rm(list=ls(all=T))
options(digits=4, scipen=12)
library(dplyr); library(ggplot2)議題：使用歌曲的屬性，預測它會不會進入流行歌曲排行榜的前10名
學習重點：
【1.1】How many observations (songs) are from the year 2010?
A = read.csv("data/songs.csv")
nrow(subset(A,A$year == 2010)) #373[1] 373【1.2】How many songs does the dataset include for which the artist name is “Michael Jackson”?
nrow(subset(A,A$artistname == "Michael Jackson"))
[1] 18【1.3】Which of these songs by Michael Jackson made it to the Top 10? Select all that apply.
【1.4】(a) What are the values of timesignature that occur in our dataset? (b) Which timesignature value is the most frequent among songs in our dataset?
table(A$timesignature) #4
0 1 3 4 5 7
10 143 503 6787 112 19 【1.5】 Which of the following songs has the highest tempo?
A[which.max(A$tempo), 1:5] #Wanna Be Startin' Somethin'We wish to predict whether or not a song will make it to the Top 10. To do this, first use the subset function to split the data into a training set “SongsTrain” consisting of all the observations up to and including 2009 song releases, and a testing set “SongsTest”, consisting of the 2010 song releases.
【2.1 依時間分割資料】How many observations (songs) are in the training set?
TR = subset(A,A$year <= 2009)
TS = subset(A,A$year == 2010)
nrow(TR)[1] 7201【2.2 建立模型、模型摘要】What is the value of the Akaike Information Criterion (AIC)?
nonvars = c("year", "songtitle", "artistname", "songID", "artistID")
#去除非numeric的屬性
TR = TR[ , !(names(TR) %in% nonvars) ]
TS = TS[ , !(names(TS) %in% nonvars) ]
glm1 = glm(Top10~.,TR,family = binomial())
summary(glm1)
Call:
glm(formula = Top10 ~ ., family = binomial(), data = TR)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.922 -0.540 -0.346 -0.184 3.077
Coefficients:
Estimate Std. Error z value
(Intercept) 14.6999882 1.8063875 8.14
timesignature 0.1263948 0.0867357 1.46
timesignature_confidence 0.7449923 0.1953053 3.81
loudness 0.2998794 0.0291654 10.28
tempo 0.0003634 0.0016915 0.21
tempo_confidence 0.4732270 0.1421740 3.33
key 0.0158820 0.0103895 1.53
key_confidence 0.3086751 0.1411562 2.19
energy -1.5021445 0.3099240 -4.85
pitch -44.9077399 6.8348831 -6.57
timbre_0_min 0.0231589 0.0042562 5.44
timbre_0_max -0.3309820 0.0256926 -12.88
timbre_1_min 0.0058810 0.0007798 7.54
timbre_1_max -0.0002449 0.0007152 -0.34
timbre_2_min -0.0021274 0.0011260 -1.89
timbre_2_max 0.0006586 0.0009066 0.73
timbre_3_min 0.0006920 0.0005985 1.16
timbre_3_max -0.0029673 0.0005815 -5.10
timbre_4_min 0.0103956 0.0019850 5.24
timbre_4_max 0.0061105 0.0015503 3.94
timbre_5_min -0.0055980 0.0012767 -4.38
timbre_5_max 0.0000774 0.0007935 0.10
timbre_6_min -0.0168562 0.0022640 -7.45
timbre_6_max 0.0036681 0.0021895 1.68
timbre_7_min -0.0045492 0.0017815 -2.55
timbre_7_max -0.0037737 0.0018320 -2.06
timbre_8_min 0.0039110 0.0028510 1.37
timbre_8_max 0.0040113 0.0030030 1.34
timbre_9_min 0.0013673 0.0029981 0.46
timbre_9_max 0.0016027 0.0024336 0.66
timbre_10_min 0.0041263 0.0018391 2.24
timbre_10_max 0.0058250 0.0017694 3.29
timbre_11_min -0.0262523 0.0036933 -7.11
timbre_11_max 0.0196734 0.0033855 5.81
Pr(>|z|)
(Intercept) 0.0000000000000004 ***
timesignature 0.14505
timesignature_confidence 0.00014 ***
loudness < 2e-16 ***
tempo 0.82989
tempo_confidence 0.00087 ***
key 0.12635
key_confidence 0.02876 *
energy 0.0000012545913310 ***
pitch 0.0000000000501890 ***
timbre_0_min 0.0000000529331342 ***
timbre_0_max < 2e-16 ***
timbre_1_min 0.0000000000000464 ***
timbre_1_max 0.73209
timbre_2_min 0.05884 .
