Exploring Spotify Features with Unsupervised Learning
Muhammed Rizal Abdul Aziz
27 April, 2023
Introduction
This is an unsupervised learning analysis of spotify tracks dataset which can be downloaded at:
https://www.kaggle.com/datasets/zaheenhamidani/ultimate-spotify-tracks-db
The dataset is composed of tracks characterized by the following musical measures :
popularity, acousticness, danceability, duration_ms, energy, instrumentalness, key, liveness, loudnes, mode, speechiness, tempo, time_signature, valence.
The dataset have no target label variable and so are classified using Principal Component Analysis and then visualized using K-Means clustering.
Library
Invoke the required libraries.
library(tm)
library(tidyverse)
library(lubridate)
library(cluster)
library(ggforce)
library(GGally)
library(scales)
library(cowplot)
library(plotly)
library(FactoMineR)
library(factoextra)
library(dplyr)
library(ggcorrplot)
options(scipen = 100, max.print = 101)Data Exploration
Import the dataset and use glimpse() to view the data fields’ information.
data <- read.csv("SpotifyFeatures.csv")
glimpse(data)## Rows: 232,725
## Columns: 20
## $ genre <chr> "Movie", "Movie", "Movie", "Movie", "Movie", "Movie",…
## $ artist_name <chr> "Henri Salvador", "Martin & les fées", "Joseph Willia…
## $ track_name <chr> "C'est beau de faire un Show", "Perdu d'avance (par G…
## $ track_id <chr> "0BRjO6ga9RKCKjfDqeFgWV", "0BjC1NfoEOOusryehmNudP", "…
## $ popularity <chr> "0", "1", "3", "0", "4", "0", "2", "15", "0", "10", "…
## $ acousticness <chr> "0.611", "0.246", "0.952", "0.703", "0.95", "0.749", …
## $ danceability <dbl> 0.389, 0.590, 0.663, 0.240, 0.331, 0.578, 0.703, 0.41…
## $ duration_ms <dbl> 99373, 137373, 170267, 152427, 82625, 160627, 212293,…
## $ energy <dbl> 0.9100, 0.7370, 0.1310, 0.3260, 0.2250, 0.0948, 0.270…
## $ instrumentalness <dbl> 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.123…
## $ key <chr> "C#", "F#", "C", "C#", "F", "C#", "C#", "F#", "C", "G…
## $ liveness <chr> "0.346", "0.151", "0.103", "0.0985", "0.202", "0.107"…
## $ loudness <chr> "-1.828", "-5.559", "-13.879", "-12.178", "-21.15", "…
## $ mode <chr> "Major", "Minor", "Minor", "Major", "Major", "Major",…
## $ speechiness <chr> "0.0525", "0.0868", "0.0362", "0.0395", "0.0456", "0.…
## $ tempo <chr> "166.969", "174.003", "99.488", "171.758", "140.576",…
## $ time_signature <chr> "4/4", "4/4", "5/4", "4/4", "4/4", "4/4", "4/4", "4/4…
## $ valence <chr> "0.814", "0.816", "0.368", "0.227", "0.39", "0.358", …
## $ X <chr> "", "", "", "", "", "", "", "", "", "", "", "", "", "…
## $ X.1 <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…Check the unique values of data$x.
unique(data$x)## NULLCheck the unique values of data$x.1.
unique(data$x.1)## NULLCheck the unique values of instrumentalness.
unique(data$instrumentalness)## [1] 0.00000000 0.12300000 0.00086000 0.00125000 0.52900000 0.88700000
## [7] 0.07290000 0.93300000 0.00000725 0.04220000 0.00000813 0.00032800
## [13] 0.00110000 0.00200000 0.00000127 0.91900000 0.00000832 0.97600000
## [19] 0.00004900 0.00073200 0.00068300 0.00002940 0.06080000 0.89100000
## [25] 0.04180000 0.02860000 0.00001660 0.01170000 0.00002440 0.01060000
## [31] 0.00018400 0.00008630 0.00000900 0.00016900 0.00445000 0.85500000
## [37] 0.00004810 0.00038100 0.00000603 0.00003550 0.00002950 0.00000316
## [43] 0.00007440 0.33100000 0.95900000 0.00007550 0.00000805 0.00000295
## [49] 0.86100000 0.03270000 0.22900000 0.00000655 0.00000140 0.13900000
## [55] 0.32700000 0.00051200 0.00061400 0.88100000 0.78500000 0.00000859
## [61] 0.92600000 0.14500000 0.00000503 0.00000395 0.00243000 0.00013000
## [67] 0.00020800 0.00000833 0.00000807 0.01820000 0.00000927 0.00013100
## [73] 0.00006590 0.00050100 0.09980000 0.00000761 0.00000141 0.00012700
## [79] 0.01610000 0.00001140 0.00000515 0.00000210 0.00000378 0.25400000
## [85] 0.00020000 0.01840000 0.00002880 0.00000588 0.00001780 0.00018900
## [91] 0.00001190 0.00132000 0.00000865 0.00016100 0.00005070 0.00003030
## [97] 0.00000108 0.00452000 0.00000139 0.01260000 0.00131000
## [ reached getOption("max.print") -- omitted 5309 entries ]Check the unique values of acousticness.
unique(data$acousticness)## [1] "0.611" "0.246" "0.952" "0.703" "0.95" "0.749" "0.344"
