Reading Data

Pertama, download data dari link dataset yang sudah disediakan. Selanjutnya, import dataset ke dalam variabel data.

data__ <- read.csv("D:/Semester 4/data11.csv")
head(data__)
##   StationId       Date PM2.5   PM10   NO   NO2   NOx   NH3   CO   SO2     O3
## 1     AP001 2017-11-24 71.36 115.75 1.75 20.65 12.40 12.19 0.10 10.76 109.26
## 2     AP001 2017-11-25 81.40 124.50 1.44 20.50 12.08 10.72 0.12 15.24 127.09
## 3     AP001 2017-11-26 78.32 129.06 1.26 26.00 14.85 10.28 0.14 26.96 117.44
## 4     AP001 2017-11-27 88.76 135.32 6.60 30.85 21.77 12.91 0.11 33.59 111.81
## 5     AP001 2017-11-28 64.18 104.09 2.56 28.07 17.01 11.42 0.09 19.00 138.18
## 6     AP001 2017-11-29 72.47 114.84 5.23 23.20 16.59 12.25 0.16 10.55 109.74
##   Benzene Toluene Xylene AQI AQI_Bucket
## 1    0.17    5.92   0.10  NA           
## 2    0.20    6.50   0.06 184   Moderate
## 3    0.22    7.95   0.08 197   Moderate
## 4    0.29    7.63   0.12 198   Moderate
## 5    0.17    5.02   0.07 188   Moderate
## 6    0.21    4.71   0.08 173   Moderate

Import Library

Import library esensial untuk memudahkan proses analisis

library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.5.3
## Warning: package 'readr' was built under R version 4.5.3
## Warning: package 'forcats' was built under R version 4.5.3
## Warning: package 'lubridate' was built under R version 4.5.3
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.2.0     ✔ readr     2.2.0
## ✔ forcats   1.0.1     ✔ stringr   1.6.0
## ✔ ggplot2   4.0.2     ✔ tibble    3.3.1
## ✔ lubridate 1.9.5     ✔ tidyr     1.3.2
## ✔ purrr     1.2.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(flexclust)
## Warning: package 'flexclust' was built under R version 4.5.3
library(dbscan)
## Warning: package 'dbscan' was built under R version 4.5.3
## 
## Attaching package: 'dbscan'
## 
## The following object is masked from 'package:stats':
## 
##     as.dendrogram
library(meanShiftR)
library(e1071)
## Warning: package 'e1071' was built under R version 4.5.3
## 
## Attaching package: 'e1071'
## 
## The following object is masked from 'package:flexclust':
## 
##     bclust
## 
## The following object is masked from 'package:ggplot2':
## 
##     element
library(cluster)
## Warning: package 'cluster' was built under R version 4.5.3
library(fpc)
## Warning: package 'fpc' was built under R version 4.5.3
## 
## Attaching package: 'fpc'
## 
## The following object is masked from 'package:dbscan':
## 
##     dbscan
library(mclust)
## Warning: package 'mclust' was built under R version 4.5.3
## Package 'mclust' version 6.1.2
## Type 'citation("mclust")' for citing this R package in publications.
## 
## Attaching package: 'mclust'
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##     count
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##     map

Preprocessing

Tahap pertama yang dilakukan adalah memilah atau subset variabel yang bukan numerik.

