattern corresponding to the note content of $Q_{1}$. This is because $Q_{1}$ occurs again independently of the accompaniment in bars 19-22 (not shown here). The ground truth also contains nested patterns, such as $P_{1}$ in Fig. 1A being a subset of the sectional repetition $S_{1}$, 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 (Collins et al., 2014).

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 2015: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. There were no submissions to the symPoly category this year, so three versions of the task ran. Submitted algorithms are shown in Table 1.

Sub code	Submission name	Abstract	Contributors
Task Version	symMono
PLM1	SYMCHM	PDF	Matevž Pesek, Urša Medvešek, Aleš Leonardis, Matija Marolt
OL1'14	PatMinr	PDF	Olivier Lartillot
VM2'14	VM2	PDF	Gissel Velarde, David Meredith
Task Version	audMono
WHD1	VMO Motif Discovery	PDF	Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
WDH1	VMO Motif Discovery FML	PDF	Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
NF1'14	MotivesExtractor	PDF	Oriol Nieto, Morwaread Farbood
Task Version	audPoly
WHD1	VMO Motif Discovery	PDF	Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
WDH1	VMO Motif Discovery FML	PDF	Cheng-i Wang, Jennifer Hsu, Shlomo Dubnov
NF1'14	MotivesExtractor	PDF	Oriol Nieto, Morwaread Farbood

Table 1. Algorithms submitted to DRTS. Strong-performing algorithms from 2014 (submission codes ending '14) are included for the sake of comparisons.

Results in Brief

(For mathematical definitions of the various metrics, please see 2015:Discovery_of_Repeated_Themes_&_Sections#Evaluation_Procedure.)

Pesek, Leonardis, and Marolt (2015) submitted a compositional hierarchical model – applied to automatic chord recognition and F0-estimation previously (Pesek, Leonardis, & Marolt, 2014) – to the symMono version of the task. Given that their submission SYMCHM (PLM1) is a general-purpose algorithm for which pattern discovery is one application domain and that this is a popular version of the task (four algorithms submitted in 2014; seven in 2013), SYMCHM (PLM1) did well (Figs. 4-12). It was still not as strong as the previous best performer, VM2 (Velarde & Meredith, 2014), with regards discovering at least one occurrence of each ground truth pattern (Fig. 2): this algorithm, VM2, tested significantly stronger according to Friedman's test than PLM1 ($\chi ^{2}(1)=8.1,\ p<.05$, Bonferroni-corrected). Likewise, it was not as strong as the previous best performer, OL1 (Lartillot, 2014), with regards discovering all occurrences of a given ground truth pattern (Fig. 3): OL1 tested significantly stronger according to Friedman's test than PLM1 ($\chi ^{2}(1)=10.71,\ p<.01$, Bonferroni-corrected), but we should note that the decision to average results for OL1 on piece 5 could be driving this result. It should also be noted that the runtimes for PLM1 (Fig. 13) are somewhat harsh, because the Windows Virtual Machine on which it ran is considerably slower than the Linux machines on which the other submissions ran.

Wang, Hsu, and Dubnov (2015a, 2015b) submitted a motif discovery system based on a Variable Markov Oracle to audMono and audPoly versions of the task. On the audMono task this algorithm, WHD1, was not significantly different to NF1 according to Friedman's test ($\chi ^{2}(1)=.23,\ p=.631$) at discovering at least one occurrence of each ground truth pattern (Fig. 14). Similarly, WHD1 was not significantly different to NF1 according to Friedman's test ($\chi ^{2}(1)=.89,\ p=.346$) at discovering all occurrences of a given ground truth pattern (Fig. 15). These results suggest that WHD1 is on a par with state-of-the-art performance on the audMono task. Results for the audPoly task were similar, and WHD1 was significantly better than previous state-of-the-art performance ($\chi ^{2}(1)=6.43,\ p=<.05$) with regards discovering at least one occurrence of each ground truth pattern (Fig. 26). (To avoid a bias toward the more numerous submissions of Wang et al. (2015), WHD1 was preselected over WDH1 for comparison with Nieto and Farbood's (2014a) submission, based on performance for the Development Database.)

