import musicntd.scripts.hide_code as hide
C:\Users\amarmore\AppData\Local\Continuum\anaconda3\envs\NTD_segmentation\lib\site-packages\librosa\util\decorators.py:9: NumbaDeprecationWarning: An import was requested from a module that has moved location. Import requested from: 'numba.decorators', please update to use 'numba.core.decorators' or pin to Numba version 0.48.0. This alias will not be present in Numba version 0.50.0. from numba.decorators import jit as optional_jit C:\Users\amarmore\AppData\Local\Continuum\anaconda3\envs\NTD_segmentation\lib\site-packages\librosa\util\decorators.py:9: NumbaDeprecationWarning: An import was requested from a module that has moved location. Import of 'jit' requested from: 'numba.decorators', please update to use 'numba.core.decorators' or pin to Numba version 0.48.0. This alias will not be present in Numba version 0.50.0. from numba.decorators import jit as optional_jit
This notebook aims at studying 3 different kernels for the convolution measure.
Note, as a prerequisite, that the diagonal of all our kernels is zero. Indeed, we consider that the diagonal of autosimilarity matrices doesn't hold structural information, and that considering it is counter-productive.
More details about the design of these kernels can be found in the Notebook "Appendix - Focus on the segmentation algorithm".
This kernel is a square matrix only composed of 0 and 1. It is equal to 0 on the diagonal, and to 1 elsewhere.
It looks like:
(or, in a matrix form: $\left[ \begin{matrix} 0 & 1 & 1 & 1& 1 & 1 & 1 & 1\\ 1 & 0 & 1 & 1& 1 & 1 & 1 & 1\\ 1 & 1 & 0 & 1& 1 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1\\ 1 & 1 & 1& 1 & 1 & 1 & 0 & 1\\ 1 & 1 & 1& 1 & 1 & 1 & 1 & 0\\ \end{matrix} \right]$ (of size 8 here)).
Mathematically, for a segment ($b_1, b_2$), the associated cost will be $c_{b_1,b_2} = \frac{1}{b_2 - b_1 + 1}\sum_{i,j = 0, i \ne j}^{n - 1} a_{i + b_1, j + b_1}$.
By construction, this kernel catches the similarity everywhere around the diagonal. As high similarity means higher values (and dark zones) in our autosimilarities, the higher this kernel, the more similar is the zone we are studying.
(You should read the "Appendix - Focus on the segmentation algorithm" notebook if you don't understand well how our algorithm work, and why the kernel is important).
Below are segmentation results with different ranks values, but each time fixed over the entire RWC Pop dataset.
Results are computed with tolerance of respectively 0.5 seconds and 3 seconds.
annotations_type = "MIREX10"
ranks_rhythm = [12,16,20,24,28,32,36,40,44,48]
ranks_pattern = [12,16,20,24,28,32,36,40,44,48]
zero_five_full, three_full = hide.compute_ranks_RWC(ranks_rhythm,ranks_pattern, W = "chromas", annotations_type = annotations_type,
subdivision=96, penalty_weight = 1,penalty_func = "modulo8", convolution_type = "full")
0.5 seconds results | True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|---|
Rang Q:12 | Rang H:12 | 7.5400 | 5.5000 | 11.2700 | 0.5806 | 0.4113 | 0.4726 |
Rang H:16 | 7.8500 | 5.4200 | 10.9600 | 0.5933 | 0.4270 | 0.4881 | |
Rang H:20 | 7.9500 | 5.3900 | 10.8600 | 0.6017 | 0.4320 | 0.4941 | |
Rang H:24 | 8.0000 | 5.3100 | 10.8100 | 0.6029 | 0.4333 | 0.4958 | |
Rang H:28 | 8.0500 | 5.3800 | 10.7600 | 0.6024 | 0.4354 | 0.4970 | |
Rang H:32 | 7.8000 | 5.7300 | 11.0100 | 0.5764 | 0.4228 | 0.4788 | |
Rang H:36 | 8.1800 | 5.1200 | 10.6300 | 0.6118 | 0.4411 | 0.5045 | |
Rang H:40 | 8.1400 | 5.4600 | 10.6700 | 0.5999 | 0.4400 | 0.4994 | |
Rang H:44 | 8.2200 | 5.3500 | 10.5900 | 0.6041 | 0.4456 | 0.5046 | |
Rang H:48 | 8.1600 | 5.3000 | 10.6500 | 0.6052 | 0.4395 | 0.5010 | |
Rang Q:16 | Rang H:12 | 8.3200 | 5.8100 | 10.4900 | 0.5895 | 0.4526 | 0.5026 |
Rang H:16 | 8.7500 | 5.5600 | 10.0600 | 0.6151 | 0.4719 | 0.5256 | |
Rang H:20 | 9.1500 | 5.3700 | 9.6600 | 0.6296 | 0.4944 | 0.5451 | |
Rang H:24 | 9.1200 | 5.2700 | 9.6900 | 0.6347 | 0.4933 | 0.5477 | |
Rang H:28 | 9.0000 | 5.4600 | 9.8100 | 0.6266 | 0.4879 | 0.5403 | |
Rang H:32 | 8.8200 | 5.8400 | 9.9900 | 0.6086 | 0.4775 | 0.5274 | |
Rang H:36 | 9.1000 | 5.5800 | 9.7100 | 0.6216 | 0.4901 | 0.5407 | |
Rang H:40 | 9.2200 | 5.4300 | 9.5900 | 0.6341 | 0.4979 | 0.5500 | |
Rang H:44 | 9.2400 | 5.2400 | 9.5700 | 0.6396 | 0.4987 | 0.5533 | |
Rang H:48 | 9.1800 | 5.4900 | 9.6300 | 0.6264 | 0.4954 | 0.5459 | |
Rang Q:20 | Rang H:12 | 9.1000 | 5.5600 | 9.7100 | 0.6246 | 0.4916 | 0.5419 |
Rang H:16 | 9.3100 | 5.5300 | 9.5000 | 0.6257 | 0.5020 | 0.5483 | |
Rang H:20 | 9.5000 | 5.7600 | 9.3100 | 0.6258 | 0.5110 | 0.5541 | |
Rang H:24 | 9.6500 | 5.5100 | 9.1600 | 0.6362 | 0.5192 | 0.5642 | |
Rang H:28 | 9.7000 | 5.6100 | 9.1100 | 0.6354 | 0.5228 | 0.5656 | |
Rang H:32 | 9.4300 | 5.9500 | 9.3800 | 0.6201 | 0.5082 | 0.5503 | |
Rang H:36 | 9.6000 | 5.6400 | 9.2100 | 0.6294 | 0.5185 | 0.5609 | |
Rang H:40 | 9.8200 | 5.3600 | 8.9900 | 0.6533 | 0.5297 | 0.5764 | |
Rang H:44 | 9.5000 | 5.7400 | 9.3100 | 0.6248 | 0.5128 | 0.5547 | |
Rang H:48 | 9.7200 | 5.4600 | 9.0900 | 0.6413 | 0.5221 | 0.5677 | |
Rang Q:24 | Rang H:12 | 9.2800 | 5.8700 | 9.5300 | 0.6203 | 0.5028 | 0.5473 |
Rang H:16 | 9.3200 | 5.6800 | 9.4900 | 0.6229 | 0.5042 | 0.5499 | |
Rang H:20 | 9.6400 | 5.7800 | 9.1700 | 0.6267 | 0.5226 | 0.5627 | |
Rang H:24 | 9.9500 | 5.7400 | 8.8600 | 0.6412 | 0.5365 | 0.5761 | |
Rang H:28 | 9.8800 | 5.9400 | 8.9300 | 0.6252 | 0.5319 | 0.5671 | |
Rang H:32 | 9.8100 | 6.0900 | 9.0000 | 0.6219 | 0.5300 | 0.5655 | |
Rang H:36 | 10.0900 | 5.7200 | 8.7200 | 0.6415 | 0.5432 | 0.5812 | |
Rang H:40 | 9.8600 | 6.0000 | 8.9500 | 0.6253 | 0.5326 | 0.5685 | |
Rang H:44 | 9.9500 | 5.9400 | 8.8600 | 0.6264 | 0.5356 | 0.5712 | |
Rang H:48 | 9.9000 | 5.7600 | 8.9100 | 0.6377 | 0.5329 | 0.5743 | |
Rang Q:28 | Rang H:12 | 9.4700 | 5.9200 | 9.3400 | 0.6160 | 0.5116 | 0.5507 |
Rang H:16 | 9.7100 | 6.1500 | 9.1000 | 0.6137 | 0.5225 | 0.5567 | |
Rang H:20 | 9.8400 | 5.9600 | 8.9700 | 0.6206 | 0.5292 | 0.5643 | |
Rang H:24 | 9.8700 | 6.1300 | 8.9400 | 0.6181 | 0.5318 | 0.5652 | |
Rang H:28 | 10.2800 | 5.8500 | 8.5300 | 0.6381 | 0.5517 | 0.5846 | |
Rang H:32 | 9.7400 | 6.4900 | 9.0700 | 0.6013 | 0.5252 | 0.5540 | |
Rang H:36 | 10.2600 | 5.7400 | 8.5500 | 0.6399 | 0.5536 | 0.5861 | |
Rang H:40 | 10.0100 | 5.9200 | 8.8000 | 0.6275 | 0.5374 | 0.5722 | |
Rang H:44 | 10.0300 | 6.0100 | 8.7800 | 0.6251 | 0.5410 | 0.5729 | |