str(data__)
## 'data.frame':    108035 obs. of  16 variables:
##  $ StationId : chr  "AP001" "AP001" "AP001" "AP001" ...
##  $ Date      : chr  "2017-11-24" "2017-11-25" "2017-11-26" "2017-11-27" ...
##  $ PM2.5     : num  71.4 81.4 78.3 88.8 64.2 ...
##  $ PM10      : num  116 124 129 135 104 ...
##  $ NO        : num  1.75 1.44 1.26 6.6 2.56 5.23 4.69 4.58 7.71 0.97 ...
##  $ NO2       : num  20.6 20.5 26 30.9 28.1 ...
##  $ NOx       : num  12.4 12.1 14.8 21.8 17 ...
##  $ NH3       : num  12.2 10.7 10.3 12.9 11.4 ...
##  $ CO        : num  0.1 0.12 0.14 0.11 0.09 0.16 0.12 0.1 0.1 0.15 ...
##  $ SO2       : num  10.8 15.2 27 33.6 19 ...
##  $ O3        : num  109 127 117 112 138 ...
##  $ Benzene   : num  0.17 0.2 0.22 0.29 0.17 0.21 0.16 0.17 0.25 0.23 ...
##  $ Toluene   : num  5.92 6.5 7.95 7.63 5.02 4.71 3.52 2.85 2.79 3.82 ...
##  $ Xylene    : num  0.1 0.06 0.08 0.12 0.07 0.08 0.06 0.04 0.07 0.04 ...
##  $ AQI       : num  NA 184 197 198 188 173 165 191 191 227 ...
##  $ AQI_Bucket: chr  "" "Moderate" "Moderate" "Moderate" ...
data_NUM <- data__[, sapply(data__, is.numeric)]
str(data_NUM)
## 'data.frame':    108035 obs. of  13 variables:
##  $ PM2.5  : num  71.4 81.4 78.3 88.8 64.2 ...
##  $ PM10   : num  116 124 129 135 104 ...
##  $ NO     : num  1.75 1.44 1.26 6.6 2.56 5.23 4.69 4.58 7.71 0.97 ...
##  $ NO2    : num  20.6 20.5 26 30.9 28.1 ...
##  $ NOx    : num  12.4 12.1 14.8 21.8 17 ...
##  $ NH3    : num  12.2 10.7 10.3 12.9 11.4 ...
##  $ CO     : num  0.1 0.12 0.14 0.11 0.09 0.16 0.12 0.1 0.1 0.15 ...
##  $ SO2    : num  10.8 15.2 27 33.6 19 ...
##  $ O3     : num  109 127 117 112 138 ...
##  $ Benzene: num  0.17 0.2 0.22 0.29 0.17 0.21 0.16 0.17 0.25 0.23 ...
##  $ Toluene: num  5.92 6.5 7.95 7.63 5.02 4.71 3.52 2.85 2.79 3.82 ...
##  $ Xylene : num  0.1 0.06 0.08 0.12 0.07 0.08 0.06 0.04 0.07 0.04 ...
##  $ AQI    : num  NA 184 197 198 188 173 165 191 191 227 ...

Menghapus baris yang terdeteksi memiliki nilai kosong.

for(i in 1:ncol(data_NUM)){
  data_NUM[is.na(data_NUM[,i]), i] <- mean(data_NUM[,i], na.rm = TRUE)
}
set.seed(123)
data_sample <- data_NUM[sample(nrow(data_NUM), 1000), ]
sum(is.na(data_sample))
## [1] 0

distribusi data

library(ggplot2)

data_long <- data_sample %>%
  pivot_longer(cols = everything(),
               names_to = "Variable",
               values_to = "Value")

ggplot(data_long, aes(x = Variable, y = Value)) +
  geom_boxplot(fill = "skyblue", color = "black") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  labs(title = "Boxplot Masing-Masing Variabel",
       x = "Variabel",
       y = "Nilai")

scale data untuk memastikan bahwa metrics jarak tidak bias

data_scaled <- scale(data_sample)

mencari jumlah cluster (k) untuk k-means menggunakan elbow method

# Elbow Method using base R and a loop
wss <- sapply(1:10, function(k){
 kmeans(data_scaled, centers = k, nstart = 20)$tot.withinss
})
par(mfrow = c(1, 1))
plot(1:10, wss, type = "b", pch = 19, frame = FALSE,
 xlab = "Number of clusters K",
 ylab = "Total within-clusters sum of squares",
 main = "Elbow Method")

avg_sil <- function(k) {
 km_res <- kmeans(data_scaled, centers = k, nstart = 25)
 ss <- silhouette(km_res$cluster, dist(data_scaled))
 mean(ss[, 3])
}
k_values <- 2:10
avg_sil_values <- sapply(k_values, avg_sil)
par(mfrow = c(1, 1))
plot(k_values, avg_sil_values, type = "b", pch = 19, frame = FALSE,
 xlab = "Number of clusters K",
 ylab = "Average Silhouette Width",
 main = "Silhouette Analysis")

datates <- data_scaled[, c("AQI", "PM2.5")]