## [8] "0.939" "0.00104" "0.319" "0.921" "0.0383" "0.215" "0.958"
## [15] "0.97" "0.548" "0.7" "0.488" "0.381" "0.161" "0.852"
## [22] "0.513" "0.689" "0.669" "0.706" "0.882" "0.159" "0.864"
## [29] "0.716" "0.184" "0.00323" "0.305" "0.922" "0.942" "0.123"
## [36] "0.767" "0.164" "0.619" "0.932" "0.508" "0.649" "0.983"
## [43] "0.934" "0.576" "0.751" "0.614" "0.0287" "0.285" "0.659"
## [50] "0.581" "0.902" "0.386" "0.712" "0.917" "0.924" "0.967"
## [57] "0.989" "0.728" "0.871" "0.126" "0.929" "0.455" "0.733"
## [64] "0.71" "0.0575" "0.667" "0.791" "0.334" "0.933" "0.48"
## [71] "0.615" "0.979" "0.695" "0.756" "0.91" "0.776" "0.715"
## [78] "0.778" "0.398" "0.761" "0.616" "0.962" "0.525" "0.876"
## [85] "0.847" "0.66" "0.366" "0.357" "0.813" "0.345" "0.79"
## [92] "0.0367" "0.744" "0" "0.844" "0.987" "0.414" "0.636"
## [99] "0.951" "0.974" "0.523"
## [ reached getOption("max.print") -- omitted 4686 entries ]Check the unique values of popularity.
unique(data$popularity)## [1] "0" "1" "3"
## [4] "4" "2" "15"
## [7] "10" "8" "5"
## [10] "6" "7" "11"
## [13] "3NXlNZSmjO3DsJ3DQuyU8e" "65" "63"
## [16] "62" "61" "68"
## [19] "64" "66" "60"
## [22] "69" "71" "76"
## [25] "67" "70" "72"
## [28] "57" "59" "56"
## [31] "28" "31" "74"
## [34] "55" "53" "9"
## [37] "13" "23" "15hzCoAhSiWk8juLz5Jwut"
## [40] "12" "4Er5ftgKkMeKg07YPLVOd6" "7Ib5UBlT8wh2RuwbMkKRb5"
## [43] "44" "33" "25"
## [46] "26" "24" "22"
## [49] "20" "19" "18"
## [52] "16" "17" "14"
## [55] "83" "81" "73"
## [58] "78" "77" "75"
## [61] "45" "42" "46"
## [64] "54" "41" "52"
## [67] "58" "51" "43"
## [70] "47" "48" "40"
## [73] "50" "49" "39"
## [76] "80" "37" "35"
## [79] "21" "38" "36"
## [82] "29" "7gNbidsHK16wvnuK2VgaVc" "34"
## [85] "32" "99" "100"
## [88] "97" "92" "91"
## [91] "95" "90" "93"
## [94] "88" "87" "89"
## [97] "96" "86" "85"
## [100] "84" "94"
## [ reached getOption("max.print") -- omitted 103 entries ]Find non numeric data values in popularity and drop rows containing such values.
data <- transform(data[grep("^\\d+$", data$popularity),,drop=F], A= as.numeric(as.character(popularity))) Check the unique values of popularity.
unique(data$popularity)## [1] "0" "1" "3" "4" "2" "15" "10" "8" "5" "6" "7" "11"
## [13] "65" "63" "62" "61" "68" "64" "66" "60" "69" "71" "76" "67"
## [25] "70" "72" "57" "59" "56" "28" "31" "74" "55" "53" "9" "13"
## [37] "23" "12" "44" "33" "25" "26" "24" "22" "20" "19" "18" "16"
## [49] "17" "14" "83" "81" "73" "78" "77" "75" "45" "42" "46" "54"
## [61] "41" "52" "58" "51" "43" "47" "48" "40" "50" "49" "39" "80"
## [73] "37" "35" "21" "38" "36" "29" "34" "32" "99" "100" "97" "92"
## [85] "91" "95" "90" "93" "88" "87" "89" "96" "86" "85" "84" "94"
## [97] "82" "79" "27" "30" "98"Check numeric values of new data$A.
unique(data$A)## [1] 0 1 3 4 2 15 10 8 5 6 7 11 65 63 62 61 68 64
## [19] 66 60 69 71 76 67 70 72 57 59 56 28 31 74 55 53 9 13
## [37] 23 12 44 33 25 26 24 22 20 19 18 16 17 14 83 81 73 78
## [55] 77 75 45 42 46 54 41 52 58 51 43 47 48 40 50 49 39 80
## [73] 37 35 21 38 36 29 34 32 99 100 97 92 91 95 90 93 88 87
## [91] 89 96 86 85 84 94 82 79 27 30 98Convert key, mode and time_signature to factor type.
data<-data %>%
mutate(across(c(key,
mode,time_signature),
factor))Convert key, acousticness, liveness, popularity, loudness, speechiness, tempo, and valence to numeric type.
data <- data %>% mutate_at(c('key','acousticness', 'liveness','popularity','loudness','speechiness','tempo', 'valence'), as.numeric)View structure of transformed data.
glimpse(data)## Rows: 232,603
## Columns: 21
## $ genre <chr> "Movie", "Movie", "Movie", "Movie", "Movie", "Movie",…
## $ artist_name <chr> "Henri Salvador", "Martin & les fées", "Joseph Willia…
## $ track_name <chr> "C'est beau de faire un Show", "Perdu d'avance (par G…
## $ track_id <chr> "0BRjO6ga9RKCKjfDqeFgWV", "0BjC1NfoEOOusryehmNudP", "…
## $ popularity <dbl> 0, 1, 3, 0, 4, 0, 2, 15, 0, 10, 0, 2, 4, 3, 0, 0, 0, …
## $ acousticness <dbl> 0.61100, 0.24600, 0.95200, 0.70300, 0.95000, 0.74900,…
## $ danceability <dbl> 0.389, 0.590, 0.663, 0.240, 0.331, 0.578, 0.703, 0.41…
## $ duration_ms <dbl> 99373, 137373, 170267, 152427, 82625, 160627, 212293,…
## $ energy <dbl> 0.9100, 0.7370, 0.1310, 0.3260, 0.2250, 0.0948, 0.270…
## $ instrumentalness <dbl> 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.123…
## $ key <dbl> 5, 10, 4, 5, 9, 5, 5, 10, 4, 11, 8, 4, 10, 7, 11, 12,…
## $ liveness <dbl> 0.3460, 0.1510, 0.1030, 0.0985, 0.2020, 0.1070, 0.105…
## $ loudness <dbl> -1.828, -5.559, -13.879, -12.178, -21.150, -14.970, -…
## $ mode <fct> Major, Minor, Minor, Major, Major, Major, Major, Majo…
## $ speechiness <dbl> 0.0525, 0.0868, 0.0362, 0.0395, 0.0456, 0.1430, 0.953…
## $ tempo <dbl> 166.969, 174.003, 99.488, 171.758, 140.576, 87.479, 8…
## $ time_signature <fct> 4/4, 4/4, 5/4, 4/4, 4/4, 4/4, 4/4, 4/4, 4/4, 4/4, 4/4…
## $ valence <dbl> 0.8140, 0.8160, 0.3680, 0.2270, 0.3900, 0.3580, 0.533…
## $ X <chr> "", "", "", "", "", "", "", "", "", "", "", "", "", "…
## $ X.1 <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ A <dbl> 0, 1, 3, 0, 4, 0, 2, 15, 0, 10, 0, 2, 4, 3, 0, 0, 0, …Check for missing values.