Rang H:48 | 10.0100 | 6.3300 | 8.8000 | 0.6089 | 0.5413 | 0.5672 | |
Rang Q:32 | Rang H:12 | 9.6000 | 6.1500 | 9.2100 | 0.6104 | 0.5196 | 0.5530 |
Rang H:16 | 9.9200 | 6.4400 | 8.8900 | 0.6128 | 0.5343 | 0.5640 | |
Rang H:20 | 9.9000 | 6.2200 | 8.9100 | 0.6112 | 0.5330 | 0.5634 | |
Rang H:24 | 9.9500 | 6.7200 | 8.8600 | 0.5970 | 0.5320 | 0.5554 | |
Rang H:28 | 9.8100 | 6.6600 | 9.0000 | 0.5956 | 0.5263 | 0.5523 | |
Rang H:32 | 10.3900 | 5.8100 | 8.4200 | 0.6421 | 0.5603 | 0.5922 | |
Rang H:36 | 10.3000 | 6.0000 | 8.5100 | 0.6341 | 0.5557 | 0.5836 | |
Rang H:40 | 10.1200 | 6.0500 | 8.6900 | 0.6271 | 0.5427 | 0.5749 | |
Rang H:44 | 10.0600 | 6.1900 | 8.7500 | 0.6158 | 0.5403 | 0.5688 | |
Rang H:48 | 10.2900 | 5.9900 | 8.5200 | 0.6320 | 0.5540 | 0.5840 | |
Rang Q:36 | Rang H:12 | 9.6500 | 6.0100 | 9.1600 | 0.6152 | 0.5203 | 0.5563 |
Rang H:16 | 9.9900 | 5.9500 | 8.8200 | 0.6236 | 0.5380 | 0.5704 | |
Rang H:20 | 10.0900 | 6.2400 | 8.7200 | 0.6149 | 0.5430 | 0.5706 | |
Rang H:24 | 10.3900 | 6.1200 | 8.4200 | 0.6286 | 0.5563 | 0.5832 | |
Rang H:28 | 9.8400 | 6.4400 | 8.9700 | 0.6013 | 0.5313 | 0.5576 | |
Rang H:32 | 9.9300 | 6.5600 | 8.8800 | 0.5982 | 0.5313 | 0.5564 | |
Rang H:36 | 10.2600 | 6.4300 | 8.5500 | 0.6135 | 0.5523 | 0.5748 | |
Rang H:40 | 10.5400 | 6.1400 | 8.2700 | 0.6296 | 0.5655 | 0.5891 | |
Rang H:44 | 10.1200 | 6.3100 | 8.6900 | 0.6135 | 0.5404 | 0.5679 | |
Rang H:48 | 10.2600 | 6.2300 | 8.5500 | 0.6212 | 0.5527 | 0.5783 | |
Rang Q:40 | Rang H:12 | 9.5900 | 6.0300 | 9.2200 | 0.6104 | 0.5199 | 0.5546 |
Rang H:16 | 9.5600 | 6.5400 | 9.2500 | 0.5932 | 0.5137 | 0.5426 | |
Rang H:20 | 10.1100 | 6.4100 | 8.7000 | 0.6077 | 0.5430 | 0.5662 | |
Rang H:24 | 9.9800 | 6.4600 | 8.8300 | 0.6054 | 0.5332 | 0.5600 | |
Rang H:28 | 9.9900 | 6.5600 | 8.8200 | 0.6010 | 0.5347 | 0.5587 | |
Rang H:32 | 10.0000 | 6.6700 | 8.8100 | 0.6010 | 0.5370 | 0.5604 | |
Rang H:36 | 10.1300 | 6.5600 | 8.6800 | 0.6080 | 0.5422 | 0.5664 | |
Rang H:40 | 10.2800 | 6.3400 | 8.5300 | 0.6212 | 0.5513 | 0.5773 | |
Rang H:44 | 10.1400 | 6.4000 | 8.6700 | 0.6150 | 0.5462 | 0.5710 | |
Rang H:48 | 9.9300 | 6.5100 | 8.8800 | 0.6049 | 0.5340 | 0.5600 | |
Rang Q:44 | Rang H:12 | 9.8900 | 6.1300 | 8.9200 | 0.6169 | 0.5324 | 0.5634 |
Rang H:16 | 10.1800 | 6.4000 | 8.6300 | 0.6146 | 0.5461 | 0.5700 | |
Rang H:20 | 10.1700 | 6.3200 | 8.6400 | 0.6169 | 0.5444 | 0.5721 | |
Rang H:24 | 10.3500 | 6.1200 | 8.4600 | 0.6294 | 0.5528 | 0.5823 | |
Rang H:28 | 9.9800 | 6.7700 | 8.8300 | 0.5929 | 0.5333 | 0.5547 | |
Rang H:32 | 10.3200 | 6.1600 | 8.4900 | 0.6251 | 0.5522 | 0.5792 | |
Rang H:36 | 10.0700 | 6.6300 | 8.7400 | 0.6042 | 0.5411 | 0.5633 | |
Rang H:40 | 10.1600 | 6.6100 | 8.6500 | 0.6071 | 0.5418 | 0.5655 | |
Rang H:44 | 9.9200 | 6.8400 | 8.8900 | 0.5939 | 0.5309 | 0.5534 | |
Rang H:48 | 9.8500 | 6.8300 | 8.9600 | 0.5943 | 0.5299 | 0.5526 | |
Rang Q:48 | Rang H:12 | 10.0200 | 6.1400 | 8.7900 | 0.6150 | 0.5404 | 0.5683 |
Rang H:16 | 9.8700 | 6.4600 | 8.9400 | 0.6021 | 0.5299 | 0.5561 | |
Rang H:20 | 9.7000 | 6.6700 | 9.1100 | 0.5925 | 0.5202 | 0.5470 | |
Rang H:24 | 9.8600 | 6.7000 | 8.9500 | 0.5950 | 0.5281 | 0.5523 | |
Rang H:28 | 10.0000 | 6.5600 | 8.8100 | 0.6015 | 0.5334 | 0.5592 | |
Rang H:32 | 10.1400 | 6.6100 | 8.6700 | 0.6039 | 0.5411 | 0.5641 | |
Rang H:36 | 9.3900 | 7.2300 | 9.4200 | 0.5643 | 0.5053 | 0.5259 | |
Rang H:40 | 9.8700 | 6.9500 | 8.9400 | 0.5863 | 0.5290 | 0.5500 | |
Rang H:44 | 9.8300 | 6.7700 | 8.9800 | 0.5925 | 0.5271 | 0.5506 | |
Rang H:48 | 9.6700 | 7.1000 | 9.1400 | 0.5761 | 0.5151 | 0.5374 |
3 seconds results | True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|---|
Rang Q:12 | Rang H:12 | 10.0300 | 3.0100 | 8.7800 | 0.7840 | 0.5425 | 0.6296 |
Rang H:16 | 10.1600 | 3.1100 | 8.6500 | 0.7796 | 0.5506 | 0.6341 | |
Rang H:20 | 10.1900 | 3.1500 | 8.6200 | 0.7809 | 0.5523 | 0.6356 | |
Rang H:24 | 10.2000 | 3.1100 | 8.6100 | 0.7781 | 0.5510 | 0.6344 | |
Rang H:28 | 10.2800 | 3.1500 | 8.5300 | 0.7792 | 0.5554 | 0.6378 | |
Rang H:32 | 10.2800 | 3.2500 | 8.5300 | 0.7750 | 0.5554 | 0.6355 | |
Rang H:36 | 10.2800 | 3.0200 | 8.5300 | 0.7814 | 0.5549 | 0.6387 | |
Rang H:40 | 10.2900 | 3.3100 | 8.5200 | 0.7698 | 0.5567 | 0.6357 | |
Rang H:44 | 10.4700 | 3.1000 | 8.3400 | 0.7838 | 0.5669 | 0.6470 | |
Rang H:48 | 10.3600 | 3.1000 | 8.4500 | 0.7826 | 0.5596 | 0.6419 | |
Rang Q:16 | Rang H:12 | 10.8700 | 3.2600 | 7.9400 | 0.7837 | 0.5881 | 0.6598 |
Rang H:16 | 11.0700 | 3.2400 | 7.7400 | 0.7889 | 0.5961 | 0.6684 | |
Rang H:20 | 11.3500 | 3.1700 | 7.4600 | 0.7968 | 0.6126 | 0.6813 | |
Rang H:24 | 11.2400 | 3.1500 | 7.5700 | 0.7952 | 0.6075 | 0.6792 | |
Rang H:28 | 11.2600 | 3.2000 | 7.5500 | 0.7908 | 0.6090 | 0.6774 | |
Rang H:32 | 11.3600 | 3.3000 | 7.4500 | 0.7898 | 0.6110 | 0.6785 | |
Rang H:36 | 11.3300 | 3.3500 | 7.4800 | 0.7847 | 0.6094 | 0.6764 | |
Rang H:40 | 11.2800 | 3.3700 | 7.5300 | 0.7842 | 0.6073 | 0.6746 | |
Rang H:44 | 11.2000 | 3.2800 | 7.6100 | 0.7850 | 0.6027 | 0.6728 | |
Rang H:48 | 11.4100 | 3.2600 | 7.4000 | 0.7890 | 0.6146 | 0.6814 | |
Rang Q:20 | Rang H:12 | 11.2400 | 3.4200 | 7.5700 | 0.7815 | 0.6051 | 0.6713 |
Rang H:16 | 11.6200 | 3.2200 | 7.1900 | 0.7979 | 0.6272 | 0.6911 | |
Rang H:20 | 11.6600 | 3.6000 | 7.1500 | 0.7806 | 0.6272 | 0.6848 | |
Rang H:24 | 11.7100 | 3.4500 | 7.1000 | 0.7850 | 0.6305 | 0.6896 | |
Rang H:28 | 11.9000 | 3.4100 | 6.9100 | 0.7902 | 0.6418 | 0.6981 | |
Rang H:32 | 11.6700 | 3.7100 | 7.1400 | 0.7712 | 0.6273 | 0.6815 | |
Rang H:36 | 11.7900 | 3.4500 | 7.0200 | 0.7855 | 0.6354 | 0.6923 | |
Rang H:40 | 11.8100 | 3.3700 | 7.0000 | 0.7917 | 0.6358 | 0.6945 | |
Rang H:44 | 11.6200 | 3.6200 | 7.1900 | 0.7738 | 0.6267 | 0.6817 | |
Rang H:48 | 11.7800 | 3.4000 | 7.0300 | 0.7894 | 0.6333 | 0.6927 | |
Rang Q:24 | Rang H:12 | 11.5500 | 3.6000 | 7.2600 | 0.7756 | 0.6227 | 0.6803 |
Rang H:16 | 11.5800 | 3.4200 | 7.2300 | 0.7823 | 0.6253 | 0.6854 | |
Rang H:20 | 11.7900 | 3.6300 | 7.0200 | 0.7750 | 0.6354 | 0.6887 | |
Rang H:24 | 12.0100 | 3.6800 | 6.8000 | 0.7801 | 0.6457 | 0.6963 | |
Rang H:28 | 12.0900 | 3.7300 | 6.7200 | 0.7730 | 0.6496 | 0.6961 | |
Rang H:32 | 12.1800 | 3.7200 | 6.6300 | 0.7765 | 0.6551 | 0.7018 | |
Rang H:36 | 12.0000 | 3.8100 | 6.8100 | 0.7727 | 0.6459 | 0.6944 | |
Rang H:40 | 11.9900 | 3.8700 | 6.8200 | 0.7668 | 0.6457 | 0.6925 | |
Rang H:44 | 12.2700 | 3.6200 | 6.5400 | 0.7790 | 0.6583 | 0.7056 | |
