所有的code可以詳見https://github.com/E94016021/mir-hw2，相關之輸出在該檔同名之txt檔中
Q1 (20%): Evaluate your tempo estimation algorithm on the Ballroom dataset using the Fourier tempogram.
使用的方法：
先做出tempogram之後再依每個時間取peak的點，將其所對應之tempo與其value存入累加之後，以累計的數量由大排到小，再利用自製的click聲（即最純淨的tempo音)，得出累計value最大所對應的tempo T1與次大的Tempo T2，再利用實驗結果調整參數，可得完全符合之tempo，在預測click之tempo時可以完美cover。
BPM/value_of_tempo_we_get = const ?
60/31.23999255259728 = 1.9206150545324514
78/41.21020294172407 = 1.892735158579561
120/63.809346490411464 = 1.8806022408963587
134/71.12083410910445 = 1.8841173852718658
160/84.4144479612735 = 1.8954101325569601
171/90.39657419474958 = 1.8916646070192784
mean = 1.8941907631427457
由上述實驗得到參數 1.8941907631427457
所以我們所輸出的
tempo = idx數單位idx的tempo數1.8941907631427457
在結果上我們可以看這張圖表
Cha Cha : avg.P-score = 0.0194 , avg.ALOTC = 0.06306306306306306
Jive : avg.P-score = 0.8908 , avg.ALOTC = 0.9166666666666666
Quickstep : avg.P-score = 0.7948 , avg.ALOTC = 0.8048780487804879
Rumba : avg.P-score = 0.0318 , avg.ALOTC = 0.05102040816326531
Samba : avg.P-score = 0.0690 , avg.ALOTC = 0.1744186046511628
Tango : avg.P-score = 0.3569 , avg.ALOTC = 0.4883720930232558
Viennese Waltz : avg.P-score = 0.4996 , avg.ALOTC = 0.5076923076923077
Slow Waltz : avg.P-score = 0.1538 , avg.ALOTC = 0.2818181818181818
可以看得出來在 Jive和Quickstep有較高的P-score與ALOTC
一樣也是參考圖表 Cha Cha : avg.t2/t1 = 1.4537 , avg.t1/gt = 1.7842 , avg.t2/gt = 2.0464 Jive : avg.t2/t1 = 1.1017 , avg.t1/gt = 1.0095 , avg.t2/gt = 1.0723 Quickstep : avg.t2/t1 = 1.3960 , avg.t1/gt = 0.8201 , avg.t2/gt = 0.9590 Rumba : avg.t2/t1 = 1.4777 , avg.t1/gt = 1.5919 , avg.t2/gt = 1.8927 Samba : avg.t2/t1 = 1.7279 , avg.t1/gt = 2.5271 , avg.t2/gt = 3.3165 Tango : avg.t2/t1 = 1.6480 , avg.t1/gt = 0.9703 , avg.t2/gt = 1.3311 Viennese Waltz : avg.t2/t1 = 1.5206 , avg.t1/gt = 0.5402 , avg.t2/gt = 0.7107 Slow Waltz : avg.t2/t1 = 1.3978 , avg.t1/gt = 0.8671 , avg.t2/gt = 1.1524 其實這個很有趣，可以發現一些有趣的現象，比如說cha cha cha會產生 t2/t1 = 1.4537，t1/gt = 1.7842，t2/gt = 2.0464 這組數字，而在每一個genre都會出先一個pattern，不斷地出現(可詳見q2.txt) eg. Jive avg.t2/t1 = 1.1017 , avg.t1/gt = 1.0095 , avg.t2/gt = 1.0723 便可觀察出通常是某節奏是某節奏的一倍、兩倍、三倍等等
在除2除3除4的狀況下觀察到一些現象：
T/2
Cha Cha : avg.P-score = 0.1516 , avg.ALOTC = 0.8108108108108109
Jive : avg.P-score = 0.8455 , avg.ALOTC = 0.9166666666666666
Quickstep : avg.P-score = 0.7693 , avg.ALOTC = 0.8048780487804879
Rumba : avg.P-score = 0.0754 , avg.ALOTC = 0.7040816326530612
Samba : avg.P-score = 0.0623 , avg.ALOTC = 0.32558139534883723
Tango : avg.P-score = 0.3346 , avg.ALOTC = 0.6395348837209303
Viennese Waltz : avg.P-score = 0.4846 , avg.ALOTC = 0.5076923076923077
Slow Waltz : avg.P-score = 0.1290 , avg.ALOTC = 0.35454545454545455
T/3
Cha Cha : avg.P-score = 0.0024 , avg.ALOTC = 0.009009009009009009
Jive : avg.P-score = 0.8254 , avg.ALOTC = 0.8833333333333333
Quickstep : avg.P-score = 0.7692 , avg.ALOTC = 0.8048780487804879
Rumba : avg.P-score = 0.0265 , avg.ALOTC = 0.04081632653061224
Samba : avg.P-score = 0.0416 , avg.ALOTC = 0.06976744186046512
Tango : avg.P-score = 0.2912 , avg.ALOTC = 0.43023255813953487
Viennese Waltz : avg.P-score = 0.4844 , avg.ALOTC = 0.5076923076923077
Slow Waltz : avg.P-score = 0.1249 , avg.ALOTC = 0.2545454545454545
T/4
Cha Cha : avg.P-score = 0.0027 , avg.ALOTC = 0.009009009009009009
Jive : avg.P-score = 0.8249 , avg.ALOTC = 0.8833333333333333
Quickstep : avg.P-score = 0.7690 , avg.ALOTC = 0.8048780487804879
Rumba : avg.P-score = 0.0264 , avg.ALOTC = 0.04081632653061224
Samba : avg.P-score = 0.0646 , avg.ALOTC = 0.47674418604651164
Tango : avg.P-score = 0.2904 , avg.ALOTC = 0.43023255813953487
Viennese Waltz : avg.P-score = 0.4844 , avg.ALOTC = 0.5076923076923077
Slow Waltz : avg.P-score = 0.1254 , avg.ALOTC = 0.24545454545454545
Q4 (20%): Using the ACF tempogram and repeat Q1 and Q2. What do you see? Compare the result with Q1 and Q2.