colSums(is.na(data))## genre artist_name track_name track_id
## 0 0 0 0
## popularity acousticness danceability duration_ms
## 0 0 0 0
## energy instrumentalness key liveness
## 0 0 0 0
## loudness mode speechiness tempo
## 0 0 0 0
## time_signature valence X X.1
## 0 0 0 232603
## A
## 0Remove non meaningful columns.
data_cleaned <- data %>% select(-c(X, X.1, A, track_id))Check number of rows and display the transformed and cleaned data.
nrow(data_cleaned)## [1] 232603rmarkdown::paged_table(data_cleaned )We drop columns with non meaningful values for Principle Component Analysis clusterization. These are artist_name, track_name, genre, mode, time_signature; and convert “key” column into factor type.
spotify_reduced <- data_cleaned %>% select(-c(artist_name, track_name, genre, mode, time_signature))
spotify_reduced$key <- as.factor(data_cleaned$key)Scale the chosen data columns.
spotify_reduced.scaled <- scale(spotify_reduced[, c('energy', 'liveness', 'tempo', 'speechiness' , 'acousticness', 'instrumentalness', 'danceability' , 'duration_ms' ,'loudness', 'valence')])View the scaled data.
spotify_reduced.scaled## energy liveness tempo speechiness acousticness
## 1 1.28677820573 0.66067044236 1.59553078739 -0.368026641 0.683600143
## 2 0.63011056975 -0.32280635876 1.82317135659 -0.183147727 -0.345290172
## 3 -1.67012403954 -0.56489295596 -0.58834940172 -0.455884551 1.644837396
## 4 -0.92994953655 -0.58758857445 1.75051666824 -0.438097367 0.942936880
## 5 -1.31332197143 -0.06558934924 0.74137702809 -0.405218026 1.639199641
## 6 -1.80753079343 -0.54471907286 -0.97699534934 0.119773409 1.072605248
## 7 -1.14251247074 -0.55480601441 -1.12605882129 4.485718606 -0.069040170
## 8 -1.14630823742 -0.51445824821 -0.67446705237 -0.496848975 1.608191987
## 9 -0.34160570084 -0.69854493150 0.23988168258 -0.403062004 -1.035802423
## 10 0.50864603592 0.67580085469 0.64169932648 -0.499544003 -0.139512109
## instrumentalness danceability duration_ms loudness
## 1 -0.489868378 -0.890999212 -1.14294225406 1.290537266908
## 2 -0.489868378 0.191875596 -0.82295591648 0.668520702628
## 3 -0.489868378 0.585158487 -0.54596563785 -0.718554562664
## 4 -0.489868378 -1.693727303 -0.69619080264 -0.434971025854
## 5 -0.083649263 -1.203470549 -1.28397202200 -1.930744977801
## 6 -0.489868378 0.127226354 -0.62714111927 -0.900441475457
## 7 -0.489868378 0.800655961 -0.19207758987 -0.517828767062
## 8 -0.489868378 -0.745538417 0.04179874012 0.103354218332
## 9 -0.487028147 0.967666503 -0.07497101101 0.307414329476
## 10 -0.485740135 0.234975091 -0.69394247759 0.296577803966
## valence
## 1 1.3809857490
## 2 1.3886766187
## 3 -0.3340781846
## 4 -0.8762844954
## 5 -0.2494786183
## 6 -0.3725325329
## 7 0.3004185622
## 8 -0.6955490585
## 9 1.1925594424
## 10 1.0118240055
## [ reached getOption("max.print") -- omitted 232593 rows ]
## attr(,"scaled:center")
## energy liveness tempo speechiness
## 0.5709965 0.2150048 117.6677546 0.1207788
## acousticness instrumentalness danceability duration_ms
## 0.3684921 0.1483283 0.5543846 235103.1876803
## loudness valence
## -9.5689426 0.4548766
## attr(,"scaled:scale")
## energy liveness tempo speechiness
## 0.2634514 0.1982762 30.8995889 0.1855268
## acousticness instrumentalness danceability duration_ms
## 0.3547511 0.3027923 0.1856170 118755.0702572
## loudness valence
## 5.9982325 0.2600486Check for correlation between columns in dataset using cor().
corr_matrix <- cor(spotify_reduced.scaled)
ggcorrplot(corr_matrix)
Clusterization
We will use princomp() and prcomp() to generate new dimensions to describe the dataset.
PRINCOMP
Check importance of each newly computed components using princomp().
data.pca <- princomp(corr_matrix)
summary(data.pca)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.0334851 0.4790364 0.36319775 0.30096532 0.23594290
## Proportion of Variance 0.6501807 0.1396891 0.08029933 0.05513895 0.03388749
## Cumulative Proportion 0.6501807 0.7898698 0.87016915 0.92530810 0.95919559
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## Standard deviation 0.16690440 0.14901480 0.124957342 0.0368111108 0
## Proportion of Variance 0.01695748 0.01351713 0.009504935 0.0008248661 0
## Cumulative Proportion 0.97615307 0.98967020 0.999175134 1.0000000000 1From the above process, we notice that 10 principal components have been generated (Comp.1 to Comp.10).
In the Cumulative Proportion section, the first principal component explains almost 65% of the total variance.