Rang H:48 | 12.0100 | 3.6500 | 6.8000 | 0.7746 | 0.6453 | 0.6964 | |
Rang Q:28 | Rang H:12 | 11.7300 | 3.6600 | 7.0800 | 0.7717 | 0.6318 | 0.6841 |
Rang H:16 | 12.0000 | 3.8600 | 6.8100 | 0.7695 | 0.6463 | 0.6920 | |
Rang H:20 | 12.0300 | 3.7700 | 6.7800 | 0.7678 | 0.6466 | 0.6929 | |
Rang H:24 | 12.2700 | 3.7300 | 6.5400 | 0.7758 | 0.6588 | 0.7039 | |
Rang H:28 | 12.2400 | 3.8900 | 6.5700 | 0.7679 | 0.6576 | 0.6996 | |
Rang H:32 | 12.2000 | 4.0300 | 6.6100 | 0.7581 | 0.6554 | 0.6944 | |
Rang H:36 | 12.1500 | 3.8500 | 6.6600 | 0.7626 | 0.6554 | 0.6958 | |
Rang H:40 | 12.1700 | 3.7600 | 6.6400 | 0.7703 | 0.6540 | 0.6990 | |
Rang H:44 | 12.1500 | 3.8900 | 6.6600 | 0.7629 | 0.6532 | 0.6947 | |
Rang H:48 | 12.4000 | 3.9400 | 6.4100 | 0.7657 | 0.6672 | 0.7046 | |
Rang Q:32 | Rang H:12 | 11.9200 | 3.8300 | 6.8900 | 0.7624 | 0.6409 | 0.6857 |
Rang H:16 | 12.2900 | 4.0700 | 6.5200 | 0.7588 | 0.6591 | 0.6967 | |
Rang H:20 | 12.1900 | 3.9300 | 6.6200 | 0.7604 | 0.6551 | 0.6954 | |
Rang H:24 | 12.3900 | 4.2800 | 6.4200 | 0.7525 | 0.6645 | 0.6963 | |
Rang H:28 | 12.3200 | 4.1500 | 6.4900 | 0.7550 | 0.6607 | 0.6960 | |
Rang H:32 | 12.4000 | 3.8000 | 6.4100 | 0.7699 | 0.6666 | 0.7067 | |
Rang H:36 | 12.3700 | 3.9300 | 6.4400 | 0.7675 | 0.6656 | 0.7023 | |
Rang H:40 | 12.3700 | 3.8000 | 6.4400 | 0.7728 | 0.6652 | 0.7065 | |
Rang H:44 | 12.3100 | 3.9400 | 6.5000 | 0.7615 | 0.6626 | 0.7001 | |
Rang H:48 | 12.5900 | 3.6900 | 6.2200 | 0.7794 | 0.6758 | 0.7158 | |
Rang Q:36 | Rang H:12 | 11.8400 | 3.8200 | 6.9700 | 0.7617 | 0.6383 | 0.6846 |
Rang H:16 | 12.1200 | 3.8200 | 6.6900 | 0.7624 | 0.6521 | 0.6935 | |
Rang H:20 | 12.2200 | 4.1100 | 6.5900 | 0.7527 | 0.6556 | 0.6922 | |
Rang H:24 | 12.4500 | 4.0600 | 6.3600 | 0.7607 | 0.6680 | 0.7027 | |
Rang H:28 | 12.2000 | 4.0800 | 6.6100 | 0.7540 | 0.6556 | 0.6921 | |
Rang H:32 | 12.4700 | 4.0200 | 6.3400 | 0.7612 | 0.6666 | 0.7023 | |
Rang H:36 | 12.4600 | 4.2300 | 6.3500 | 0.7521 | 0.6701 | 0.7006 | |
Rang H:40 | 12.6100 | 4.0700 | 6.2000 | 0.7613 | 0.6762 | 0.7076 | |
Rang H:44 | 12.3900 | 4.0400 | 6.4200 | 0.7593 | 0.6646 | 0.7004 | |
Rang H:48 | 12.4100 | 4.0800 | 6.4000 | 0.7562 | 0.6675 | 0.7005 | |
Rang Q:40 | Rang H:12 | 11.9100 | 3.7100 | 6.9000 | 0.7695 | 0.6424 | 0.6906 |
Rang H:16 | 12.0700 | 4.0300 | 6.7400 | 0.7560 | 0.6481 | 0.6874 | |
Rang H:20 | 12.3800 | 4.1400 | 6.4300 | 0.7524 | 0.6653 | 0.6966 | |
Rang H:24 | 12.4000 | 4.0400 | 6.4100 | 0.7615 | 0.6643 | 0.7003 | |
Rang H:28 | 12.4100 | 4.1400 | 6.4000 | 0.7535 | 0.6642 | 0.6968 | |
Rang H:32 | 12.3300 | 4.3400 | 6.4800 | 0.7477 | 0.6613 | 0.6929 | |
Rang H:36 | 12.3200 | 4.3700 | 6.4900 | 0.7455 | 0.6609 | 0.6923 | |
Rang H:40 | 12.5700 | 4.0500 | 6.2400 | 0.7640 | 0.6744 | 0.7078 | |
Rang H:44 | 12.2500 | 4.2900 | 6.5600 | 0.7496 | 0.6595 | 0.6917 | |
Rang H:48 | 12.3500 | 4.0900 | 6.4600 | 0.7629 | 0.6641 | 0.7007 | |
Rang Q:44 | Rang H:12 | 12.2700 | 3.7500 | 6.5400 | 0.7779 | 0.6607 | 0.7039 |
Rang H:16 | 12.3500 | 4.2300 | 6.4600 | 0.7528 | 0.6638 | 0.6947 | |
Rang H:20 | 12.4100 | 4.0800 | 6.4000 | 0.7581 | 0.6660 | 0.7013 | |
Rang H:24 | 12.4400 | 4.0300 | 6.3700 | 0.7588 | 0.6659 | 0.7017 | |
Rang H:28 | 12.4200 | 4.3300 | 6.3900 | 0.7490 | 0.6662 | 0.6964 | |
Rang H:32 | 12.5000 | 3.9800 | 6.3100 | 0.7616 | 0.6711 | 0.7050 | |
Rang H:36 | 12.4700 | 4.2300 | 6.3400 | 0.7535 | 0.6699 | 0.6996 | |
Rang H:40 | 12.4100 | 4.3600 | 6.4000 | 0.7487 | 0.6635 | 0.6947 | |
Rang H:44 | 12.3700 | 4.3900 | 6.4400 | 0.7455 | 0.6631 | 0.6926 | |
Rang H:48 | 12.3500 | 4.3300 | 6.4600 | 0.7481 | 0.6628 | 0.6935 | |
Rang Q:48 | Rang H:12 | 12.2400 | 3.9200 | 6.5700 | 0.7651 | 0.6577 | 0.6976 |
Rang H:16 | 12.3000 | 4.0300 | 6.5100 | 0.7610 | 0.6612 | 0.6971 | |
Rang H:20 | 12.1800 | 4.1900 | 6.6300 | 0.7508 | 0.6541 | 0.6900 | |
Rang H:24 | 12.2500 | 4.3100 | 6.5600 | 0.7435 | 0.6548 | 0.6869 | |
Rang H:28 | 12.2500 | 4.3100 | 6.5600 | 0.7403 | 0.6559 | 0.6878 | |
Rang H:32 | 12.3500 | 4.4000 | 6.4600 | 0.7401 | 0.6614 | 0.6901 | |
Rang H:36 | 12.1700 | 4.4500 | 6.6400 | 0.7407 | 0.6531 | 0.6839 | |
Rang H:40 | 12.2900 | 4.5300 | 6.5200 | 0.7350 | 0.6579 | 0.6866 | |
Rang H:44 | 12.1500 | 4.4500 | 6.6600 | 0.7381 | 0.6516 | 0.6830 | |
Rang H:48 | 12.3200 | 4.4500 | 6.4900 | 0.7410 | 0.6601 | 0.6895 |
In this condition, we only keep the ranks leading to the highest F measure.
In that sense, it's an optimistic upper bound on metrics.
hide.printmd("**A 0.5 secondes:**")
best_chr_zero_five = hide.best_f_one_score_rank(zero_five_full)
hide.printmd("**A 3 secondes:**")
best_chr_three = hide.best_f_one_score_rank(three_full)
A 0.5 secondes:
True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|
Maximizing the f measure on each song: | 12.51 | 3.75 | 6.3 | 0.7719 | 0.6721 | 0.7116 |
A 3 secondes:
True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|
Maximizing the f measure on each song: | 14.3 | 2.09 | 4.51 | 0.8783 | 0.7696 | 0.8143 |
Below is presented the distribution of the optimal ranks in the "oracle ranks" condition, i.e. the distribution of the ranks for $H$ and $Q$ which result in the highest F measure for the different songs.
hide.plot_3d_ranks_study(zero_five_full, ranks_rhythm, ranks_pattern)
Below is shown the distribution histogram of the F measure obtained with the oracle ranks.
hide.plot_f_mes_histogram(zero_five_full)
This kernel focuses on local similarities in the 8 bars surrounding each bar of the diagonal (4 bars in the future, 4 bars in the past). Concretely, this kernel is a matrix where the only non-zero elements are the 8 closest bands parallel to the diagonal.
It looks like:
(or, in a matrix form: $\left[ \begin{matrix} 0 & 1 & 1 & 1& 1 & 0 & 0 & 0\\ 1 & 0 & 1 & 1& 1 & 1 & 0 & 0\\ 1 & 1 & 0 & 1& 1 & 1 & 1 & 0\\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1\\ 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1\\ 0 & 0 & 1& 1 & 1 & 1 & 0 & 1\\ 0 & 0 & 0& 1 & 1 & 1 & 1 & 0\\ \end{matrix} \right]$ (of size 8 here)).
Mathematically, for a segment ($b_1, b_2$), the associated cost will be $c_{b_1,b_2} = \frac{1}{b_2 - b_1 + 1}\sum_{i,j = 0, 1 \leq |i - j| \leq 4}^{n - 1} a_{i + b_1, j + b_1}$.
Below are segmentation results with different ranks values, but each time fixed over the entire RWC Pop dataset.
Results are computed with tolerance of respectively 0.5 seconds and 3 seconds.