timbre_2_max 0.46757
timbre_3_min 0.24758
timbre_3_max 0.0000003344570390 ***
timbre_4_min 0.0000001632385067 ***
timbre_4_max 0.0000809670432888 ***
timbre_5_min 0.0000116146773897 ***
timbre_5_max 0.92234
timbre_6_min 0.0000000000000966 ***
timbre_6_max 0.09388 .
timbre_7_min 0.01066 *
timbre_7_max 0.03941 *
timbre_8_min 0.17012
timbre_8_max 0.18162
timbre_9_min 0.64836
timbre_9_max 0.51019
timbre_10_min 0.02485 *
timbre_10_max 0.00099 ***
timbre_11_min 0.0000000000011760 ***
timbre_11_max 0.0000000062068661 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6017.5 on 7200 degrees of freedom
Residual deviance: 4759.2 on 7167 degrees of freedom
AIC: 4827
Number of Fisher Scoring iterations: 6【2.3 模型係數判讀】The LOWER or HIGHER our confidence about time signature, key and tempo, the more likely the song is to be in the Top 10
#HIGHER 因為estimate都是正的 【2.4 進行推論】What does Model 1 suggest in terms of complexity?
#Mainstream listeners tend to prefer less complex songs
#signature,key,tempo的confidence低，代表歌的複雜度高。但模型顯示confidence高，越能進入top10，代表大眾較喜愛不複雜的歌【2.5 檢查異常係數】 Songs with heavier instrumentation tend to be louder (have higher values in the variable “loudness”) and more energetic (have higher values in the variable “energy”).
#loudness的estimate為正
#energy的esimate為負
#(a) Mainstream listeners prefer songs with heavy instrumentation
#(b) 與a相反【3.1 檢查相關係數】What is the correlation between loudness and energy in the training set?
cor(TR$loudness,TR$energy)
[1] 0.7399Create Model 2, which is Model 1 without the independent variable “loudness”. This can be done with the following command:
SongsLog2 = glm(Top10 ~ . - loudness, data=SongsTrain, family=binomial)We just subtracted the variable loudness. We couldn’t do this with the variables “songtitle” and “artistname”, because they are not numeric variables, and we might get different values in the test set that the training set has never seen. But this approach (subtracting the variable from the model formula) will always work when you want to remove numeric variables.
Look at the summary of SongsLog2, and inspect the coefficient of the variable “energy”. What do you observe?
【3.2 重新建立模型、檢查係數】Look at the summary of SongsLog2, and inspect the coefficient of the variable “energy”. What do you observe?
lm2 = glm(Top10~.-loudness,data= TR,family = binomial)
#以Top10其他全部屬性為independent var（減去loudness）
summary(lm2)
Call:
glm(formula = Top10 ~ . - loudness, family = binomial, data = TR)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.098 -0.561 -0.360 -0.190 3.311
Coefficients:
Estimate Std. Error z value
(Intercept) -2.240612 0.746484 -3.00
timesignature 0.162461 0.087341 1.86
timesignature_confidence 0.688471 0.192419 3.58
tempo 0.000552 0.001665 0.33
tempo_confidence 0.549657 0.140736 3.91
key 0.017403 0.010256 1.70
key_confidence 0.295367 0.139446 2.12
energy 0.181260 0.260768 0.70
pitch -51.498579 6.856544 -7.51
timbre_0_min 0.024789 0.004240 5.85
timbre_0_max -0.100697 0.011776 -8.55
timbre_1_min 0.007143 0.000771 9.27
timbre_1_max -0.000783 0.000706 -1.11
timbre_2_min -0.001579 0.001109 -1.42
timbre_2_max 0.000389 0.000896 0.43
timbre_3_min 0.000650 0.000595 1.09
timbre_3_max -0.002462 0.000567 -4.34
timbre_4_min 0.009115 0.001952 4.67
timbre_4_max 0.006306 0.001532 4.12
timbre_5_min -0.005641 0.001255 -4.50
timbre_5_max 0.000694 0.000781 0.89
timbre_6_min -0.016122 0.002235 -7.21
timbre_6_max 0.003814 0.002157 1.77
timbre_7_min -0.005102 0.001755 -2.91
timbre_7_max -0.003158 0.001811 -1.74
timbre_8_min 0.004488 0.002810 1.60
timbre_8_max 0.006422 0.002950 2.18
timbre_9_min -0.000428 0.002955 -0.14
timbre_9_max 0.003525 0.002377 1.48
timbre_10_min 0.002993 0.001804 1.66
timbre_10_max 0.007367 0.001731 4.25
timbre_11_min -0.028370 0.003630 -7.82
timbre_11_max 0.018294 0.003341 5.48
Pr(>|z|)
(Intercept) 0.00269 **
timesignature 0.06287 .