Discussion

Since this task began in 2013, it has been observed that the discovery of repeated sections tends to be addressed well by submissions, and the discovery of shorter themes/motifs less well. This in itself is not a particularly surprising observation, since it mirrors the way music analysts might agree on the large-scale repetitive structure of a song/piece, but differ in interpreting its themes and/or motifs. It was exciting to see, however, that WDH1 and WHD1 (Wang et al., 2015a, 2015b) had high establishment recall compared with previous years for seven- and nine-note patterns in piece 1, a five-note pattern in piece 2, and nine- and thirteen-note patterns in piece 4 (see Fig. 14 for details). Whereas WHD1's establishment recall dropped off for six- and nine-note patterns in piece 5, establishment recall remained comparatively high for WDH1. The difference between these submissions was a fixed minimum length (FML) criterion that applied to WDH1 but not to WHD1. The criterion seems to have helped WDH1 to perform well on this aspect of the task.

The PLM1 submission (Pesek et al., 2015) is of interest because it (1) is the first deep architecture to be submitted to the task and (2) has been applied to other MIR tasks such as chord and multi-F0 estimation (Pesek et al., 2014). It outperformed previous algorithms on piece 1 (see Figs. 4-6), demonstrating its potential, but had lower establishment recall for pieces 2-5 (see Fig. 4). For those who have called for multipurpose, integrated MIR solutions, this approach represents an encouraging development.

It is good to see submissions from two new groups this year, and that the emphasis the task places on retrieving and evaluating hierarchical structure is being acknowledged and championed elsewhere (McFee, Nieto, & Bello, 2015). Next year we may switch to new training and test databases that focus not directly on the discovery task itself, but on an application of pattern discovery that can be used as a proxy to evaluate the extent to which algorithms have retrieved relevant repetitive material. If you are interested in helping out with the preparation of a new version of the task, you are welcome to get in touch.

Tom Collins, Leicester, 2015

Results in Detail

symPoly

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 ($c=.75$) 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 ($c=.75$) 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 ($c=.75$) 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 $|P\cap Q|/\max\{|P|,|Q|\}$ as a similarity measure (which is the default for establishment recall), three-layer recall uses $2|P\cap Q|/(|P|+|Q|)$, which is a kind of F1 measure.

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

symMono

(Submission PLM1 did not complete on piece 5. The task captain took the decision to assign the mean of the evaluation metrics for PLM1 calculated across the remaining pieces. Apart from runtime, in which case the maximum across the remaining pieces was assigned.)

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 ($c=.75$) 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 ($c=.75$) 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 ($c=.75$) 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 $|P\cap Q|/\max\{|P|,|Q|\}$ as a similarity measure (which is the default for establishment recall), three-layer recall uses $2|P\cap Q|/(|P|+|Q|)$, which is a kind of F1 measure.

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

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	PLM1	piece1	5	18.000	0.700	0.731	0.715	0.726	0.419	0.531	0.378	0.499	0.430	29100.000	0.000	0.480	0.294	0.579	0.433	0.495	0.000	0.000	0.000
1	PLM1	piece2	5	31.000	0.209	0.454	0.286	0.755	0.505	0.605	0.222	0.413	0.289	19260.000	0.000	0.174	0.177	0.670	0.573	0.617	0.032	0.200	0.056
1	PLM1	piece3	10.000	8	0.426	0.277	0.336	0.834	0.695	0.758	0.501	0.305	0.379	180.000	0.000	0.242	0.505	0.834	0.695	0.758	0.000	0.000	0.000
1	PLM1	piece4	8	2	0.967	0.277	0.431	0.967	0.967	0.967	0.983	0.273	0.428	660.000	0.000	0.277	0.983	0.967	0.967	0.967	0.500	0.125	0.200
1	PLM1	piece5	13.000	35.000	0.366	0.331	0.348	0.785	0.406	0.535	0.354	0.372	0.363	69240.000	0.000	0.103	0.226	0.617	0.456	0.525	0.000	0.000	0.000
2	OL1_14	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_14	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_14	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_14	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_14	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	VM2_14	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
3	VM2_14	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
3	VM2_14	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
3	VM2_14	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
3	VM2_14	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

download these results as csv

Table 2. Tabular version of Figures 4-13.