annotations_type = "MIREX10"
ranks_rhythm = [12,16,20,24,28,32,36,40,44,48]
ranks_pattern = [12,16,20,24,28,32,36,40,44,48]
zero_five_eight, three_eight = hide.compute_ranks_RWC(ranks_rhythm,ranks_pattern, W = "chromas", annotations_type = annotations_type,
subdivision=96, penalty_weight = 1,penalty_func = "modulo8", convolution_type = "eight_bands")
0.5 seconds results | True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|---|
Rang Q:12 | Rang H:12 | 10.3000 | 13.3900 | 8.5100 | 0.4498 | 0.5533 | 0.4900 |
Rang H:16 | 10.8100 | 12.7400 | 8.0000 | 0.4753 | 0.5809 | 0.5163 | |
Rang H:20 | 11.3800 | 11.9200 | 7.4300 | 0.5059 | 0.6083 | 0.5455 | |
Rang H:24 | 11.0700 | 12.4400 | 7.7400 | 0.4865 | 0.5916 | 0.5271 | |
Rang H:28 | 11.1300 | 12.2200 | 7.6800 | 0.4919 | 0.5950 | 0.5315 | |
Rang H:32 | 10.6900 | 12.9300 | 8.1200 | 0.4684 | 0.5719 | 0.5083 | |
Rang H:36 | 11.1700 | 12.2500 | 7.6400 | 0.4945 | 0.5969 | 0.5340 | |
Rang H:40 | 11.3700 | 12.2500 | 7.4400 | 0.5002 | 0.6074 | 0.5416 | |
Rang H:44 | 11.3100 | 12.2500 | 7.5000 | 0.4972 | 0.6036 | 0.5382 | |
Rang H:48 | 11.1200 | 12.3300 | 7.6900 | 0.4888 | 0.5936 | 0.5294 | |
Rang Q:16 | Rang H:12 | 10.9900 | 12.7400 | 7.8200 | 0.4816 | 0.5930 | 0.5244 |
Rang H:16 | 11.5700 | 11.7400 | 7.2400 | 0.5172 | 0.6173 | 0.5560 | |
Rang H:20 | 11.7900 | 11.7900 | 7.0200 | 0.5234 | 0.6325 | 0.5655 | |
Rang H:24 | 11.5100 | 12.0200 | 7.3000 | 0.5098 | 0.6211 | 0.5526 | |
Rang H:28 | 11.7200 | 11.7900 | 7.0900 | 0.5189 | 0.6268 | 0.5605 | |
Rang H:32 | 11.1700 | 12.4300 | 7.6400 | 0.4953 | 0.6009 | 0.5363 | |
Rang H:36 | 11.4100 | 12.0700 | 7.4000 | 0.5055 | 0.6091 | 0.5451 | |
Rang H:40 | 11.6300 | 11.9200 | 7.1800 | 0.5130 | 0.6238 | 0.5559 | |
Rang H:44 | 11.7200 | 11.8000 | 7.0900 | 0.5193 | 0.6263 | 0.5608 | |
Rang H:48 | 11.5800 | 11.7600 | 7.2300 | 0.5169 | 0.6190 | 0.5561 | |
Rang Q:20 | Rang H:12 | 11.7700 | 11.9600 | 7.0400 | 0.5160 | 0.6306 | 0.5605 |
Rang H:16 | 11.7700 | 11.7400 | 7.0400 | 0.5194 | 0.6266 | 0.5610 | |
Rang H:20 | 12.0000 | 11.3600 | 6.8100 | 0.5355 | 0.6406 | 0.5762 | |
Rang H:24 | 12.0600 | 11.4000 | 6.7500 | 0.5366 | 0.6447 | 0.5783 | |
Rang H:28 | 11.9300 | 11.3800 | 6.8800 | 0.5338 | 0.6399 | 0.5753 | |
Rang H:32 | 11.7800 | 11.7200 | 7.0300 | 0.5272 | 0.6341 | 0.5690 | |
Rang H:36 | 11.9300 | 11.3800 | 6.8800 | 0.5365 | 0.6408 | 0.5775 | |
Rang H:40 | 12.1200 | 11.1500 | 6.6900 | 0.5441 | 0.6506 | 0.5855 | |
Rang H:44 | 11.5900 | 11.8700 | 7.2200 | 0.5195 | 0.6234 | 0.5592 | |
Rang H:48 | 11.8400 | 11.5800 | 6.9700 | 0.5296 | 0.6333 | 0.5697 | |
Rang Q:24 | Rang H:12 | 11.7200 | 11.8100 | 7.0900 | 0.5213 | 0.6280 | 0.5632 |
Rang H:16 | 11.8300 | 11.3900 | 6.9800 | 0.5321 | 0.6334 | 0.5713 | |
Rang H:20 | 11.8800 | 11.6200 | 6.9300 | 0.5287 | 0.6385 | 0.5715 | |
Rang H:24 | 11.9900 | 11.3200 | 6.8200 | 0.5368 | 0.6416 | 0.5773 | |
Rang H:28 | 12.1700 | 11.2000 | 6.6400 | 0.5445 | 0.6510 | 0.5858 | |
Rang H:32 | 11.8800 | 11.5600 | 6.9300 | 0.5325 | 0.6391 | 0.5746 | |
Rang H:36 | 12.1300 | 11.0900 | 6.6800 | 0.5460 | 0.6491 | 0.5862 | |
Rang H:40 | 11.9500 | 11.3500 | 6.8600 | 0.5337 | 0.6392 | 0.5750 | |
Rang H:44 | 12.1100 | 11.0600 | 6.7000 | 0.5434 | 0.6467 | 0.5836 | |
Rang H:48 | 12.2200 | 10.9500 | 6.5900 | 0.5539 | 0.6535 | 0.5920 | |
Rang Q:28 | Rang H:12 | 11.8400 | 11.4100 | 6.9700 | 0.5331 | 0.6374 | 0.5736 |
Rang H:16 | 11.8400 | 11.6000 | 6.9700 | 0.5237 | 0.6299 | 0.5648 | |
Rang H:20 | 11.8900 | 11.3000 | 6.9200 | 0.5317 | 0.6342 | 0.5714 | |
Rang H:24 | 11.9500 | 11.1300 | 6.8600 | 0.5394 | 0.6384 | 0.5780 | |
Rang H:28 | 12.0700 | 11.1300 | 6.7400 | 0.5430 | 0.6443 | 0.5821 | |
Rang H:32 | 12.0000 | 11.3900 | 6.8100 | 0.5332 | 0.6425 | 0.5756 | |
Rang H:36 | 12.4200 | 10.9000 | 6.3900 | 0.5564 | 0.6663 | 0.5990 | |
Rang H:40 | 12.2200 | 10.8900 | 6.5900 | 0.5506 | 0.6526 | 0.5900 | |
Rang H:44 | 11.8900 | 11.0300 | 6.9200 | 0.5370 | 0.6362 | 0.5762 | |
Rang H:48 | 12.1400 | 11.2400 | 6.6700 | 0.5420 | 0.6497 | 0.5842 | |
Rang Q:32 | Rang H:12 | 11.6100 | 11.7300 | 7.2000 | 0.5210 | 0.6223 | 0.5606 |
Rang H:16 | 11.9700 | 11.3700 | 6.8400 | 0.5368 | 0.6435 | 0.5785 | |
Rang H:20 | 11.7700 | 11.4300 | 7.0400 | 0.5318 | 0.6323 | 0.5708 | |
Rang H:24 | 11.8300 | 11.7300 | 6.9800 | 0.5214 | 0.6329 | 0.5647 | |
Rang H:28 | 12.1200 | 11.3700 | 6.6900 | 0.5347 | 0.6493 | 0.5796 | |
Rang H:32 | 12.0600 | 11.0500 | 6.7500 | 0.5401 | 0.6471 | 0.5822 | |
Rang H:36 | 11.8100 | 11.2900 | 7.0000 | 0.5337 | 0.6328 | 0.5715 | |
Rang H:40 | 11.8500 | 11.2900 | 6.9600 | 0.5320 | 0.6336 | 0.5709 | |
Rang H:44 | 11.6100 | 11.4500 | 7.2000 | 0.5213 | 0.6222 | 0.5601 | |
Rang H:48 | 11.8400 | 11.0200 | 6.9700 | 0.5376 | 0.6347 | 0.5749 | |
Rang Q:36 | Rang H:12 | 11.9500 | 11.2500 | 6.8600 | 0.5375 | 0.6394 | 0.5767 |
Rang H:16 | 11.9300 | 10.8700 | 6.8800 | 0.5412 | 0.6392 | 0.5791 | |
Rang H:20 | 11.9600 | 11.1100 | 6.8500 | 0.5364 | 0.6393 | 0.5763 | |
Rang H:24 | 11.8400 | 11.2200 | 6.9700 | 0.5324 | 0.6320 | 0.5707 | |
Rang H:28 | 11.8500 | 11.0600 | 6.9600 | 0.5343 | 0.6344 | 0.5736 | |
Rang H:32 | 11.5400 | 11.5500 | 7.2700 | 0.5163 | 0.6144 | 0.5543 | |
Rang H:36 | 12.0000 | 10.9500 | 6.8100 | 0.5445 | 0.6447 | 0.5833 | |
Rang H:40 | 12.1700 | 10.9400 | 6.6400 | 0.5457 | 0.6509 | 0.5865 | |
Rang H:44 | 11.6800 | 11.4200 | 7.1300 | 0.5225 | 0.6249 | 0.5626 | |
Rang H:48 | 12.1700 | 10.7500 | 6.6400 | 0.5493 | 0.6519 | 0.5891 | |
Rang Q:40 | Rang H:12 | 11.6800 | 11.3200 | 7.1300 | 0.5269 | 0.6266 | 0.5658 |
Rang H:16 | 11.7000 | 11.2200 | 7.1100 | 0.5339 | 0.6268 | 0.5697 | |
Rang H:20 | 12.1500 | 11.0000 | 6.6600 | 0.5466 | 0.6499 | 0.5864 | |
Rang H:24 | 11.9700 | 10.9000 | 6.8400 | 0.5419 | 0.6386 | 0.5794 | |
Rang H:28 | 11.6900 | 11.0900 | 7.1200 | 0.5308 | 0.6263 | 0.5684 | |
Rang H:32 | 11.8900 | 10.9000 | 6.9200 | 0.5389 | 0.6370 | 0.5773 | |
Rang H:36 | 12.2400 | 10.7100 | 6.5700 | 0.5492 | 0.6551 | 0.5908 | |
Rang H:40 | 11.8800 | 11.1100 | 6.9300 | 0.5386 | 0.6361 | 0.5764 | |
Rang H:44 | 11.7200 | 11.3200 | 7.0900 | 0.5288 | 0.6291 | 0.5679 | |
Rang H:48 | 11.7200 | 11.2500 | 7.0900 | 0.5280 | 0.6270 | 0.5669 | |
Rang Q:44 | Rang H:12 | 11.6600 | 11.4700 | 7.1500 | 0.5285 | 0.6231 | 0.5643 |
Rang H:16 | 12.2600 | 10.8300 | 6.5500 | 0.5508 | 0.6554 | 0.5915 | |
Rang H:20 | 11.6400 | 11.0500 | 7.1700 | 0.5309 | 0.6185 | 0.5645 | |
Rang H:24 | 11.8700 | 11.0700 | 6.9400 | 0.5377 | 0.6351 | 0.5754 | |
Rang H:28 | 11.5900 | 11.1200 | 7.2200 | 0.5255 | 0.6189 | 0.5625 | |
Rang H:32 | 11.7700 | 10.9800 | 7.0400 | 0.5362 | 0.6280 | 0.5715 | |
Rang H:36 | 11.6800 | 11.0500 | 7.1300 | 0.5312 | 0.6239 | 0.5674 | |
Rang H:40 | 11.7000 | 11.0700 | 7.1100 | 0.5268 | 0.6226 | 0.5643 | |
Rang H:44 | 11.5500 | 11.2400 | 7.2600 | 0.5232 | 0.6152 | 0.5586 | |
Rang H:48 | 11.2400 | 11.4400 | 7.5700 | 0.5081 | 0.6039 | 0.5453 | |
Rang Q:48 | Rang H:12 | 11.9800 | 10.7300 | 6.8300 | 0.5500 | 0.6417 | 0.5849 |
Rang H:16 | 11.6500 | 11.2400 | 7.1600 | 0.5242 | 0.6212 | 0.5615 | |
Rang H:20 | 11.5800 | 11.2500 | 7.2300 | 0.5228 | 0.6187 | 0.5602 | |
Rang H:24 | 11.3000 | 11.6700 | 7.5100 | 0.5034 | 0.6035 | 0.5428 | |
Rang H:28 | 11.7800 | 10.9300 | 7.0300 | 0.5326 | 0.6292 | 0.5712 | |
Rang H:32 | 11.7200 | 11.1100 | 7.0900 | 0.5271 | 0.6260 | 0.5655 | |
Rang H:36 | 11.2300 | 11.5200 | 7.5800 | 0.5034 | 0.5981 | 0.5407 | |