Check the loadings of the original data columns in these computed components.
data.pca$loadings[, 1:10]## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## energy 0.449644805 0.04786607 0.279328068 0.02257737 0.31478102
## liveness -0.005136535 0.59660419 0.283635807 0.14279390 0.14268476
## tempo 0.146381788 -0.30077103 0.229791191 0.67724938 -0.49283877
## speechiness -0.008476668 0.64207534 0.035882341 0.06415608 -0.11204161
## acousticness -0.447070449 0.17618493 -0.246276321 0.06311711 -0.25705228
## instrumentalness -0.350406265 -0.28870737 -0.009199244 0.05068814 0.59923333
## danceability 0.329996145 0.05870279 -0.490869353 -0.26034338 -0.16405562
## duration_ms -0.100046536 -0.13924179 0.510883549 -0.66017224 -0.39099361
## loudness 0.476212127 -0.03522546 0.181103843 -0.04347133 0.12774580
## valence 0.328561091 -0.02408548 -0.438115336 -0.06533427 -0.06200723
## Comp.6 Comp.7 Comp.8 Comp.9
## energy 0.0095242526 0.005779868 0.2636812874 0.67995478
## liveness -0.4925077364 -0.087449578 -0.5100175147 -0.06092720
## tempo -0.0004688077 -0.297290639 -0.0849707459 -0.01288403
## speechiness 0.4296343651 -0.400505024 0.4366140774 -0.18384812
## acousticness -0.0854219621 0.372514068 0.1424843321 0.15562320
## instrumentalness 0.0476624965 -0.493676127 -0.0254341232 -0.17879015
## danceability 0.2997240167 -0.281325644 -0.5391899815 0.15977990
## duration_ms -0.1336673784 -0.253536172 0.0387082601 -0.02449449
## loudness 0.1642318553 0.386369173 0.0008389973 -0.62182042
## valence -0.6546123502 -0.261427754 0.3991602237 -0.17609233
## Comp.10
## energy 0.29311593
## liveness 0.09379477
## tempo 0.19488565
## speechiness 0.01698776
## acousticness 0.66917203
## instrumentalness 0.39182696
## danceability 0.25841212
## duration_ms 0.19144493
## loudness 0.39756666
## valence 0.06488294Display a scree plot from data.pca to see the importance of each component.
fviz_eig(data.pca, addlabels = TRUE)
The scree plot above show that the first component explains 65% of the variance in the dataset. Plot a graph to view loadings of original variables on the new components. As this can only be visualized in two dimensions we can only see the loadings for component 1 and 2.
# Graph of the variables
fviz_pca_var(data.pca, col.var = "black")
Check to view how much of each original variable is represented in dimensions 1 and 2.
fviz_cos2(data.pca, choice = "var", axes = 1:2)
fviz_pca_var(data.pca, col.var = "cos2",
gradient.cols = c("black", "orange", "green"),
repel = TRUE)
View the same information as above but for all dimensions in a tabular format.
# Eigenvalues
eig.val <- get_eigenvalue(data.pca)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.068091524 65.01807063 65.01807
## Dim.2 0.229475833 13.96891146 78.98698
## Dim.3 0.131912609 8.02993295 87.01692
## Dim.4 0.090580122 5.51389526 92.53081
## Dim.5 0.055669050 3.38874915 95.91956
## Dim.6 0.027857080 1.69574755 97.61531
## Dim.7 0.022205412 1.35171285 98.96702
## Dim.8 0.015614337 0.95049354 99.91751
## Dim.9 0.001355058 0.08248661 100.00000
## Dim.10 0.000000000 0.00000000 100.00000# Results for Variables
res.var <- get_pca_var(data.pca)
res.var$coord # Coordinates## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## energy 0.464701222 0.02292959 0.101451327 0.006795006 0.07427034
## liveness -0.005308532 0.28579510 0.103015888 0.042976011 0.03366545
## tempo 0.151283402 -0.14408026 0.083459645 0.203828575 -0.11628181
## speechiness -0.008760510 0.30757744 0.013032386 0.019308754 -0.02643542
## acousticness -0.462040663 0.08439899 -0.089447007 0.018996060 -0.06064966
## instrumentalness -0.362139667 -0.13830133 -0.003341145 0.015255373 0.14138485
## danceability 0.341046111 0.02812077 -0.178282647 -0.078354327 -0.03870776
## duration_ms -0.103396608 -0.06670188 0.185551758 -0.198688947 -0.09225216
## loudness 0.492158155 -0.01687428 0.065776509 -0.013083363 0.03014071
## valence 0.339563004 -0.01153782 -0.159122506 -0.019663351 -0.01463016
## Dim.6 Dim.7 Dim.8 Dim.9
## energy 0.00158963969 0.0008612859 0.0329489129 0.0250298909
## liveness -0.08220170994 -0.0130312818 -0.0637304331 -0.0022427978
## tempo -0.00007824606 -0.0443007063 -0.0106177186 -0.0004742756
## speechiness 0.07170786742 -0.0596811776 0.0545581347 -0.0067676535
## acousticness -0.01425730162 0.0555101109 0.0178044634 0.0057286630
## instrumentalness 0.00795508055 -0.0735650514 -0.0031781804 -0.0065814639
## danceability 0.05002525821 -0.0419216857 -0.0673757470 0.0058816755
## duration_ms -0.02230967406 -0.0377806430 0.0048368813 -0.0009016694
## loudness 0.02741101983 0.0575747266 0.0001048389 -0.0228899005
## valence -0.10925768382 -0.0389566055 0.0498780007 -0.0064821542
## Dim.10
## energy 0
## liveness 0
## tempo 0
## speechiness 0
## acousticness 0
## instrumentalness 0
## danceability 0
## duration_ms 0
## loudness 0
## valence 0res.var$contrib # Contributions to the PCs## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## energy 20.218045069 0.22911607 7.802416950 0.05097377 9.9087088
## liveness 0.002638399 35.59365613 8.044927097 2.03900975 2.0358940
## tempo 2.142762774 9.04632134 5.280399140 45.86667251 24.2890057
## speechiness 0.007185389 41.22607485 0.128754243 0.41160024 1.2553323
## acousticness 19.987198643 3.10411307 6.065202651 0.39837692 6.6075877
## instrumentalness 12.278455087 8.33519470 0.008462608 0.25692877 35.9080580
## danceability 10.889745598 0.34460181 24.095272199 6.77786745 2.6914248
## duration_ms 1.000930932 1.93882772 26.100200094 43.58273817 15.2876002
## loudness 22.677799031 0.12408330 3.279860212 0.18897567 1.6318990
## valence 10.795239077 0.05801102 19.194504806 0.42685674 0.3844896
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## energy 0.00907113871 0.003340688 6.95278213231 46.23385075 NaN