Kmeans

km_res <- kmeans(data_scaled, centers = 3)

visualisasi

plot(datates, col = km_res$cluster, main = "K-means")

kmedian

# --- 2. K-median ---
# Using flexclust; 'kcca' is the general function for centroid-based clustering
kmed_res <- kcca(data_scaled, k = 3, family = kccaFamily("kmedians"))
## Found more than one class "kcca" in cache; using the first, from namespace 'flexclust'
## Also defined by 'kernlab'
## Found more than one class "kcca" in cache; using the first, from namespace 'flexclust'
## Also defined by 'kernlab'

visualisasi

plot(datates, col = clusters(kmed_res), main = "K-medians")

DBSCAN

db_res <- dbscan(data_scaled, eps = 1, MinPts = 15)

visualisasi

plot(datates, col = db_res$cluster + 1L, main = "DBSCAN")

mean shift

ms_res <- meanShift(data_scaled)

visualisasi

plot(datates, col = ms_res$assignment, main = "Mean Shift")

fuzzy c-means

fcm_res <- cmeans(data_scaled, centers = 3, m = 2) # m = 2 is the fuzziness parameter

visualisasi

plot(datates, col = fcm_res$cluster, main = "Fuzzy C-means")

km_res$centers
##        PM2.5       PM10         NO        NO2        NOx        NH3         CO
## 1  2.4920725  2.5757612  2.7703622  2.1847392  2.6223440  1.5343878  0.3312041
## 2  0.3898740  0.3253367  0.1893929  0.3585502  0.3004405  0.1267733  0.2341986
## 3 -0.5084961 -0.4714539 -0.3951667 -0.4574681 -0.4585225 -0.2341171 -0.1947259
##          SO2          O3    Benzene    Toluene      Xylene        AQI
## 1  0.5131853  0.48377170  1.4307127  1.7908173  0.08719201  2.2872285
## 2  0.2534683  0.03544812  0.1339228  0.1423602  0.14611621  0.5451632
## 3 -0.2254444 -0.07066168 -0.2292540 -0.2693395 -0.11014405 -0.5972968
kmed_res@centers
##            PM2.5        PM10          NO          NO2         NOx          NH3
## [1,] -0.82305878 -1.08423789 -0.55385419 -0.786460097 -0.55609102 -0.926705452
## [2,]  0.01747389  0.00479915 -0.01682686 -0.004734821 -0.00702352 -0.002394755
## [3,] -0.49633105  0.00479915 -0.54500465 -0.506495804 -0.52511374 -0.002394755
##               CO          SO2           O3     Benzene       Toluene     Xylene
## [1,] -0.28208013 -0.343665550 -0.441358246 -0.26680634 -7.621613e-05 0.04018485
## [2,] -0.01279538 -0.004629688  0.004486845  0.02992548 -7.621613e-05 0.04018485
## [3,] -0.21973341 -0.404582582  0.004486845 -0.46222882 -5.654928e-01 0.04018485
##              AQI
## [1,] -0.91180608
## [2,]  0.03358787
## [3,] -0.60834417
db_res$cluster
##    [1] 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 2 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0
##   [38] 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0
##   [75] 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 2 0 0 0 0
##  [112] 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0
##  [149] 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 2 1 0 0 0 0 1 0 0 1 0 0 1 0
##  [186] 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 2
##  [223] 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1
##  [260] 0 0 0 0 1 1 2 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 2 1 1 0 0 0 1 0 0 0 1 0 0 0
##  [297] 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0
##  [334] 0 1 0 1 1 0 2 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0
##  [371] 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1
##  [408] 0 0 0 1 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1
##  [445] 0 0 2 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
##  [482] 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0
##  [519] 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 2 2 1 1
##  [556] 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0
##  [593] 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0
##  [630] 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0
##  [667] 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 2
##  [704] 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0
##  [741] 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0
##  [778] 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1
##  [815] 2 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0
##  [852] 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0
##  [889] 0 2 2 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1
##  [926] 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0
##  [963] 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1
## [1000] 1
ms_res$assignment