timesignature_confidence 0.00035 ***
tempo 0.74023
tempo_confidence 0.0000940005473689 ***
key 0.08974 .
key_confidence 0.03416 *
energy 0.48699
pitch 0.0000000000000587 ***
timbre_0_min 0.0000000050055433 ***
timbre_0_max < 2e-16 ***
timbre_1_min < 2e-16 ***
timbre_1_max 0.26765
timbre_2_min 0.15453
timbre_2_max 0.66443
timbre_3_min 0.27452
timbre_3_max 0.0000143015554481 ***
timbre_4_min 0.0000030176578261 ***
timbre_4_max 0.0000387139806484 ***
timbre_5_min 0.0000069522013076 ***
timbre_5_max 0.37426
timbre_6_min 0.0000000000005452 ***
timbre_6_max 0.07698 .
timbre_7_min 0.00364 **
timbre_7_max 0.08109 .
timbre_8_min 0.11025
timbre_8_max 0.02950 *
timbre_9_min 0.88479
timbre_9_max 0.13802
timbre_10_min 0.09700 .
timbre_10_max 0.0000209292079939 ***
timbre_11_min 0.0000000000000055 ***
timbre_11_max 0.0000000434235974 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6017.5 on 7200 degrees of freedom
Residual deviance: 4871.8 on 7168 degrees of freedom
AIC: 4938
Number of Fisher Scoring iterations: 6#Model 2 suggests that songs with high energy levels tend to be more popular. This contradicts our observation in Model 1.
#energy的estimate為正，但沒有顯著【3.3 選擇模型】 Now, create Model 3, which should be exactly like Model 1, but without the variable “energy”.
Look at the summary of Model 3 and inspect the coefficient of the variable “loudness”. Remembering that higher loudness and energy both occur in songs with heavier instrumentation, do we make the same observation about the popularity of heavy instrumentation as we did with Model 2?
do we make the same observation about the popularity of heavy instrumentation as we did with Model 2?
lm3 = glm(Top10~. -energy,data = TR , family = binomial)
summary(lm3)
Call:
glm(formula = Top10 ~ . - energy, family = binomial, data = TR)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.918 -0.542 -0.348 -0.187 3.417
Coefficients:
Estimate Std. Error z value
(Intercept) 11.9605621 1.7141947 6.98
timesignature 0.1150942 0.0872615 1.32
timesignature_confidence 0.7142698 0.1946175 3.67
loudness 0.2305565 0.0252798 9.12
tempo -0.0006460 0.0016655 -0.39
tempo_confidence 0.3840930 0.1398350 2.75
key 0.0164946 0.0103514 1.59
key_confidence 0.3394064 0.1408744 2.41
pitch -53.2840575 6.7328544 -7.91
timbre_0_min 0.0220452 0.0042394 5.20
timbre_0_max -0.3104800 0.0253654 -12.24
timbre_1_min 0.0054160 0.0007643 7.09
timbre_1_max -0.0005115 0.0007110 -0.72
timbre_2_min -0.0022544 0.0011203 -2.01
timbre_2_max 0.0004119 0.0009020 0.46
timbre_3_min 0.0003179 0.0005869 0.54
timbre_3_max -0.0029637 0.0005758 -5.15
timbre_4_min 0.0110465 0.0019779 5.58
timbre_4_max 0.0064668 0.0015413 4.20
timbre_5_min -0.0051345 0.0012690 -4.05
timbre_5_max 0.0002979 0.0007856 0.38
timbre_6_min -0.0178447 0.0022460 -7.94
timbre_6_max 0.0034469 0.0021821 1.58
timbre_7_min -0.0051284 0.0017685 -2.90
timbre_7_max -0.0033935 0.0018198 -1.86