Rang H:40 | 11.7300 | 10.8500 | 7.0800 | 0.5314 | 0.6249 | 0.5684 | |
Rang H:44 | 11.2300 | 11.3800 | 7.5800 | 0.5098 | 0.6021 | 0.5452 | |
Rang H:48 | 11.1100 | 11.6600 | 7.7000 | 0.4993 | 0.5913 | 0.5351 |
3 seconds results | True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|---|
Rang Q:12 | Rang H:12 | 14.1200 | 9.5700 | 4.6900 | 0.6178 | 0.7543 | 0.6714 |
Rang H:16 | 14.2700 | 9.2800 | 4.5400 | 0.6282 | 0.7621 | 0.6807 | |
Rang H:20 | 14.3400 | 8.9600 | 4.4700 | 0.6392 | 0.7659 | 0.6887 | |
Rang H:24 | 14.2600 | 9.2500 | 4.5500 | 0.6284 | 0.7614 | 0.6805 | |
Rang H:28 | 14.4000 | 8.9500 | 4.4100 | 0.6406 | 0.7692 | 0.6902 | |
Rang H:32 | 14.3800 | 9.2400 | 4.4300 | 0.6338 | 0.7671 | 0.6854 | |
Rang H:36 | 14.3000 | 9.1200 | 4.5100 | 0.6321 | 0.7642 | 0.6838 | |
Rang H:40 | 14.3800 | 9.2400 | 4.4300 | 0.6328 | 0.7687 | 0.6859 | |
Rang H:44 | 14.5000 | 9.0600 | 4.3100 | 0.6381 | 0.7742 | 0.6914 | |
Rang H:48 | 14.4500 | 9.0000 | 4.3600 | 0.6390 | 0.7729 | 0.6915 | |
Rang Q:16 | Rang H:12 | 14.4800 | 9.2500 | 4.3300 | 0.6366 | 0.7753 | 0.6900 |
Rang H:16 | 14.6000 | 8.7100 | 4.2100 | 0.6524 | 0.7801 | 0.7023 | |
Rang H:20 | 14.8800 | 8.7000 | 3.9300 | 0.6587 | 0.7970 | 0.7126 | |
Rang H:24 | 14.6800 | 8.8500 | 4.1300 | 0.6509 | 0.7867 | 0.7031 | |
Rang H:28 | 14.6700 | 8.8400 | 4.1400 | 0.6479 | 0.7828 | 0.7006 | |
Rang H:32 | 14.6200 | 8.9800 | 4.1900 | 0.6478 | 0.7828 | 0.7001 | |
Rang H:36 | 14.4000 | 9.0800 | 4.4100 | 0.6401 | 0.7701 | 0.6904 | |
Rang H:40 | 14.4300 | 9.1200 | 4.3800 | 0.6367 | 0.7717 | 0.6895 | |
Rang H:44 | 14.4800 | 9.0400 | 4.3300 | 0.6426 | 0.7745 | 0.6940 | |
Rang H:48 | 14.6100 | 8.7300 | 4.2000 | 0.6528 | 0.7818 | 0.7028 | |
Rang Q:20 | Rang H:12 | 14.8400 | 8.8900 | 3.9700 | 0.6496 | 0.7948 | 0.7064 |
Rang H:16 | 14.8900 | 8.6200 | 3.9200 | 0.6596 | 0.7958 | 0.7127 | |
Rang H:20 | 14.8700 | 8.4900 | 3.9400 | 0.6626 | 0.7941 | 0.7141 | |
Rang H:24 | 14.8600 | 8.6000 | 3.9500 | 0.6614 | 0.7930 | 0.7125 | |
Rang H:28 | 14.7700 | 8.5400 | 4.0400 | 0.6591 | 0.7915 | 0.7114 | |
Rang H:32 | 14.6600 | 8.8400 | 4.1500 | 0.6495 | 0.7857 | 0.7029 | |
Rang H:36 | 14.7800 | 8.5300 | 4.0300 | 0.6597 | 0.7920 | 0.7119 | |
Rang H:40 | 14.9700 | 8.3000 | 3.8400 | 0.6685 | 0.8023 | 0.7211 | |
Rang H:44 | 14.6500 | 8.8100 | 4.1600 | 0.6516 | 0.7845 | 0.7031 | |
Rang H:48 | 14.8800 | 8.5400 | 3.9300 | 0.6633 | 0.7960 | 0.7150 | |
Rang Q:24 | Rang H:12 | 14.7500 | 8.7800 | 4.0600 | 0.6515 | 0.7870 | 0.7049 |
Rang H:16 | 15.0700 | 8.1500 | 3.7400 | 0.6729 | 0.8046 | 0.7246 | |
Rang H:20 | 14.8900 | 8.6100 | 3.9200 | 0.6579 | 0.7963 | 0.7124 | |
Rang H:24 | 14.9600 | 8.3500 | 3.8500 | 0.6664 | 0.7991 | 0.7183 | |
Rang H:28 | 15.0500 | 8.3200 | 3.7600 | 0.6714 | 0.8049 | 0.7238 | |
Rang H:32 | 15.2200 | 8.2200 | 3.5900 | 0.6740 | 0.8140 | 0.7296 | |
Rang H:36 | 14.9500 | 8.2700 | 3.8600 | 0.6699 | 0.8000 | 0.7211 | |
Rang H:40 | 15.1100 | 8.1900 | 3.7000 | 0.6723 | 0.8062 | 0.7250 | |
Rang H:44 | 14.9300 | 8.2400 | 3.8800 | 0.6675 | 0.7966 | 0.7181 | |
Rang H:48 | 15.1800 | 7.9900 | 3.6300 | 0.6820 | 0.8097 | 0.7315 | |
Rang Q:28 | Rang H:12 | 15.1000 | 8.1500 | 3.7100 | 0.6717 | 0.8064 | 0.7245 |
Rang H:16 | 14.9600 | 8.4800 | 3.8500 | 0.6632 | 0.7973 | 0.7154 | |
Rang H:20 | 14.9700 | 8.2200 | 3.8400 | 0.6668 | 0.7984 | 0.7184 | |
Rang H:24 | 15.0700 | 8.0100 | 3.7400 | 0.6771 | 0.8042 | 0.7271 | |
Rang H:28 | 15.1000 | 8.1000 | 3.7100 | 0.6729 | 0.8037 | 0.7239 | |
Rang H:32 | 15.1200 | 8.2700 | 3.6900 | 0.6679 | 0.8064 | 0.7221 | |
Rang H:36 | 15.2000 | 8.1200 | 3.6100 | 0.6746 | 0.8113 | 0.7281 | |
Rang H:40 | 14.9900 | 8.1200 | 3.8200 | 0.6741 | 0.8008 | 0.7235 | |
Rang H:44 | 15.0000 | 7.9200 | 3.8100 | 0.6731 | 0.7991 | 0.7233 | |
Rang H:48 | 15.1200 | 8.2600 | 3.6900 | 0.6718 | 0.8081 | 0.7253 | |
Rang Q:32 | Rang H:12 | 15.0300 | 8.3100 | 3.7800 | 0.6672 | 0.8004 | 0.7196 |
Rang H:16 | 15.2000 | 8.1400 | 3.6100 | 0.6733 | 0.8115 | 0.7277 | |
Rang H:20 | 15.1200 | 8.0800 | 3.6900 | 0.6769 | 0.8088 | 0.7284 | |
Rang H:24 | 15.1400 | 8.4200 | 3.6700 | 0.6639 | 0.8069 | 0.7199 | |
Rang H:28 | 15.3400 | 8.1500 | 3.4700 | 0.6750 | 0.8189 | 0.7316 | |
Rang H:32 | 15.1100 | 8.0000 | 3.7000 | 0.6713 | 0.8063 | 0.7249 | |
Rang H:36 | 14.8100 | 8.2900 | 4.0000 | 0.6631 | 0.7913 | 0.7127 | |
Rang H:40 | 15.2400 | 7.9000 | 3.5700 | 0.6816 | 0.8114 | 0.7320 | |
Rang H:44 | 14.9700 | 8.0900 | 3.8400 | 0.6701 | 0.7986 | 0.7199 | |
Rang H:48 | 14.9300 | 7.9300 | 3.8800 | 0.6740 | 0.7952 | 0.7210 | |
Rang Q:36 | Rang H:12 | 14.8700 | 8.3300 | 3.9400 | 0.6635 | 0.7925 | 0.7137 |
Rang H:16 | 15.0900 | 7.7100 | 3.7200 | 0.6828 | 0.8046 | 0.7304 | |
Rang H:20 | 14.8600 | 8.2100 | 3.9500 | 0.6661 | 0.7938 | 0.7160 | |
Rang H:24 | 14.7600 | 8.3000 | 4.0500 | 0.6614 | 0.7881 | 0.7107 | |
Rang H:28 | 14.7800 | 8.1300 | 4.0300 | 0.6609 | 0.7872 | 0.7107 | |
Rang H:32 | 14.8400 | 8.2500 | 3.9700 | 0.6625 | 0.7898 | 0.7124 | |
Rang H:36 | 14.9100 | 8.0400 | 3.9000 | 0.6703 | 0.7968 | 0.7197 | |
Rang H:40 | 14.8900 | 8.2200 | 3.9200 | 0.6655 | 0.7950 | 0.7161 | |
Rang H:44 | 14.7700 | 8.3300 | 4.0400 | 0.6617 | 0.7896 | 0.7121 | |
Rang H:48 | 15.0800 | 7.8400 | 3.7300 | 0.6764 | 0.8057 | 0.7270 | |
Rang Q:40 | Rang H:12 | 14.8200 | 8.1800 | 3.9900 | 0.6666 | 0.7919 | 0.7161 |
Rang H:16 | 14.8800 | 8.0400 | 3.9300 | 0.6702 | 0.7919 | 0.7176 | |
Rang H:20 | 14.9000 | 8.2500 | 3.9100 | 0.6646 | 0.7944 | 0.7152 | |
Rang H:24 | 14.9200 | 7.9500 | 3.8900 | 0.6734 | 0.7951 | 0.7209 | |
Rang H:28 | 14.8300 | 7.9500 | 3.9800 | 0.6670 | 0.7899 | 0.7159 | |
Rang H:32 | 14.7200 | 8.0700 | 4.0900 | 0.6651 | 0.7863 | 0.7127 | |
Rang H:36 | 14.8800 | 8.0700 | 3.9300 | 0.6635 | 0.7943 | 0.7152 | |
Rang H:40 | 14.8700 | 8.1200 | 3.9400 | 0.6688 | 0.7934 | 0.7176 | |
Rang H:44 | 14.8300 | 8.2100 | 3.9800 | 0.6644 | 0.7922 | 0.7147 | |
Rang H:48 | 14.9700 | 8.0000 | 3.8400 | 0.6739 | 0.7992 | 0.7235 | |
Rang Q:44 | Rang H:12 | 14.9700 | 8.1600 | 3.8400 | 0.6749 | 0.7987 | 0.7225 |
Rang H:16 | 15.0600 | 8.0300 | 3.7500 | 0.6722 | 0.8018 | 0.7231 | |
Rang H:20 | 14.4600 | 8.2300 | 4.3500 | 0.6593 | 0.7700 | 0.7022 | |
Rang H:24 | 15.0300 | 7.9100 | 3.7800 | 0.6794 | 0.8047 | 0.7283 | |
Rang H:28 | 14.8000 | 7.9100 | 4.0100 | 0.6691 | 0.7893 | 0.7169 | |
Rang H:32 | 14.7800 | 7.9700 | 4.0300 | 0.6719 | 0.7889 | 0.7174 | |
Rang H:36 | 14.7500 | 7.9800 | 4.0600 | 0.6665 | 0.7861 | 0.7136 | |
Rang H:40 | 14.6500 | 8.1200 | 4.1600 | 0.6598 | 0.7802 | 0.7073 | |
Rang H:44 | 14.7000 | 8.0900 | 4.1100 | 0.6660 | 0.7834 | 0.7115 | |
Rang H:48 | 14.6500 | 8.0300 | 4.1600 | 0.6640 | 0.7841 | 0.7111 | |
Rang Q:48 | Rang H:12 | 14.8800 | 7.8300 | 3.9300 | 0.6770 | 0.7934 | 0.7219 |
Rang H:16 | 14.8200 | 8.0700 | 3.9900 | 0.6663 | 0.7921 | 0.7152 | |
Rang H:20 | 14.8700 | 7.9600 | 3.9400 | 0.6723 | 0.7937 | 0.7199 | |
Rang H:24 | 14.4500 | 8.5200 | 4.3600 | 0.6457 | 0.7709 | 0.6952 | |
Rang H:28 | 14.6400 | 8.0700 | 4.1700 | 0.6605 | 0.7827 | 0.7096 | |
Rang H:32 | 14.7000 | 8.1300 | 4.1100 | 0.6606 | 0.7859 | 0.7097 | |
Rang H:36 | 14.3900 | 8.3600 | 4.4200 | 0.6469 | 0.7668 | 0.6943 | |
Rang H:40 | 14.7000 | 7.8800 | 4.1100 | 0.6650 | 0.7811 | 0.7112 | |
Rang H:44 | 14.7300 | 7.8800 | 4.0800 | 0.6698 | 0.7879 | 0.7152 | |
Rang H:48 | 14.5000 | 8.2700 | 4.3100 | 0.6518 | 0.7716 | 0.6990 |
In this condition, we only keep the ranks leading to the highest F measure.