## liveness 24.25638703706 0.764742877 26.01178653443 0.37121233 NaN
## tempo 0.00002197806 8.838172401 0.72200276519 0.01659983 NaN
## speechiness 18.45856876904 16.040427389 19.06318525778 3.38001312 NaN
## acousticness 0.72969116007 13.876673104 2.03017848825 2.42185812 NaN
## instrumentalness 0.22717135725 24.371611861 0.06468946210 3.19659164 NaN
## danceability 8.98344861934 7.914411791 29.07258361037 2.55296156 NaN
## duration_ms 1.78669680504 6.428059063 0.14983294023 0.05999801 NaN
## loudness 2.69721022834 14.928113788 0.00007039164 38.66606387 NaN
## valence 42.85173290708 6.834447039 15.93288841770 3.10085077 NaNres.var$cos2 # Quality of representation ## Dim.1 Dim.2 Dim.3 Dim.4
## energy 0.21594722573 0.0005257660 0.01029237176 0.00004617211
## liveness 0.00002818051 0.0816788389 0.01061227322 0.00184693753
## tempo 0.02288666758 0.0207591213 0.00696551227 0.04154608809
## speechiness 0.00007674653 0.0946038788 0.00016984308 0.00037282800
## acousticness 0.21348157462 0.0071231893 0.00800076705 0.00036085030
## instrumentalness 0.13114513808 0.0191272575 0.00001116325 0.00023272640
## danceability 0.11631244973 0.0007907779 0.03178470219 0.00613940063
## duration_ms 0.01069085845 0.0044491411 0.03442945488 0.03947729757
## loudness 0.24221964931 0.0002847412 0.00432654918 0.00017117439
## valence 0.11530303360 0.0001331213 0.02531997206 0.00038664736
## Dim.5 Dim.6 Dim.7
## energy 0.0055160841 0.000002526954357 0.0000007418134
## liveness 0.0011333628 0.006757121116775 0.0001698143054
## tempo 0.0135214588 0.000000006122446 0.0019625525811
## speechiness 0.0006988316 0.005142018249633 0.0035618429633
## acousticness 0.0036783813 0.000203270649454 0.0030813724130
## instrumentalness 0.0199896749 0.000063283306491 0.0054118167867
## danceability 0.0014982906 0.002502526459297 0.0017574277331
## duration_ms 0.0085104618 0.000497721556479 0.0014273769884
## loudness 0.0009084627 0.000751364008270 0.0033148491470
## valence 0.0002140417 0.011937241472705 0.0015176171121
## Dim.8 Dim.9 Dim.10
## energy 0.00108563085923 0.0006264954376 0
## liveness 0.00406156810728 0.0000050301419 0
## tempo 0.00011273594763 0.0000002249373 0
## speechiness 0.00297659006096 0.0000458011341 0
## acousticness 0.00031699891851 0.0000328175794 0
## instrumentalness 0.00001010083086 0.0000433156669 0
## danceability 0.00453949128915 0.0000345941068 0
## duration_ms 0.00002339542079 0.0000008130078 0
## loudness 0.00000001099119 0.0005239475453 0
## valence 0.00248781495145 0.0000420183226 0Using a biplot method to view loadings on dimension 1 and 2.
biplot.data.pca <- biplot(data.pca)
biplot.data.pca## NULLPRCOMP
Now we use another Principal Component Analysis (PCA) method :- prcomp() function; to reduce the dimensionality - from the currently ten(10) attributes.
km_pca = prcomp(spotify_reduced.scaled)
print(km_pca)## Standard deviations (1, .., p=10):
## [1] 1.8598987 1.2736103 1.0805238 0.9755786 0.8911513 0.8340208 0.7224191
## [8] 0.6290964 0.5260709 0.3395067
##
## Rotation (n x k) = (10 x 10):
## PC1 PC2 PC3 PC4 PC5
## energy -0.46288362 0.048539594 -0.262962371 0.02410196 0.23315823
## liveness -0.05451613 0.641679889 -0.228647374 0.14427840 0.07137532
## tempo -0.16182899 -0.206137689 -0.316727458 0.67371223 -0.59241483
## speechiness -0.05355133 0.675961422 0.009716966 0.06414449 -0.14133312
## acousticness 0.42027103 0.226232382 0.225490866 0.06090180 -0.26438028
## instrumentalness 0.33290119 -0.173276562 -0.086712133 0.04730942 0.04374225
## danceability -0.34159993 0.034058937 0.461889968 -0.26365828 -0.29686399
## duration_ms 0.06634947 -0.002321853 -0.579893204 -0.66220086 -0.46787149
## loudness -0.47466331 -0.062343730 -0.161817820 -0.04173756 0.20751005
## valence -0.34621007 -0.014705015 0.379462602 -0.06989459 -0.38433023
## PC6 PC7 PC8 PC9 PC10
## energy -0.22946948 0.02421827 -0.27005340 -0.14286895 -0.716035365
## liveness -0.20752260 -0.43614997 0.52092257 -0.01047949 0.048187408
## tempo 0.05790394 0.10561876 0.10484265 -0.02186972 -0.013430821
## speechiness -0.03120918 0.54042965 -0.40616092 0.15627919 0.183293004
## acousticness 0.13436722 -0.16894027 -0.19459832 -0.70479380 -0.257955243
## instrumentalness -0.85631733 0.25492526 0.04860984 -0.17932361 0.121224354
## danceability -0.06876644 0.38419642 0.54825682 -0.14141793 -0.195557997
## duration_ms 0.01555523 -0.03386144 -0.01948756 -0.01152142 -0.001206506
## loudness 0.07275085 0.05022084 -0.05318060 -0.62128597 0.550619014
## valence -0.37195949 -0.51104191 -0.36841180 0.13984949 0.168916196PCA transforms the variables of the original data set into principal components (PC1:PC10). The degree to which each principal component explains the variance in the original data is also inferred from the standard deviation of each principal component and its calculated variance.