timbre_8_min 0.0036861 0.0028331 1.30
timbre_8_max 0.0046578 0.0029879 1.56
timbre_9_min -0.0000932 0.0029569 -0.03
timbre_9_max 0.0013417 0.0024239 0.55
timbre_10_min 0.0040500 0.0018270 2.22
timbre_10_max 0.0057925 0.0017586 3.29
timbre_11_min -0.0263767 0.0036829 -7.16
timbre_11_max 0.0198361 0.0033646 5.90
Pr(>|z|)
(Intercept) 0.0000000000030077 ***
timesignature 0.18718
timesignature_confidence 0.00024 ***
loudness < 2e-16 ***
tempo 0.69811
tempo_confidence 0.00602 **
key 0.11106
key_confidence 0.01598 *
pitch 0.0000000000000025 ***
timbre_0_min 0.0000001992236315 ***
timbre_0_max < 2e-16 ***
timbre_1_min 0.0000000000013757 ***
timbre_1_max 0.47193
timbre_2_min 0.04419 *
timbre_2_max 0.64791
timbre_3_min 0.58808
timbre_3_max 0.0000002640646649 ***
timbre_4_min 0.0000000233875661 ***
timbre_4_max 0.0000272139788370 ***
timbre_5_min 0.0000520513667576 ***
timbre_5_max 0.70453
timbre_6_min 0.0000000000000019 ***
timbre_6_max 0.11420
timbre_7_min 0.00373 **
timbre_7_max 0.06221 .
timbre_8_min 0.19323
timbre_8_max 0.11902
timbre_9_min 0.97486
timbre_9_max 0.57990
timbre_10_min 0.02664 *
timbre_10_max 0.00099 ***
timbre_11_min 0.0000000000007958 ***
timbre_11_max 0.0000000037350899 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6017.5 on 7200 degrees of freedom
Residual deviance: 4782.7 on 7168 degrees of freedom
AIC: 4849
Number of Fisher Scoring iterations: 6#loudness 顯著，estimate為正
#Yes【4.1 正確性】What is the accuracy of Model 3 on the test set, using a threshold of 0.45?
pred = predict(lm3, newdata=TS, type="response")
#type= "response" 代表output為機率
x = table(actual = TS$Top10, predict = pred >= 0.45); x predict
actual FALSE TRUE
0 309 5
1 40 19#confusion matrix,actural和predict為matrix上、左名稱
#threshold 0.45，代表>0.45才會被視為y=1
#ACC = TN+TP/全部
diag(x) #回傳矩陣對角 309,19[1] 309 19sum(diag(x))/sum(x) # ACC = 0.8794 [1] 0.8794【4.2 底線正確率】What would the accuracy of the baseline model be on the test set? ?
table(TS$Top10)
0 1
314 59 1 - mean(TS$Top10)[1] 0.8418#? 為什麼直接減mean【4.3 正確性 vs. 辨識率】How many songs does Model 3 correctly predict as Top 10 hits in 2010? How many non-hit songs does Model 3 predict will be Top 10 hits?
#lm3在testing data的TP = 19, FP = 5【Q】不能大幅度增加正確性的模型也會有用嗎？為甚麼？
我認為ACC不是一個很好代表模型好壞的指標，所以不能大幅增加應該也沒關係
【4.4 敏感性 & 明確性】What is the sensitivity and specificity of Model 3 on the test set, using a threshold of 0.45?
#sensitivity = TP/TP+FN(在實際上為1的狀況下找到他的機率)
sen = 19 / (19+40) ; sen[1] 0.322#specificity = TN/TN+FP
spec = 309 / (309+5) ; spec[1] 0.9841【4.5 結論】What conclusions can you make about our model?
#Model 3 has a very high specificity, meaning that it favors specificity over sensitivity. While Model 3 only captures less than half of the Top 10 songs, it still can offer a competitive edge, since it is very conservative in its predictions.
#model3有較高的specificity
#但sensitivity只有0.32，不到0.5，代表他只抓不到一半的TOP10歌曲
【Q】從這個結論我們學到什麼？