有經過ＡＣＦ處理過後，明顯各種score都高很多，除了Waltz系列的，且Viennese Waltz還反而降低 Cha Cha : avg.P-score = 0.9910 , avg.ALOTC = 0.4463 avg.t2/t1 = 1.5547 avg.t1/gt = 0.9212 avg.t2/gt = 1.4249 Jive : avg.P-score = 0.8333 , avg.ALOTC = 0.7694 avg.t2/t1 = 1.7219 avg.t1/gt = 0.5766 avg.t2/gt = 0.9550 Quickstep : avg.P-score = 0.0854 , avg.ALOTC = 0.0814 avg.t2/t1 = 1.1772 avg.t1/gt = 0.4999 avg.t2/gt = 0.5893 Rumba : avg.P-score = 0.8673 , avg.ALOTC = 0.3679 avg.t2/t1 = 1.4911 avg.t1/gt = 1.0397 avg.t2/gt = 1.5225 Samba : avg.P-score = 0.8721 , avg.ALOTC = 0.1670 avg.t2/t1 = 1.3423 avg.t1/gt = 1.0168 avg.t2/gt = 1.3572 Tango : avg.P-score = 1.0000 , avg.ALOTC = 0.8883 avg.t2/t1 = 1.1545 avg.t1/gt = 0.9187 avg.t2/gt = 1.0389 Viennese Waltz : avg.P-score = 0.4154 , avg.ALOTC = 0.3782 avg.t2/t1 = 1.3613 avg.t1/gt = 0.6078 avg.t2/gt = 0.8079 Slow Waltz : avg.P-score = 0.3000 , avg.ALOTC = 0.1185 avg.t2/t1 = 1.2522 avg.t1/gt = 1.3324 avg.t2/gt = 1.6236
Q5 (10%): Instead of using your estimated [𝑇 , 𝑇 ] in evaluation, try to use [𝑇 /2,𝑇 /2], [𝑇 /3,𝑇 /3], and [𝑇 /4,𝑇 /4]. Or, try to use [2𝑇 ,2𝑇 ], [3𝑇 ,3𝑇 ], and [4𝑇 , 4𝑇 ]. What are the resulting P-scores? Discuss the result.
基本上使用ACF之後已經非常準確，只有在tempo算成1/2倍與2倍比較有機會產生，也就是所謂除與2和乘與2之後還剩下一點點的P-score
diff = 2 mul = 2
Cha Cha : avg.P-score = 0.4054 Cha Cha : avg.P-score = 0.0631
Jive : avg.P-score = 0.0167 Jive : avg.P-score = 0.8000
Quickstep : avg.P-score = 0.0000 Quickstep : avg.P-score = 0.9512
Rumba : avg.P-score = 0.4286 Rumba : avg.P-score = 0.0102
Samba : avg.P-score = 0.1163 Samba : avg.P-score = 0.0000
Tango : avg.P-score = 0.0116 Tango : avg.P-score = 0.0116
Viennese Waltz : avg.P-score = 0.0000 Viennese Waltz : avg.P-score = 0.4923
Slow Waltz : avg.P-score = 0.3273 Slow Waltz : avg.P-score = 0.0000
diff = 3 mul = 3
Cha Cha : avg.P-score = 0.0000 Cha Cha : avg.P-score = 0.0000
Jive : avg.P-score = 0.0000 Jive : avg.P-score = 0.0000
Quickstep : avg.P-score = 0.0000 Quickstep : avg.P-score = 0.0122
Rumba : avg.P-score = 0.0000 Rumba : avg.P-score = 0.0000
Samba : avg.P-score = 0.0000 Samba : avg.P-score = 0.0000
Tango : avg.P-score = 0.0000 Tango : avg.P-score = 0.0000
Viennese Waltz : avg.P-score = 0.0000 Viennese Waltz : avg.P-score = 0.0000
Slow Waltz : avg.P-score = 0.0000 Slow Waltz : avg.P-score = 0.0000
diff = 4 mul = 4
Cha Cha : avg.P-score = 0.0000 Cha Cha : avg.P-score = 0.0000
Jive : avg.P-score = 0.0000 Jive : avg.P-score = 0.0000
Quickstep : avg.P-score = 0.0000 Quickstep : avg.P-score = 0.0000
Rumba : avg.P-score = 0.0000 Rumba : avg.P-score = 0.0000
Samba : avg.P-score = 0.0000 Samba : avg.P-score = 0.0000
Tango : avg.P-score = 0.0000 Tango : avg.P-score = 0.0000
Viennese Waltz : avg.P-score = 0.0000 Viennese Waltz : avg.P-score = 0.0000
Slow Waltz : avg.P-score = 0.0000 Slow Waltz : avg.P-score = 0.0000
Q6 (10%): From the above discussion, do you have any idea in improving the current algorithms using either the Fourier tempogram (Q1) or the ACF tempogram (Q4)? Please propose one tempo estimation algorithm that outperforms the current ones. (Hint: you may modify the definition of the weighting factor 𝑆1, or find some ways in combining the Fourier tempogram and the ACF tempogram.)
經過acf的研究可以發現他所找到的tempi似乎有一定的出現規律與比重，也許可以丟入深度學習的模型試試看。
ChaCha P: 0.2435 R: 0.2701 F: 0.2561
Slow Waltz P: 0.2179 R: 0.3003 F: 0.2343