pca_tbl = tibble(proportional_variance = km_pca$sdev^2/sum(km_pca$sdev^2) , PC =paste0("PC", 1:10))
print(pca_tbl)## # A tibble: 10 × 2
## proportional_variance PC
## <dbl> <chr>
## 1 0.346 PC1
## 2 0.162 PC2
## 3 0.117 PC3
## 4 0.0952 PC4
## 5 0.0794 PC5
## 6 0.0696 PC6
## 7 0.0522 PC7
## 8 0.0396 PC8
## 9 0.0277 PC9
## 10 0.0115 PC10In contrast to the PRINCOMP() function method, here the first component only explains 35% of the variance in data. We plot the Cumulative Variance Explained.
ggplot(pca_tbl, aes(x = 1:10, y = cumsum(proportional_variance))) +
geom_line() +
geom_point() +
scale_x_continuous(breaks = 1:10, labels = pca_tbl$PC, name = "Principal Component") +
scale_y_continuous(name = "Cummulative Variance Explained", breaks = seq.default(from = 0.6, to = 1, by = 0.05), labels = scales::percent_format(accuracy = 1)) +
labs(caption = "Fig. 1 Explaining dataset variance using PCA")
The above shows that only using first six (6) principal components - PC1 to PC6 - we can explain more than 85% of the data set’s variance. We plot the importance of these principal components using a scree plot.
fviz_eig(km_pca, addlabels = TRUE)
Plot the loadings of the original variables on components 1 and 2.
# Graph of the variables
fviz_pca_var(km_pca, col.var = "black")
Check to view how much of each original variable is represented in dimensions 1 and 2.
fviz_cos2(km_pca, choice = "var", axes = 1:2)
fviz_pca_var(km_pca, col.var = "cos2",
gradient.cols = c("black", "orange", "green"),
repel = TRUE)
View the same information as above but for all dimensions in a tabular format.
# Eigenvalues
eig.val <- get_eigenvalue(km_pca)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 3.4592233 34.592233 34.59223
## Dim.2 1.6220832 16.220832 50.81307
## Dim.3 1.1675317 11.675317 62.48838
## Dim.4 0.9517536 9.517536 72.00592
## Dim.5 0.7941506 7.941506 79.94742
## Dim.6 0.6955907 6.955907 86.90333
## Dim.7 0.5218893 5.218893 92.12222
## Dim.8 0.3957622 3.957622 96.07985
## Dim.9 0.2767506 2.767506 98.84735
## Dim.10 0.1152648 1.152648 100.00000# Results for Variables
res.var <- get_pca_var(km_pca)
res.var$coord # Coordinates## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## energy -0.86091667 0.061820527 -0.28413710 0.02351336 0.20777925
## liveness -0.10139448 0.817250120 -0.24705893 0.14075491 0.06360620
## tempo -0.30098554 -0.262539085 -0.34223155 0.65725922 -0.52793123
## speechiness -0.09960005 0.860911433 0.01049941 0.06257799 -0.12594919
## acousticness 0.78166156 0.288131893 0.24364824 0.05941449 -0.23560282
## instrumentalness 0.61916250 -0.220686815 -0.09369452 0.04615405 0.03898096
## danceability -0.63534128 0.043377814 0.49908310 -0.25721937 -0.26455072
## duration_ms 0.12340329 -0.002957136 -0.62658840 -0.64602897 -0.41694427
## loudness -0.88282569 -0.079401617 -0.17484800 -0.04071827 0.18492284
## valence -0.64391568 -0.018728458 0.41001837 -0.06818766 -0.34249637
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## energy -0.19138232 0.01749574 -0.16988961 -0.075159195 -0.2430988365
## liveness -0.17307817 -0.31508306 0.32771049 -0.005512956 0.0163599500
## tempo 0.04829309 0.07630101 0.06595613 -0.011505021 -0.0045598543
## speechiness -0.02602910 0.39041668 -0.25551436 0.082213934 0.0622292113
## acousticness 0.11206506 -0.12204567 -0.12242110 -0.370771499 -0.0875775449
## instrumentalness -0.71418647 0.18416287 0.03058027 -0.094336932 0.0411564859
## danceability -0.05735264 0.27755082 0.34490637 -0.074395855 -0.0663932591
## duration_ms 0.01297338 -0.02446215 -0.01225955 -0.006061084 -0.0004096168
## loudness 0.06067572 0.03628049 -0.03345572 -0.326840463 0.1869388693
## valence -0.31022195 -0.36918642 -0.23176652 0.073570747 0.0573481881res.var$contrib # Contributions to the PCs## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## energy 21.4261250 0.2356092189 6.914920880 0.05809046 5.4362759
## liveness 0.2972008 41.1753079632 5.227962142 2.08162554 0.5094436
## tempo 2.6188623 4.2492746845 10.031628234 45.38881732 35.0955335
## speechiness 0.2867745 45.6923843487 0.009441943 0.41145162 1.9975051
## acousticness 17.6627739 5.1181090659 5.084613056 0.37090295 6.9896932
## instrumentalness 11.0823202 3.0024766882 0.751899395 0.22381809 0.1913384
## danceability 11.6690512 0.1160011219 21.334234287 6.95156898 8.8128229
## duration_ms 0.4402252 0.0005391002 33.627612760 43.85099731 21.8903730
## loudness 22.5305254 0.3886740625 2.618500696 0.17420238 4.3060420
## valence 11.9861415 0.0216237461 14.399186608 0.48852534 14.7709724
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## energy 5.26562428 0.05865244 7.29288371 2.04115365 51.2706644603