AlgIdx	AlgStub	Piece	n_P	R_est	R_occ(c=.75)	R_occ(c=.5)
1	PLM1	piece1	5
0.941	1.000	0.312	0.600	0.800
0.614	0.410	0.000	0.000	0.267
0.614	0.410	0.000	0.000	0.267
1	PLM1	piece2	5
0.800	0.812	0.300	0.244	0.114
0.300	0.709	0.000	0.000	0.000
0.300	0.709	0.000	0.000	0.000
1	PLM1	piece3	10.000
0.409	0.442	0.846	0.227	0.361	0.263	0.222	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
0.00000	0.000	0.695	0.000	0.000	0.000	0.000	0.000	0.000	0.000
1	PLM1	piece4	8
0.00000	0.000	0.000	0.286	0.933	1.000	0.000	0.000
0.00000	0.000	0.000	0.000	0.933	1.000	0.000	0.000
0.00000	0.000	0.000	0.000	0.933	1.000	0.000	0.000
1	PLM1	piece5	13.000
0.255	0.193	0.117	0.079	0.545	0.357	0.417	0.155	0.177	0.829	0.591	0.342	0.246
0.00000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.406	0.000	0.000	0.000
0.00000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.406	0.000	0.000	0.000
2	OL1_14	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_14	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_14	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_14	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_14	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	VM2_14	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
3	VM2_14	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
3	VM2_14	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
3	VM2_14	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
3	VM2_14	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

download these results as csv

Table 3. Tabular version of Figures 2 and 3.

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	WHD1	piece1	5	131.000	0.250	0.651	0.362	0.506	0.133	0.211	0.098	0.338	0.152	845.000	0.000	0.089	0.112	0.416	0.213	0.282	0.000	0.000	0.000
1	WHD1	piece2	5	3	0.612	0.339	0.436	0.956	0.956	0.956	0.708	0.356	0.474	244.000	0.000	0.339	0.708	0.754	0.754	0.754	0.000	0.000	0.000
1	WHD1	piece3	10.000	7	0.611	0.402	0.485	0.000	0.000	0.000	0.562	0.399	0.467	92.000	0.000	0.344	0.551	0.603	0.486	0.538	0.000	0.000	0.000
1	WHD1	piece4	8	88.000	0.301	0.800	0.438	0.601	0.331	0.427	0.157	0.609	0.250	251.000	0.000	0.257	0.278	0.523	0.291	0.373	0.023	0.250	0.042
1	WHD1	piece5	13.000	3	0.644	0.221	0.329	0.947	0.947	0.947	0.743	0.231	0.353	519.000	0.000	0.221	0.743	0.821	0.821	0.821	0.000	0.000	0.000
2	WDH1	piece1	5	56.000	0.326	0.629	0.429	0.506	0.133	0.211	0.130	0.299	0.181	852.000	0.000	0.436	0.240	0.464	0.203	0.283	0.000	0.000	0.000
2	WDH1	piece2	5	11.000	0.307	0.494	0.379	0.956	0.956	0.956	0.258	0.419	0.319	243.000	0.000	0.317	0.268	0.754	0.754	0.754	0.000	0.000	0.000
2	WDH1	piece3	10.000	13.000	0.596	0.530	0.561	1.000	0.214	0.353	0.471	0.441	0.456	92.000	0.000	0.265	0.475	0.538	0.381	0.446	0.000	0.000	0.000
2	WDH1	piece4	8	45.000	0.312	0.800	0.448	0.815	0.536	0.647	0.206	0.609	0.308	259.000	0.000	0.208	0.247	0.706	0.458	0.555	0.044	0.250	0.075
2	WDH1	piece5	13.000	23.000	0.511	0.593	0.549	0.829	0.468	0.598	0.395	0.469	0.429	518.000	0.000	0.251	0.444	0.663	0.355	0.462	0.000	0.000	0.000
3	NF1_14	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
3	NF1_14	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
3	NF1_14	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
3	NF1_14	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
3	NF1_14	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

download these results as csv

Table 4. Taublar version of Figures 16-25.