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## [1000,]    1
fcm_res$cluster
##  51663  57870   2986  29925  95246 103065  68293  62555  45404  65161  46435 
##      2      1      1      2      2      3      2      1      1      1      1 
## 104474   9642  59134  52132  96849  14183  15180  27168  89709   9097  30538 
##      2      1      1      2      1      2      1      2      1      2      2 
##  56219  94517   7989  13536  90077   6216  83519  29394  53241  28825 106773 
##      2      2      2      1      3      1      1      2      1      2      2 
##     41  14426 105695  72820  51656  94038  58527  77009  43042  77837   6134 
##      1      2      2      1      2      1      1      1      3      2      1 
##  33523  21812  39895   9640  85278   9326  26510  20960  14403  64502  71503 
##      3      2      1      1      1      2      3      2      2      1      2 
##  45221  94335  92372  77585  80686  70563  32606  16152  25559  14215  14287 
##      2      1      1      1      1      1      1      2      3      2      2 
##  23194  90094  34976  14491  82949  77584  40503  34724 103662  86013  17369 
##      2      1      1      2      1      2      3      3      1      1      1 
##  31542 102537  59106  86605  40632  96111  43204  37544  99289  84427  76820 
##      2      3      1      1      1      2      2      2      2      1      1 
##  82115  44196  92337  44983  91438  36717  28078  69369  91564  43406  41488 
##      1      1      1      2      2      1      1      1      2      3      2 
##  47485  63528  14536  83069  51465  26503 103319  88299  32953    413  10762 
##      2      1      2      3      1      3      1      2      3      2      2 
##  48182  30571  42521  74522  14745  25946  80340  43928   6601  57701  53518 
##      3      2      2      1      2      2      2      3      3      1      2 
##  72326  52353  66154  47802  31517  66075  32263  95989  69161  81118  56157 
##      2      3      1      1      2      1      2      2      1      1      1 
##  19392  46137  67747   2286  59970  84298  54661  32281 107575  64085   7826 
##      2      2      2      1      1      1      1      1      1      2      3 
##  80287  89799  25449 106385  63405  76223  64616  27455  54740  78173  20193 
##      1      1      3      3      1      1      1      3      2      2      1 
##  66701  97201  22467  95362  63167  79225  63658  49862  84032  79331  84955 
##      1      2      2      2      1      2      1      3      1      1      2 
##  51491  15703   6623   8983  37769  29479  70943  98170  78121  86621   1835 
##      2      2      3      1      1      2      2      1      1      1      1 
##  42221  21099  41043  90978  56529  36940 105689  97455  76099  38265  76384 
##      2      2      1      1      2      3      2      1      1      2      1 
##  46438  75176  88461  69350   8176  94119  76369  17746  53873  29133     31 
##      1      1      1      1      3      2      1      2      1      3      2 
##   7588   4620  45980  68783  51573  89552  70778  11667  33027  87905  70945 
##      3      2      2      1      2      1      1      3      2      1      2 
##  91467  76792  89436   2450  44500   1673  19851  48434  83529   6007  83680 
##      2      1      1      1      1      1      2      1      1      2      1 
##  55992  90779  78967 104003 100264  66596  60906  78715  93289  46468   1204 
##      2      1      1      2      2      1      1      2      1      1      1 
##  97653  53272  24111  75455  43694 103727   3984   7880  57722  22119  67632 
##      1      3      3      2      3      1      2      3      1      2      1 
##  86409  52523  53918  24522   6333  68430  90232  89419  55737  19955  55368 
##      1      3      2      2      2      1      2      1      1      2      1 
##  47818  14417  49286  92916  25244 106545   5596  40276  60101  37167  69232 
##      1      2      3      1      3      1      1      3      1      1      1 
##  22974  52851   4913  10301  76908  99701  18547 104024  78774  29370  46843 
##      2      2      2      1      1      1      2      2      1      1      1 
##  58102  