## liveness 4.30656312 19.02267994 27.13603230 0.01098198 0.2322026282
## tempo 0.33528657 1.11553222 1.09919804 0.04782845 0.0180386949
## speechiness 0.09740128 29.20642047 16.49666962 2.44231866 3.3596325361
## acousticness 1.80545505 2.85408139 3.78685076 49.67342992 6.6540907199
## instrumentalness 73.32793643 6.49868897 0.23629163 3.21569579 1.4695343998
## danceability 0.47288229 14.76068858 30.05855449 1.99990307 3.8242930266
## duration_ms 0.02419651 0.11465971 0.03797649 0.01327431 0.0001455656
## loudness 0.52926860 0.25221327 0.28281767 38.59962610 30.3181298278
## valence 13.83538589 26.11638301 13.57272528 1.95578808 2.8532681407res.var$cos2 # Quality of representation ## Dim.1 Dim.2 Dim.3 Dim.4
## energy 0.741177516 0.003821777587 0.0807338904 0.0005528781
## liveness 0.010280841 0.667897758379 0.0610381131 0.0198119452
## tempo 0.090592294 0.068926771332 0.1171224354 0.4319896863
## speechiness 0.009920169 0.741168496148 0.0001102377 0.0039160054
## acousticness 0.610994795 0.083019987982 0.0593644671 0.0035300821
## instrumentalness 0.383362205 0.048702670333 0.0087786635 0.0021301967
## danceability 0.403658542 0.001881634725 0.2490839392 0.0661618055
## duration_ms 0.015228373 0.000008744654 0.3926130247 0.4173534296
## loudness 0.779381192 0.006304616722 0.0305718246 0.0016579774
## valence 0.414627403 0.000350755155 0.1681150621 0.0046495573
## Dim.5 Dim.6 Dim.7 Dim.8
## energy 0.043172216 0.0366271938 0.0003061008 0.0288624793
## liveness 0.004045749 0.0299560533 0.0992773330 0.1073941668
## tempo 0.278711378 0.0023322223 0.0058218434 0.0043502107
## speechiness 0.015863198 0.0006775143 0.1524251862 0.0652875877
## acousticness 0.055508688 0.0125585777 0.0148951457 0.0149869251
## instrumentalness 0.001519515 0.5100623201 0.0339159630 0.0009351530
## danceability 0.069987083 0.0032893253 0.0770344558 0.1189604058
## duration_ms 0.173842522 0.0001683087 0.0005983968 0.0001502966
## loudness 0.034196457 0.0036815432 0.0013162741 0.0011192855
## valence 0.117303761 0.0962376602 0.1362986110 0.0537157204
## Dim.9 Dim.10
## energy 0.00564890454 0.059097044285
## liveness 0.00003039269 0.000267647965
## tempo 0.00013236551 0.000020792271
## speechiness 0.00675913101 0.003872474735
## acousticness 0.13747150463 0.007669826364
## instrumentalness 0.00889945671 0.001693856329
## danceability 0.00553474330 0.004408064860
## duration_ms 0.00003673674 0.000000167786
## loudness 0.10682468851 0.034946140838
## valence 0.00541265481 0.003288814675Plot the dataset using new dimensional components 1 and 2 and ‘danceability’ as 3rd variable in terms of color tone.
# would not render into .pdf
# ggplot2::autoplot(km_pca, data = data_cleaned, colour = 'danceability')Plot the dataset using new dimensional components 1 and 2 and ‘energy’ as 3rd variable in terms of color tone.
# would not render into .pdf
# ggplot2::autoplot(km_pca, data = data_cleaned, colour = 'energy')KMEANS
Use k-means() to cluster dataset into 10 centers.
set.seed(123)
km_10 <- kmeans( spotify_reduced.scaled, centers = 10)
km_10## K-means clustering with 10 clusters of sizes 22325, 35951, 9630, 3952, 52237, 28236, 46794, 108, 21086, 12284
##
## Cluster means:
## energy liveness tempo speechiness acousticness instrumentalness
## 1 -1.3290418 -0.1764674 -0.31024696 -0.36809381 1.3376732 -0.35598308
## 2 0.7731637 -0.1539308 1.41650750 -0.06430712 -0.7058481 -0.27337354
## 3 0.3681702 2.6126105 -0.64832710 4.17208956 1.2144820 -0.48800649
## 4 -1.3224690 -0.1758294 -0.44303299 -0.30439439 1.2101034 1.48929376
## 5 0.5918253 -0.2600115 -0.25000007 -0.10051790 -0.6329072 -0.33946172
## 6 -0.5969196 -0.3406919 -0.06118599 -0.15283855 0.7220474 -0.13622259
## 7 0.3042919 -0.2827280 -0.26654143 -0.21507673 -0.6536308 -0.15060635
## 8 -0.3753096 0.7539466 -0.80834933 2.49580982 0.9351803 -0.01980392
## 9 -1.5038465 -0.3892401 -0.45747143 -0.40931604 1.3068999 2.28914952
## 10 0.5704019 2.4069607 0.08048224 -0.03685787 -0.4366858 -0.24840148
## danceability duration_ms loudness valence
## 1 -0.91610715 -0.05680334 -0.9469556 -0.91255378
## 2 -0.26055771 -0.07760216 0.6283494 0.29094665
## 3 0.04410542 -0.12981649 -0.4107823 -0.18225243
## 4 -1.38658587 3.51740454 -1.5386806 -1.11317389
## 5 0.86109123 -0.10684960 0.5349201 1.01592334
## 6 0.59129195 -0.28915360 -0.1998337 0.45646890
## 7 0.05713629 0.11668976 0.4327238 -0.59749389
## 8 -0.17391141 23.80895659 -0.6481866 0.02627823
## 9 -1.36710407 -0.23352332 -1.8547459 -1.13155661
## 10 -0.05130122 0.16653602 0.4247701 0.15678481
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 2 2 1 1 1 1 3 1 5 5 4 9 7 6 9 8 1 5 7 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 1 6 5 6 6 6 5 6 6 5 5 3 6 6 5 6 5 6 9 6
## 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 6 9 1 6 6 6 5 5 5 6 1 10 3 1 3 1 1 10 9 7
## 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 1 6 1 6 6 2 5 1 5 6 6 1 1 6 3 1 6 1 4 3
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 98 99 100 101
## 5 6 3 9 10 6 6 1 6 6 7 6 2 6 5 1 6 9 7 5
## 102
## 6
## [ reached getOption("max.print") -- omitted 232502 entries ]
##
## Within cluster sum of squares by cluster:
## [1] 94441.126 127524.764 57243.046 41856.639 145044.366 117894.327
## [7] 166138.730 6345.525 111628.508 67389.655
## (between_SS / total_SS = 59.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"Plot the k-means result with 10 centers.