AlgIdx	AlgStub	Piece	n_P	R_est	R_occ(c=.75)	R_occ(c=.5)
1	WHD1	piece1	5
0.647	0.684	0.667	0.444	0.812
0.00000	0.000	0.000	0.000	0.133
0.00000	0.000	0.000	0.000	0.133
1	WHD1	piece2	5
0.058	0.104	0.019	0.552	0.960
0.00000	0.000	0.000	0.000	0.956
0.00000	0.000	0.000	0.000	0.956
1	WHD1	piece3	10.000
0.353	0.729	0.654	0.294	0.500	0.324	0.091	0.613	0.292	0.167
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	WHD1	piece4	8
1.00000	0.286	0.400	1.000	0.933	1.000	0.778	1.000
0.250	0.000	0.000	0.146	0.933	0.889	0.778	1.000
0.250	0.000	0.000	0.146	0.933	0.889	0.778	1.000
1	WHD1	piece5	13.000
0.060	0.019	0.947	0.697	0.057	0.042	0.015	0.017	0.021	0.152	0.049	0.308	0.487
0.00000	0.000	0.947	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
0.00000	0.000	0.947	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
2	WDH1	piece1	5
0.647	0.684	0.667	0.333	0.812
0.00000	0.000	0.000	0.000	0.133
0.00000	0.000	0.000	0.000	0.133
2	WDH1	piece2	5
0.348	0.438	0.174	0.552	0.960
0.00000	0.000	0.000	0.000	0.956
0.00000	0.000	0.000	0.000	0.956
2	WDH1	piece3	10.000
0.538	0.729	0.654	1.000	0.500	0.324	0.200	0.613	0.571	0.167
0.00000	0.000	0.000	0.214	0.000	0.000	0.000	0.000	0.000	0.000
0.00000	0.000	0.000	0.214	0.000	0.000	0.000	0.000	0.000	0.000
2	WDH1	piece4	8
1.00000	0.286	0.400	1.000	0.933	1.000	0.778	1.000
0.250	0.000	0.000	0.146	0.933	0.889	0.778	1.000
0.250	0.000	0.000	0.146	0.933	0.889	0.778	1.000
2	WDH1	piece5	13.000
0.857	0.889	0.947	0.697	0.417	0.400	0.500	0.529	0.600	0.757	0.250	0.385	0.487
0.446	0.220	0.947	0.000	0.000	0.000	0.000	0.000	0.000	0.277	0.000	0.000	0.000
0.446	0.220	0.947	0.000	0.000	0.000	0.000	0.000	0.000	0.277	0.000	0.000	0.000
3	NF1_14	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
3	NF1_14	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
3	NF1_14	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
3	NF1_14	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
3	NF1_14	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

download these results as csv

Table 5. Tabular version of Figures 14 and 15.

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	WHD1	piece1	5	89.000	0.296	0.406	0.342	0.000	0.000	0.000	0.098	0.160	0.121	121.000	0.000	0.200	0.118	0.399	0.091	0.148	0.000	0.000	0.000
1	WHD1	piece2	5	2	0.967	0.410	0.576	0.966	0.966	0.966	0.967	0.405	0.571	275.000	0.000	0.410	0.967	0.966	0.966	0.966	0.000	0.000	0.000
1	WHD1	piece3	10.000	5	0.670	0.414	0.512	0.865	0.865	0.865	0.668	0.426	0.521	84.000	0.000	0.414	0.668	0.664	0.511	0.577	0.000	0.000	0.000
1	WHD1	piece4	5	33.000	0.353	0.570	0.436	0.670	0.451	0.539	0.193	0.401	0.261	55.000	0.000	0.311	0.313	0.506	0.264	0.347	0.000	0.000	0.000
1	WHD1	piece5	13.000	4	0.581	0.243	0.342	0.950	0.950	0.950	0.675	0.265	0.381	584.000	0.000	0.243	0.675	0.686	0.585	0.631	0.000	0.000	0.000
2	WDH1	piece1	5	110.000	0.305	0.413	0.351	0.000	0.000	0.000	0.097	0.170	0.124	124.000	0.000	0.200	0.118	0.354	0.109	0.167	0.000	0.000	0.000
2	WDH1	piece2	5	10.000	0.389	0.562	0.459	0.966	0.966	0.966	0.276	0.464	0.346	270.000	0.000	0.281	0.247	0.600	0.523	0.559	0.000	0.000	0.000
2	WDH1	piece3	10.000	14.000	0.572	0.562	0.567	0.865	0.865	0.865	0.445	0.465	0.455	84.000	0.000	0.356	0.566	0.521	0.356	0.423	0.000	0.000	0.000
2	WDH1	piece4	5	7	0.335	0.261	0.293	0.804	0.804	0.804	0.214	0.229	0.221	57.000	0.000	0.261	0.300	0.589	0.444	0.506	0.000	0.000	0.000
2	WDH1	piece5	13.000	16.000	0.529	0.466	0.495	0.950	0.950	0.950	0.475	0.405	0.437	545.000	0.000	0.253	0.493	0.674	0.453	0.542	0.000	0.000	0.000
3	NF1_14	piece1	5	1	0.168	0.108	0.132	0.000	0.000	0.000	0.095	0.064	0.076	118.000	0.000	0.108	0.095	0.000	0.000	0.000	0.000	0.000	0.000
3	NF1_14	piece2	5	12.000	0.323	0.509	0.395	0.408	0.408	0.408	0.145	0.236	0.180	80.000	0.000	0.410	0.254	0.493	0.288	0.363	0.000	0.000	0.000
3	NF1_14	piece3	10.000	10.000	0.645	0.524	0.578	0.393	0.297	0.338	0.394	0.323	0.355	122.000	0.000	0.354	0.399	0.438	0.285	0.345	0.000	0.000	0.000
3	NF1_14	piece4	5	1	0.895	0.193	0.317	0.817	0.817	0.817	0.897	0.203	0.332	31.000	0.000	0.193	0.897	0.817	0.817	0.817	0.000	0.000	0.000
3	NF1_14	piece5	13.000	12.000	0.428	0.344	0.382	0.000	0.000	0.000	0.215	0.183	0.198	1096.000	0.000	0.303	0.243	0.362	0.200	0.258	0.000	0.000	0.000