In that sense, it's an optimistic upper bound on metrics.
hide.printmd("**A 0.5 secondes:**")
best_chr_zero_five = hide.best_f_one_score_rank(zero_five_eight)
hide.printmd("**A 3 secondes:**")
best_chr_three = hide.best_f_one_score_rank(three_eight)
A 0.5 secondes:
True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|
Maximizing the f measure on each song: | 14.93 | 7.67 | 3.88 | 0.6847 | 0.7999 | 0.7303 |
A 3 secondes:
True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|
Maximizing the f measure on each song: | 17.07 | 5.04 | 1.74 | 0.7948 | 0.9124 | 0.8414 |
Below is presented the distribution of the optimal ranks in the "oracle ranks" condition, i.e. the distribution of the ranks for $H$ and $Q$ which result in the highest F measure for the different songs.
hide.plot_3d_ranks_study(zero_five_eight, ranks_rhythm, ranks_pattern)
Below is shown the distribution histogram of the F measure obtained with the oracle ranks.
hide.plot_f_mes_histogram(zero_five_eight)
This kernel is a trade-off between local and "longer" term similarities.
Concretely, it is a sum of both previous kernels. It is composed of 0 in its diagonal, 2 in the 8 bands surrounding the diagonal, and 1 elsewhere.
It looks like:
(or, in a matrix form: $\left[ \begin{matrix} 0 & 2 & 2 & 2& 2 & 1 & 1 & 1\\ 2 & 0 & 2 & 2 & 2& 2 & 1 & 1\\ 2&2 & 0 & 2 & 2 & 2& 2 & 1\\ 2&2&2 & 0 & 2 & 2 & 2& 2\\ 2 & 2 & 2& 2 & 0 & 2&2&2\\ 1 & 2 & 2 & 2& 2 & 0 & 2&2\\ 1 & 1 & 2 & 2 & 2& 2 & 0 & 2\\ 1 & 1 & 1& 2 & 2 & 2& 2 & 0\\ \end{matrix} \right]$ (of size 8 here)).
Mathematically, for a segment ($b_1, b_2$), the associated cost will be $c_{b_1,b_2} = \frac{1}{b_2 - b_1 + 1}(\sum_{i,j = 0, i \ne j}^{n - 1} a_{i + b_1, j + b_1} + \sum_{i,j = 0, 1 \leq |i - j| \leq 4}^{n - 1} a_{i + b_1, j + b_1})$.
It's called mixed kernel as it mixes both previous paradigms.
Below are segmentation results with different ranks values, but each time fixed over the entire RWC Pop dataset.
Results are computed with tolerance of respectively 0.5 seconds and 3 seconds.
annotations_type = "MIREX10"
ranks_rhythm = [12,16,20,24,28,32,36,40,44,48]
ranks_pattern = [12,16,20,24,28,32,36,40,44,48]
zero_five_mixed, three_mixed = hide.compute_ranks_RWC(ranks_rhythm,ranks_pattern, W = "chromas", annotations_type = annotations_type,
subdivision=96, penalty_weight = 1,penalty_func = "modulo8", convolution_type = "mixed")
0.5 seconds results | True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|---|
Rang Q:12 | Rang H:12 | 9.4900 | 10.2300 | 9.3200 | 0.4894 | 0.5109 | 0.4945 |
Rang H:16 | 10.1200 | 9.5800 | 8.6900 | 0.5195 | 0.5428 | 0.5251 | |
Rang H:20 | 10.3100 | 9.2500 | 8.5000 | 0.5339 | 0.5516 | 0.5369 | |
Rang H:24 | 10.3600 | 9.2300 | 8.4500 | 0.5388 | 0.5539 | 0.5407 | |
Rang H:28 | 10.5000 | 9.0400 | 8.3100 | 0.5474 | 0.5620 | 0.5486 | |
Rang H:32 | 9.9300 | 9.7600 | 8.8800 | 0.5101 | 0.5329 | 0.5160 | |
Rang H:36 | 10.2100 | 9.3400 | 8.6000 | 0.5313 | 0.5474 | 0.5334 | |
Rang H:40 | 10.2900 | 9.2400 | 8.5200 | 0.5345 | 0.5510 | 0.5370 | |
Rang H:44 | 10.3500 | 9.2600 | 8.4600 | 0.5367 | 0.5536 | 0.5393 | |
Rang H:48 | 10.5600 | 9.0100 | 8.2500 | 0.5490 | 0.5640 | 0.5507 | |
Rang Q:16 | Rang H:12 | 10.1300 | 9.7700 | 8.6800 | 0.5188 | 0.5453 | 0.5261 |
Rang H:16 | 10.6200 | 9.0700 | 8.1900 | 0.5512 | 0.5732 | 0.5563 | |
Rang H:20 | 10.7000 | 8.9100 | 8.1100 | 0.5544 | 0.5740 | 0.5581 | |
Rang H:24 | 10.7500 | 8.8000 | 8.0600 | 0.5609 | 0.5778 | 0.5634 | |
Rang H:28 | 10.8700 | 8.8000 | 7.9400 | 0.5648 | 0.5840 | 0.5684 | |
Rang H:32 | 10.5900 | 9.2400 | 8.2200 | 0.5450 | 0.5709 | 0.5521 | |
Rang H:36 | 10.6300 | 8.9800 | 8.1800 | 0.5503 | 0.5695 | 0.5541 | |
Rang H:40 | 10.6300 | 8.9300 | 8.1800 | 0.5529 | 0.5721 | 0.5567 | |
Rang H:44 | 10.8200 | 8.7600 | 7.9900 | 0.5625 | 0.5784 | 0.5648 | |
Rang H:48 | 10.8400 | 8.8500 | 7.9700 | 0.5607 | 0.5800 | 0.5644 | |
Rang Q:20 | Rang H:12 | 11.0600 | 8.8000 | 7.7500 | 0.5699 | 0.5939 | 0.5764 |
Rang H:16 | 10.8300 | 8.7400 | 7.9800 | 0.5654 | 0.5809 | 0.5673 | |
Rang H:20 | 11.0400 | 8.6700 | 7.7700 | 0.5694 | 0.5917 | 0.5743 | |
Rang H:24 | 11.2800 | 8.4300 | 7.5300 | 0.5835 | 0.6049 | 0.5879 | |
Rang H:28 | 11.2100 | 8.5300 | 7.6000 | 0.5780 | 0.6013 | 0.5835 | |
Rang H:32 | 10.7400 | 9.0600 | 8.0700 | 0.5550 | 0.5782 | 0.5612 | |
Rang H:36 | 10.9000 | 8.7900 | 7.9100 | 0.5678 | 0.5871 | 0.5717 | |
Rang H:40 | 11.2700 | 8.5500 | 7.5400 | 0.5828 | 0.6077 | 0.5891 | |
Rang H:44 | 10.9500 | 8.7700 | 7.8600 | 0.5658 | 0.5883 | 0.5712 | |
Rang H:48 | 11.1700 | 8.6000 | 7.6400 | 0.5760 | 0.5990 | 0.5816 | |
Rang Q:24 | Rang H:12 | 11.0200 | 8.9500 | 7.7900 | 0.5638 | 0.5946 | 0.5737 |
Rang H:16 | 10.9800 | 8.5700 | 7.8300 | 0.5731 | 0.5905 | 0.5761 | |
Rang H:20 | 10.7800 | 8.8700 | 8.0300 | 0.5609 | 0.5819 | 0.5655 | |
Rang H:24 | 11.0700 | 8.8100 | 7.7400 | 0.5704 | 0.5968 | 0.5776 | |
Rang H:28 | 11.3500 | 8.3400 | 7.4600 | 0.5890 | 0.6089 | 0.5928 | |
Rang H:32 | 11.3300 | 8.5100 | 7.4800 | 0.5809 | 0.6069 | 0.5884 | |
Rang H:36 | 11.2400 | 8.5100 | 7.5700 | 0.5789 | 0.6031 | 0.5852 | |
Rang H:40 | 11.0300 | 8.7600 | 7.7800 | 0.5663 | 0.5931 | 0.5733 | |
Rang H:44 | 11.1700 | 8.5500 | 7.6400 | 0.5758 | 0.6007 | 0.5822 | |
Rang H:48 | 11.5100 | 8.0800 | 7.3000 | 0.6013 | 0.6178 | 0.6036 | |
Rang Q:28 | Rang H:12 | 10.8500 | 8.9900 | 7.9600 | 0.5567 | 0.5848 | 0.5651 |
Rang H:16 | 10.8800 | 8.9200 | 7.9300 | 0.5581 | 0.5814 | 0.5639 | |
Rang H:20 | 11.1900 | 8.5100 | 7.6200 | 0.5798 | 0.6001 | 0.5844 | |
Rang H:24 | 11.0300 | 8.6100 | 7.7800 | 0.5726 | 0.5910 | 0.5767 | |
Rang H:28 | 11.2600 | 8.6300 | 7.5500 | 0.5787 | 0.6041 | 0.5852 | |
Rang H:32 | 11.1300 | 8.7600 | 7.6800 | 0.5705 | 0.5964 | 0.5778 | |
Rang H:36 | 11.4400 | 8.2700 | 7.3700 | 0.5899 | 0.6143 | 0.5961 | |
Rang H:40 | 11.1900 | 8.4500 | 7.6200 | 0.5800 | 0.6009 | 0.5842 | |
Rang H:44 | 11.2000 | 8.3200 | 7.6100 | 0.5820 | 0.6011 | 0.5863 | |
Rang H:48 | 11.2300 | 8.6200 | 7.5800 | 0.5752 | 0.6034 | 0.5834 | |
Rang Q:32 | Rang H:12 | 10.9900 | 8.9100 | 7.8200 | 0.5653 | 0.5899 | 0.5720 |