# would not render into .pdf
# set.seed(1)
# autoplot(kmeans(spotify_reduced.scaled, 10), data = spotify_reduced.scaled)Use k-means() to cluster dataset into 7 centers.
set.seed(123)
km_7 <- kmeans( spotify_reduced.scaled, centers = 7)
km_7## K-means clustering with 7 clusters of sizes 22667, 39079, 10018, 23521, 56881, 31062, 49375
##
## Cluster means:
## energy liveness tempo speechiness acousticness instrumentalness
## 1 -1.3334698 -0.06860210 -0.33183609 -0.36652258 1.3419550 -0.3469254
## 2 0.7976342 0.16989815 1.37388833 -0.05595129 -0.7059861 -0.2757158
## 3 0.3599028 2.60575281 -0.64173234 4.10083161 1.1930227 -0.4867282
## 4 -1.5107929 -0.37611351 -0.46372339 -0.41159065 1.3185027 2.2779556
## 5 0.5789961 -0.14583843 -0.24627668 -0.08762423 -0.6202609 -0.3435237
## 6 -0.6116571 -0.29491438 -0.04630864 -0.16313431 0.7276884 -0.1311518
## 7 0.3453222 -0.09896193 -0.27109748 -0.21985191 -0.6706929 -0.1306630
## danceability duration_ms loudness valence
## 1 -0.977368450 0.08460353 -0.9840996 -0.9362126
## 2 -0.273900462 -0.05509184 0.6304404 0.2830091
## 3 0.041010693 0.06499160 -0.4009519 -0.1647969
## 4 -1.402124960 0.19937570 -1.8539274 -1.1570395
## 5 0.858405465 -0.10998391 0.5256913 0.9974758
## 6 0.538809220 -0.27931492 -0.2007224 0.3643702
## 7 -0.002777729 0.19902175 0.4379860 -0.5879171
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 2 2 6 1 1 1 3 1 5 5 4 4 7 6 4 3 1 5 7 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 1 6 5 6 6 6 5 6 6 5 5 3 6 6 5 6 5 6 4 6
## 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 6 4 1 6 6 6 5 5 5 6 1 2 3 6 3 1 1 1 4 7
## 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 1 6 1 6 6 2 5 6 5 6 6 1 1 6 3 6 6 1 1 3
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 98 99 100 101
## 5 6 3 4 6 6 6 6 6 6 7 6 2 6 5 1 6 4 7 5
## 102
## 6
## [ reached getOption("max.print") -- omitted 232502 entries ]
##
## Within cluster sum of squares by cluster:
## [1] 115957.15 169521.95 97929.37 167498.56 178439.09 136345.26 233534.47
## (between_SS / total_SS = 52.7 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"Plot the k-means result with 7 centers.
# set.seed(1)
# autoplot(kmeans(spotify_reduced.scaled, 7), data = spotify_reduced.scaled)Use kmeans() to cluster dataset into 3 centers.
set.seed(123)
km_3 <- kmeans( spotify_reduced.scaled, centers = 3)
km_3## K-means clustering with 3 clusters of sizes 53140, 169097, 10366
##
## Cluster means:
## energy liveness tempo speechiness acousticness instrumentalness
## 1 -1.3585806 -0.25338106 -0.3686223 -0.3778857 1.2767734 0.9674164
## 2 0.4060388 -0.07866395 0.1540547 -0.1278091 -0.4730022 -0.2742902
## 3 0.3410212 2.58214421 -0.6233460 4.0220889 1.1707034 -0.4849378
## danceability duration_ms loudness valence
## 1 -1.01051313 0.09955897 -1.3183608 -0.9145171
## 2 0.31493676 -0.03539747 0.4387450 0.2965517
## 3 0.04281365 0.06705024 -0.3986855 -0.1493891
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 2 2 1 1 1 1 3 1 2 2 1 1 2 2 1 3 3 2 2 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 1 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 1 2
## 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 2 1 1 2 3 2 2 2 2 2 1 2 3 1 3 1 1 1 1 2
## 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 1 2 1 2 2 2 2 1 2 2 2 1 1 1 3 1 2 1 1 3
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 98 99 100 101
## 2 2 3 1 2 2 2 2 2 2 2 2 2 3 2 1 2 1 2 2
## 102
## 1
## [ reached getOption("max.print") -- omitted 232502 entries ]
##
## Within cluster sum of squares by cluster:
## [1] 453830.3 908321.4 108320.2
## (between_SS / total_SS = 36.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"Plot the k-means result with 3 centers.
#would not render into .pdf
# set.seed(1)
# autoplot(kmeans(spotify_reduced.scaled, 3), data = spotify_reduced.scaled)Compute percentage of betweens for 3-center cluster.
print(paste0(round(km_3$betweenss/km_3$totss, 4)*100, "%"))## [1] "36.78%"Compute percentage of betweens for 7-center cluster.
print(paste0(round(km_7$betweenss/km_7$totss, 4)*100, "%"))## [1] "52.74%"Compute percentage of betweens for 10-center cluster.
print(paste0(round(km_10$betweenss/km_10$totss, 4)*100, "%"))## [1] "59.78%"Choose to classify original data using 7-center cluster and create new column “cluster_num” in original dataset to denote classification.
spotify_songs_final <- cbind(spotify_reduced, cluster_num = km_7$cluster)Display original dataset with new classification in new “cluster_num” column.
rmarkdown::paged_table(spotify_songs_final)Check the proportion of each type of cluster in dataset.
table("\nFrequency" = factor(spotify_songs_final$cluster_num)
) %>%
prop.table()##
## Frequency
## 1 2 3 4 5 6 7
## 0.09744930 0.16800729 0.04306909 0.10112079 0.24454113 0.13354084 0.21227155# gunakan fungsi fviz_cluster() dari package factoextra
fviz_cluster(
object =km_7,
data = spotify_reduced.scaled
)
Conclusion
We used princomp() and prcomp() as preliminaries to using k-means. The prcomp() function generated components that are similar to k-means components, in terms of the cumulative explained variance ability of the components. According to the Scree plot for prcomp() a seven(7) cluster classification can explain 85% of variances in the original dataset. We choose the seven(7) clusters to classify the original dataset. This clusterization show that 25% of the dataset lie in cluster number 7, 22% in cluster number 6, 17% in cluster number 5, and 15% in cluster number 2.