download these results as csv

Table 8. Tabular version of Figures 28-37.

AlgIdx	AlgStub	Piece	n_P	R_est	R_occ(c=.75)	R_occ(c=.5)
1	WHD1	piece1	5
0.647	0.567	0.143	0.189	0.484
0.00000	0.000	0.000	0.000	0.000
0.00000	0.000	0.000	0.000	0.000
1	WHD1	piece2	5
0.016	0.095	0.006	0.953	0.980
0.00000	0.000	0.000	0.953	0.978
0.00000	0.000	0.000	0.953	0.978
1	WHD1	piece3	10.000
0.415	0.869	0.688	0.526	0.214	0.149	0.119	0.624	0.333	0.205
0.00000	0.865	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
0.00000	0.865	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
1	WHD1	piece4	5
0.714	0.250	0.333	0.750	0.804
0.00000	0.000	0.000	0.098	0.804
0.00000	0.000	0.000	0.098	0.804
1	WHD1	piece5	13.000
0.250	0.118	0.950	0.533	0.056	0.050	0.015	0.024	0.015	0.162	0.056	0.360	0.566
0.00000	0.000	0.950	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
0.00000	0.000	0.950	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
2	WDH1	piece1	5
0.529	0.567	0.182	0.189	0.600
0.00000	0.000	0.000	0.000	0.000
0.00000	0.000	0.000	0.000	0.000
2	WDH1	piece2	5
0.200	0.574	0.100	0.953	0.980
0.00000	0.000	0.000	0.953	0.978
0.00000	0.000	0.000	0.953	0.978
2	WDH1	piece3	10.000
0.537	0.869	0.688	0.727	0.275	0.489	0.471	0.624	0.520	0.423
0.00000	0.865	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
0.00000	0.865	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
2	WDH1	piece4	5
0.00000	0.000	0.000	0.500	0.804
0.00000	0.000	0.000	0.000	0.804
0.00000	0.000	0.000	0.000	0.804
2	WDH1	piece5	13.000
0.733	0.312	0.950	0.533	0.571	0.371	0.101	0.486	0.015	0.746	0.312	0.360	0.566
0.00000	0.000	0.950	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
0.00000	0.000	0.950	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
3	NF1_14	piece1	5
0.119	0.168	0.046	0.069	0.138
0.00000	0.000	0.000	0.000	0.000
0.00000	0.000	0.000	0.000	0.000
3	NF1_14	piece2	5
0.438	0.617	0.158	0.815	0.516
0.00000	0.000	0.000	0.408	0.000
0.00000	0.000	0.000	0.408	0.000
3	NF1_14	piece3	10.000
0.436	0.688	0.639	0.395	0.574	0.787	0.178	0.793	0.480	0.271
0.00000	0.000	0.000	0.000	0.000	0.098	0.000	0.396	0.000	0.000
0.00000	0.000	0.000	0.000	0.000	0.098	0.000	0.396	0.000	0.000
3	NF1_14	piece4	5
0.00000	0.000	0.000	0.070	0.895
0.00000	0.000	0.000	0.000	0.817
0.00000	0.000	0.000	0.000	0.817
3	NF1_14	piece5	13.000
0.439	0.203	0.526	0.657	0.296	0.329	0.084	0.125	0.161	0.649	0.057	0.533	0.415
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