Rang H:16 | 10.9400 | 8.9800 | 7.8700 | 0.5590 | 0.5878 | 0.5681 | |
Rang H:20 | 11.0200 | 8.7700 | 7.7900 | 0.5655 | 0.5883 | 0.5712 | |
Rang H:24 | 11.3400 | 8.6400 | 7.4700 | 0.5758 | 0.6065 | 0.5853 | |
Rang H:28 | 10.9100 | 8.9400 | 7.9000 | 0.5596 | 0.5854 | 0.5668 | |
Rang H:32 | 11.1300 | 8.3700 | 7.6800 | 0.5802 | 0.5958 | 0.5822 | |
Rang H:36 | 11.1100 | 8.5400 | 7.7000 | 0.5757 | 0.5971 | 0.5800 | |
Rang H:40 | 11.1600 | 8.5900 | 7.6500 | 0.5717 | 0.5956 | 0.5770 | |
Rang H:44 | 11.0000 | 8.6100 | 7.8100 | 0.5695 | 0.5905 | 0.5740 | |
Rang H:48 | 11.1700 | 8.1900 | 7.6400 | 0.5871 | 0.5997 | 0.5871 | |
Rang Q:36 | Rang H:12 | 11.2700 | 8.5600 | 7.5400 | 0.5787 | 0.6053 | 0.5858 |
Rang H:16 | 11.1000 | 8.5300 | 7.7100 | 0.5763 | 0.5951 | 0.5799 | |
Rang H:20 | 11.4100 | 8.3500 | 7.4000 | 0.5877 | 0.6122 | 0.5937 | |
Rang H:24 | 11.0800 | 8.4000 | 7.7300 | 0.5779 | 0.5928 | 0.5796 | |
Rang H:28 | 11.1700 | 8.2900 | 7.6400 | 0.5851 | 0.5990 | 0.5861 | |
Rang H:32 | 10.9100 | 8.5900 | 7.9000 | 0.5676 | 0.5839 | 0.5694 | |
Rang H:36 | 11.5600 | 8.2300 | 7.2500 | 0.5940 | 0.6175 | 0.6002 | |
Rang H:40 | 11.3600 | 8.2500 | 7.4500 | 0.5876 | 0.6088 | 0.5921 | |
Rang H:44 | 11.0400 | 8.4100 | 7.7700 | 0.5746 | 0.5914 | 0.5773 | |
Rang H:48 | 11.1100 | 8.4600 | 7.7000 | 0.5768 | 0.5966 | 0.5808 | |
Rang Q:40 | Rang H:12 | 10.7600 | 9.0300 | 8.0500 | 0.5534 | 0.5782 | 0.5599 |
Rang H:16 | 11.0500 | 8.6500 | 7.7600 | 0.5757 | 0.5942 | 0.5784 | |
Rang H:20 | 11.0200 | 8.6900 | 7.7900 | 0.5719 | 0.5909 | 0.5751 | |
Rang H:24 | 11.0700 | 8.3600 | 7.7400 | 0.5812 | 0.5928 | 0.5809 | |
Rang H:28 | 10.7300 | 8.7300 | 8.0800 | 0.5612 | 0.5760 | 0.5630 | |
Rang H:32 | 11.4300 | 8.0900 | 7.3800 | 0.5958 | 0.6109 | 0.5969 | |
Rang H:36 | 11.2500 | 8.3000 | 7.5600 | 0.5849 | 0.6025 | 0.5876 | |
Rang H:40 | 11.2100 | 8.3000 | 7.6000 | 0.5853 | 0.6006 | 0.5864 | |
Rang H:44 | 11.0800 | 8.4100 | 7.7300 | 0.5772 | 0.5933 | 0.5795 | |
Rang H:48 | 11.0400 | 8.5100 | 7.7700 | 0.5737 | 0.5914 | 0.5766 | |
Rang Q:44 | Rang H:12 | 11.0000 | 8.7500 | 7.8100 | 0.5699 | 0.5901 | 0.5739 |
Rang H:16 | 11.1100 | 8.6200 | 7.7000 | 0.5740 | 0.5940 | 0.5772 | |
Rang H:20 | 11.0800 | 8.4400 | 7.7300 | 0.5776 | 0.5914 | 0.5782 | |
Rang H:24 | 11.3800 | 8.2100 | 7.4300 | 0.5926 | 0.6090 | 0.5948 | |
Rang H:28 | 10.9500 | 8.5100 | 7.8600 | 0.5679 | 0.5830 | 0.5694 | |
Rang H:32 | 10.9500 | 8.4300 | 7.8600 | 0.5705 | 0.5836 | 0.5710 | |
Rang H:36 | 11.1000 | 8.3600 | 7.7100 | 0.5771 | 0.5919 | 0.5784 | |
Rang H:40 | 10.8400 | 8.4600 | 7.9700 | 0.5667 | 0.5771 | 0.5659 | |
Rang H:44 | 10.7100 | 8.7100 | 8.1000 | 0.5590 | 0.5728 | 0.5596 | |
Rang H:48 | 10.6800 | 8.7100 | 8.1300 | 0.5595 | 0.5741 | 0.5601 | |
Rang Q:48 | Rang H:12 | 11.1000 | 8.5600 | 7.7100 | 0.5768 | 0.5971 | 0.5805 |
Rang H:16 | 11.1400 | 8.4400 | 7.6700 | 0.5769 | 0.5942 | 0.5790 | |
Rang H:20 | 10.5100 | 8.9700 | 8.3000 | 0.5460 | 0.5617 | 0.5479 | |
Rang H:24 | 10.7200 | 8.7400 | 8.0900 | 0.5563 | 0.5746 | 0.5593 | |
Rang H:28 | 10.7100 | 8.6400 | 8.1000 | 0.5593 | 0.5748 | 0.5610 | |
Rang H:32 | 11.0400 | 8.3000 | 7.7700 | 0.5802 | 0.5890 | 0.5783 | |
Rang H:36 | 10.3900 | 9.0500 | 8.4200 | 0.5381 | 0.5558 | 0.5411 | |
Rang H:40 | 10.5800 | 8.7600 | 8.2300 | 0.5544 | 0.5655 | 0.5539 | |
Rang H:44 | 10.4200 | 8.9200 | 8.3900 | 0.5445 | 0.5561 | 0.5446 | |
Rang H:48 | 10.4800 | 8.6800 | 8.3300 | 0.5518 | 0.5576 | 0.5491 |
3 seconds results | True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|---|
Rang Q:12 | Rang H:12 | 13.3400 | 6.3800 | 5.4700 | 0.6885 | 0.7136 | 0.6939 |
Rang H:16 | 13.3800 | 6.3200 | 5.4300 | 0.6901 | 0.7150 | 0.6952 | |
Rang H:20 | 13.3600 | 6.2000 | 5.4500 | 0.6954 | 0.7155 | 0.6985 | |
Rang H:24 | 13.4200 | 6.1700 | 5.3900 | 0.6980 | 0.7172 | 0.7008 | |
Rang H:28 | 13.6700 | 5.8700 | 5.1400 | 0.7148 | 0.7303 | 0.7152 | |
Rang H:32 | 13.4900 | 6.2000 | 5.3200 | 0.6970 | 0.7224 | 0.7027 | |
Rang H:36 | 13.5000 | 6.0500 | 5.3100 | 0.7048 | 0.7228 | 0.7064 | |
Rang H:40 | 13.4700 | 6.0600 | 5.3400 | 0.7041 | 0.7227 | 0.7065 | |
Rang H:44 | 13.5400 | 6.0700 | 5.2700 | 0.7038 | 0.7253 | 0.7076 | |
Rang H:48 | 13.6300 | 5.9400 | 5.1800 | 0.7125 | 0.7310 | 0.7148 | |
Rang Q:16 | Rang H:12 | 13.5800 | 6.3200 | 5.2300 | 0.6922 | 0.7253 | 0.7012 |
Rang H:16 | 13.5300 | 6.1600 | 5.2800 | 0.7022 | 0.7265 | 0.7072 | |
Rang H:20 | 13.7400 | 5.8700 | 5.0700 | 0.7123 | 0.7346 | 0.7162 | |
Rang H:24 | 13.6600 | 5.8900 | 5.1500 | 0.7121 | 0.7313 | 0.7146 | |
Rang H:28 | 13.9700 | 5.7000 | 4.8400 | 0.7244 | 0.7481 | 0.7292 | |
Rang H:32 | 13.9700 | 5.8600 | 4.8400 | 0.7185 | 0.7488 | 0.7262 | |
Rang H:36 | 13.6600 | 5.9500 | 5.1500 | 0.7093 | 0.7315 | 0.7134 | |
Rang H:40 | 13.6700 | 5.8900 | 5.1400 | 0.7109 | 0.7325 | 0.7147 | |
Rang H:44 | 13.7900 | 5.7900 | 5.0200 | 0.7173 | 0.7373 | 0.7204 | |
Rang H:48 | 13.8500 | 5.8400 | 4.9600 | 0.7166 | 0.7411 | 0.7216 | |
Rang Q:20 | Rang H:12 | 13.8900 | 5.9700 | 4.9200 | 0.7110 | 0.7423 | 0.7200 |
Rang H:16 | 13.7800 | 5.7900 | 5.0300 | 0.7177 | 0.7362 | 0.7201 | |
Rang H:20 | 13.7300 | 5.9800 | 5.0800 | 0.7082 | 0.7334 | 0.7135 | |
Rang H:24 | 13.9000 | 5.8100 | 4.9100 | 0.7190 | 0.7433 | 0.7236 | |
Rang H:28 | 14.0500 | 5.6900 | 4.7600 | 0.7234 | 0.7519 | 0.7304 | |
Rang H:32 | 13.8900 | 5.9100 | 4.9200 | 0.7111 | 0.7414 | 0.7197 | |
Rang H:36 | 13.7600 | 5.9300 | 5.0500 | 0.7133 | 0.7384 | 0.7189 | |
Rang H:40 | 13.8300 | 5.9900 | 4.9800 | 0.7124 | 0.7419 | 0.7199 | |
Rang H:44 | 13.6300 | 6.0900 | 5.1800 | 0.7017 | 0.7303 | 0.7089 | |
Rang H:48 | 13.9700 | 5.8000 | 4.8400 | 0.7199 | 0.7485 | 0.7272 | |
Rang Q:24 | Rang H:12 | 13.9600 | 6.0100 | 4.8500 | 0.7087 | 0.7463 | 0.7208 |
Rang H:16 | 13.8800 | 5.6700 | 4.9300 | 0.7229 | 0.7439 | 0.7268 | |
Rang H:20 | 13.8200 | 5.8300 | 4.9900 | 0.7153 | 0.7400 | 0.7207 | |
Rang H:24 | 13.9600 | 5.9200 | 4.8500 | 0.7162 | 0.7472 | 0.7246 | |
Rang H:28 | 14.0400 | 5.6500 | 4.7700 | 0.7265 | 0.7506 | 0.7313 | |
Rang H:32 | 14.1800 | 5.6600 | 4.6300 | 0.7241 | 0.7572 | 0.7340 | |
Rang H:36 | 14.1100 | 5.6400 | 4.7000 | 0.7259 | 0.7563 | 0.7342 | |
Rang H:40 | 13.7500 | 6.0400 | 5.0600 | 0.7076 | 0.7366 | 0.7147 | |
Rang H:44 | 14.0100 | 5.7100 | 4.8000 | 0.7209 | 0.7487 | 0.7277 | |
Rang H:48 | 14.1900 | 5.4000 | 4.6200 | 0.7362 | 0.7574 | 0.7398 | |
Rang Q:28 | Rang H:12 | 14.0700 | 5.7700 | 4.7400 | 0.7209 | 0.7536 | 0.7301 |
Rang H:16 | 13.8800 | 5.9200 | 4.9300 | 0.7138 | 0.7417 | 0.7208 | |
Rang H:20 | 13.9600 | 5.7400 | 4.8500 | 0.7194 | 0.7435 | 0.7250 | |
Rang H:24 | 14.1600 | 5.4800 | 4.6500 | 0.7309 | 0.7561 | 0.7372 | |
Rang H:28 | 14.0200 | 5.8700 | 4.7900 | 0.7177 | 0.7483 | 0.7258 | |
Rang H:32 | 13.9700 | 5.9200 | 4.8400 | 0.7135 | 0.7449 | 0.7224 | |
Rang H:36 | 14.0400 | 5.6700 | 4.7700 | 0.7230 | 0.7508 | 0.7299 | |
Rang H:40 | 13.9900 | 5.6500 | 4.8200 | 0.7256 | 0.7489 | 0.7299 | |
Rang H:44 | 13.8600 | 5.6600 | 4.9500 | 0.7192 | 0.7407 | 0.7238 | |
Rang H:48 | 14.0600 | 5.7900 | 4.7500 | 0.7199 | 0.7524 | 0.7292 | |
Rang Q:32 | Rang H:12 | 14.0300 | 5.8700 | 4.7800 | 0.7160 | 0.7468 | 0.7246 |
Rang H:16 | 14.1300 | 5.7900 | 4.6800 | 0.7175 | 0.7530 | 0.7286 | |
Rang H:20 | 14.1400 | 5.6500 | 4.6700 | 0.7256 | 0.7541 | 0.7327 | |
Rang H:24 | 14.2200 | 5.7600 | 4.5900 | 0.7197 | 0.7577 | 0.7317 | |
Rang H:28 | 14.2700 | 5.5800 | 4.5400 | 0.7293 | 0.7593 | 0.7369 | |
Rang H:32 | 13.8400 | 5.6600 | 4.9700 | 0.7205 | 0.7375 | 0.7219 | |
Rang H:36 | 13.9100 | 5.7400 | 4.9000 | 0.7196 | 0.7432 | 0.7236 | |
Rang H:40 | 14.1300 | 5.6200 | 4.6800 | 0.7267 | 0.7536 | 0.7322 | |
Rang H:44 | 13.8300 | 5.7800 | 4.9800 | 0.7173 | 0.7396 | 0.7211 | |
Rang H:48 | 13.8600 | 5.5000 | 4.9500 | 0.7289 | 0.7403 | 0.7270 | |
Rang Q:36 | Rang H:12 | 13.9300 | 5.9000 | 4.8800 | 0.7155 | 0.7437 | 0.7226 |
Rang H:16 | 13.7700 | 5.8600 | 5.0400 | 0.7124 | 0.7349 | 0.7167 | |
Rang H:20 | 13.9300 | 5.8300 | 4.8800 | 0.7172 | 0.7437 | 0.7231 | |
Rang H:24 | 13.7900 | 5.6900 | 5.0200 | 0.7190 | 0.7363 | 0.7209 | |
Rang H:28 | 13.9300 | 5.5300 | 4.8800 | 0.7262 | 0.7433 | 0.7274 | |
Rang H:32 | 13.9000 | 5.6000 | 4.9100 | 0.7250 | 0.7424 | 0.7259 | |
Rang H:36 | 14.2600 | 5.5300 | 4.5500 | 0.7310 | 0.7607 | 0.7391 | |
Rang H:40 | 13.9000 | 5.7100 | 4.9100 | 0.7179 | 0.7425 | 0.7231 | |
Rang H:44 | 13.8300 | 5.6200 | 4.9800 | 0.7225 | 0.7401 | 0.7245 | |
Rang H:48 | 13.7800 | 5.7900 | 5.0300 | 0.7148 | 0.7376 | 0.7190 | |
Rang Q:40 | Rang H:12 | 13.7100 | 6.0800 | 5.1000 | 0.7044 | 0.7341 | 0.7123 |
Rang H:16 | 13.8600 | 5.8400 | 4.9500 | 0.7191 | 0.7412 | 0.7223 | |
Rang H:20 | 13.8100 | 5.9000 | 5.0000 | 0.7142 | 0.7391 | 0.7189 | |
Rang H:24 | 13.9100 | 5.5200 | 4.9000 | 0.7303 | 0.7411 | 0.7282 | |
Rang H:28 | 13.8000 | 5.6600 | 5.0100 | 0.7194 | 0.7354 | 0.7204 | |
Rang H:32 | 13.8500 | 5.6700 | 4.9600 | 0.7236 | 0.7399 | 0.7239 | |
Rang H:36 | 13.9000 | 5.6500 | 4.9100 | 0.7226 | 0.7423 | 0.7250 | |
Rang H:40 | 13.9300 | 5.5800 | 4.8800 | 0.7256 | 0.7427 | 0.7264 | |
Rang H:44 | 13.7600 | 5.7300 | 5.0500 | 0.7183 | 0.7355 | 0.7200 | |
Rang H:48 | 13.8300 | 5.7200 | 4.9800 | 0.7207 | 0.7391 | 0.7230 | |
Rang Q:44 | Rang H:12 | 13.8900 | 5.8600 | 4.9200 | 0.7177 | 0.7419 | 0.7227 |
Rang H:16 | 13.7400 | 5.9900 | 5.0700 | 0.7099 | 0.7319 | 0.7130 | |
Rang H:20 | 13.6800 | 5.8400 | 5.1300 | 0.7165 | 0.7310 | 0.7162 | |
Rang H:24 | 14.0000 | 5.5900 | 4.8100 | 0.7292 | 0.7486 | 0.7317 | |
Rang H:28 | 13.8100 | 5.6500 | 5.0000 | 0.7208 | 0.7379 | 0.7222 | |
Rang H:32 | 13.8300 | 5.5500 | 4.9800 | 0.7251 | 0.7391 | 0.7250 | |
Rang H:36 | 13.7500 | 5.7100 | 5.0600 | 0.7186 | 0.7346 | 0.7191 | |
Rang H:40 | 13.5000 | 5.8000 | 5.3100 | 0.7083 | 0.7200 | 0.7070 | |
Rang H:44 | 13.6500 | 5.7700 | 5.1600 | 0.7155 | 0.7288 | 0.7147 | |
Rang H:48 | 13.7200 | 5.6700 | 5.0900 | 0.7226 | 0.7342 | 0.7205 | |
Rang Q:48 | Rang H:12 | 13.8200 | 5.8400 | 4.9900 | 0.7159 | 0.7383 | 0.7195 |
Rang H:16 | 13.8500 | 5.7300 | 4.9600 | 0.7193 | 0.7410 | 0.7223 | |
Rang H:20 | 13.6500 | 5.8300 | 5.1600 | 0.7139 | 0.7292 | 0.7144 | |
Rang H:24 | 13.6100 | 5.8500 | 5.2000 | 0.7089 | 0.7269 | 0.7104 | |
Rang H:28 | 13.4800 | 5.8700 | 5.3300 | 0.7077 | 0.7218 | 0.7076 | |
Rang H:32 | 13.7700 | 5.5700 | 5.0400 | 0.7249 | 0.7360 | 0.7226 | |
Rang H:36 | 13.5300 | 5.9100 | 5.2800 | 0.7039 | 0.7216 | 0.7055 | |
Rang H:40 | 13.6400 | 5.7000 | 5.1700 | 0.7157 | 0.7256 | 0.7131 | |
Rang H:44 | 13.5300 | 5.8100 | 5.2800 | 0.7104 | 0.7232 | 0.7096 | |
Rang H:48 | 13.5900 | 5.5700 | 5.2200 | 0.7216 | 0.7274 | 0.7174 |
In this condition, we only keep the ranks leading to the highest F measure.
In that sense, it's an optimistic upper bound on metrics.
hide.printmd("**A 0.5 secondes:**")
best_chr_zero_five = hide.best_f_one_score_rank(zero_five_mixed)
hide.printmd("**A 3 secondes:**")
best_chr_three = hide.best_f_one_score_rank(three_mixed)
A 0.5 secondes:
True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|
Maximizing the f measure on each song: | 14.13 | 5.58 | 4.68 | 0.7311 | 0.7581 | 0.7372 |
A 3 secondes:
True Positives | False Positives | False Negatives | Precision | Recall | F measure | |
---|---|---|---|---|---|---|
Maximizing the f measure on each song: | 16.37 | 3.24 | 2.44 | 0.846 | 0.874 | 0.8538 |
Below is presented the distribution of the optimal ranks in the "oracle ranks" condition, i.e. the distribution of the ranks for $H$ and $Q$ which result in the highest F measure for the different songs.
hide.plot_3d_ranks_study(zero_five_mixed, ranks_rhythm, ranks_pattern)
Below is shown the distribution histogram of the F measure obtained with the oracle ranks.
hide.plot_f_mes_histogram(zero_five_mixed)
In conclusion, we considered that the "8 bands kernel" was a reasonnable trade-off between:
In that sense, we used that kernel in our final experiments, and as the default kernel in the paper.
In future work, if this segmentation technique is still used, it might be interesting to focus on the mixed kernel instead, which seem more promising (notably on its distribution of best ranks).