download these results as csv

Table 9. Tabular version of Figures 26 and 27.

References

• Harold Barlow and Sam Morgenstern. (1948). A dictionary of musical themes. Crown Publishers, New York.
• Siglind Bruhn. (1993). J.S. Bach's Well-Tempered Clavier: in-depth analysis and interpretation. Mainer International, Hong Kong.
• Tom Collins, Sebastian Böck, Florian Krebs, and Gerhard Widmer. (2014). Bridging the audio-symbolic gap: the discovery of repeated note content directly from polyphonic music audio. In Proc. Audio Engineering Society's 53rd Conference on Semantic Audio, London, UK.
• William Drabkin. Motif. (2001). In S. Sadie and J. Tyrrell (Eds), The new Grove dictionary of music and musicians. Macmillan, London, UK, 2nd ed.
• Olivier Lartillot. (2014a). Submission to MIREX Discovery of Repeated Themes and Sections. 10th Annual Music Information Retrieval eXchange (MIREX'14), Taipei, Taiwan.
• Olivier Lartillot. (2014b). In-depth motivic analysis based on multiparametric closed pattern and cyclic sequence mining. In Proc. ISMIR, Taipei, Taiwan.
• Brian McFee, Oriol Nieto, Juan Pablo Bello. (2015). Hierarchical evaluation of segment boundary detection. In Proc. ISMIR (pp. 406-12), Malaga, Spain.
• Oriol Nieto and Morwaread Farbood. (2014a). Submission to MIREX discovery of repeated themes and sections. 10th Annual Music Information Retrieval eXchange (MIREX'14), Taipei, Taiwan.
• Oriol Nieto and Morwaread Farbood. (2014b). Identifying polyphonic musical patterns from audio recordings using music segmentation techniques. In Proc. ISMIR, Taipei, Taiwan.
• Oriol Nieto and Morwaread Farbood. (2013). Discovering musical patterns using audio structural segmentation techniques. 9th Annual Music Information Retrieval eXchange (MIREX'13), Curitiba, Brazil.
• Matevz Pesek, Ales Leonardis, and Matija Marolt. (2015). Submission to MIREX Discovery of Repeated Themes and Sections. 11th Annual Music Information Retrieval eXchange (MIREX'15), Malaga, Spain.
• Matevz Pesek, Ales Leonardis, and Matija Marolt. (2014). A compositional hierarchical model for music information retrieval. In Proc. ISMIR (pp. 131-136), Taipei, Taiwan.
• Arnold Schoenberg. (1967). Fundamentals of Musical Composition. Faber and Faber, London.
• Gissel Velarde and David Meredith. (2014). Submission to MIREX Discovery of Repeated Themes and Sections. 10th Annual Music Information Retrieval eXchange (MIREX'14), Taipei, Taiwan.
• Cheng-i Wang, Jennifer Hsu, and Shlomo Dubnov. (2015a). Submission to MIREX Discovery of Repeated Themes and Sections. 11th Annual Music Information Retrieval eXchange (MIREX'15), Malaga, Spain.
• Cheng-i Wang, Jennifer Hsu, and Shlomo Dubnov. (2015b). Music pattern discovery with variable Markov oracle: a unified approach to symbolic and audio representations. In Proc. ISMIR (pp. 176-182), Malaga, Spain.
• Ron J. Weiss and Juan Pablo Bello. (2010). Identifying repeated patterns in music using sparse convolutive non-negative matrix factorization. In Proc. ISMIR (pp. 123-128), Utrecht, The Netherlands.