36086  76723  82171 107139   9182 103746  71848  88852  82585  56519 
##      1      1      2      1      2      1      2      2      2      1      2 
## 106941  24671  93648  34134  47800  25196  65778   7071  40160   1498  57337 
##      1      3      1      3      1      3      1      3      3      1      1 
##  60587  20698  65615   9723 104685  34599   4518  62170  81882   4695  32102 
##      1      2      1      3      2      1      2      2      1      2      2 
##  78889  81025  97142  74984  92556  53289  16436  26691  53705  42887  30237 
##      1      2      2      3      1      3      2      1      2      3      1 
##  66766  35556  32076  26715  18388  82526  23977  68616  63481  31315  43755 
##      1      2      2      1      2      1      1      1      1      2      2 
##  45555  57943  74659  73799 102346  20400   4972  69045  37492   6373  73396 
##      3      1      2      2      2      3      2      1      3      1      3 
##  82756    602  74059  47606  28577   7877  58263   2777  30712  17749   7488 
##      1      1      1      2      2      3      1      3      1      2      3 
## 101452  76662 100100  45430 106945   9739  61775  19512  80143  49588 101353 
##      2      1      1      2      1      2      2      2      2      2      1 
##  49753  90499  52292 101096  38245  99046   4682  68957  37765  34827  86479 
##      3      2      2      1      2      2      1      1      1      2      1 
##   2748  56138  44859 101888  51442  78912 104620  75936  57223  67089  97664 
##      3      1      3      3      1      1      2      1      1      1      1 
##  27365  76141  87938  19927  10216   2882   4015  27913  29465   9174 102856 
##      3      2      1      1      1      1      1      1      1      2      2 
##   7657  31351  68553  83192  42155  65995  92999 106635  10044  93926  14666 
##      3      2      1      1      3      2      1      2      1      1      2 
##  26226  54371  91194  72668  38920  96855  19360  94407  22344  98763  42039 
##      3      1      1      1      2      1      2      1      1      1      3 
##  83836  51953  91407  86414  95387  36385 101138  74075 101450  36671  29343 
##      1      2      1      1      2      3      2      2      2      3      3 
##  47159  34162  70508  66396  65053 100887  83653  81490  76877  24243  74441 
##      1      2      1      1      2      3      1      1      1      1      1 
##  36829  41218  67499  23294  76805  27103  83355   1923  31466   5178   8482 
##      2      2      2      2      2      3      1      2      2      1      1 
##  49618 106467  78638  47695  48775 100232  61449  43289  91176  81547 102798 
##      2      1      1      3      2      3      1      1      1      1      1 
##  12636  20547  69340  37247  37015  53719  37208  18876  17017  26566  62506 
##      2      2      1      2      3      1      1      2      1      1      2 
##  92120 106720  74640  39264  60225  89914 107815  13763  79126  15828   4750 
##      2      3      1      2      1      1      3      3      1      1      2 
##  18807  91870 107609  91570  41609  13797  56767   8848  38947 101914  50212 
##      2      1      1      2      1      1      1      2      2      2      3 
##  12791   7196  25245  58156  64797  75869  35533  65463  98821  52572  99750 
##      2      3      2      1      1      1      2      2      1      3      1 
##   2647  80352  34796  83727  38582  68362  85929  21086  94388  18304   2761 
##      1      2      2      1      1      1      1      2      1      2      3 
##  47651  99007     76  56753  16029  37853  40302  75133   4297  61429  63754 
##      3      1      1      2      2      3      3      1      3      1      2 
##  47529  37106 101880  40838  91239  55888  83618 101534  99285  34490  55582 
##      2      2      2      2      1      3      1      1      3      3      2 
##  19879  37294  31859 101916  74482   6529  89521  15524   7053  82255   2222 
##      2      3      2      2      1      3      1      2      3      2      1 
##  87671  88940  90727  97700  20995  40459  11166  35046  95455  16322  42611 
##      2      1      1      1      2      3      2      3      2      1      2 
##  39155  65854   1627  96703  53391  32035  75938  28613  19586 103912  11735 
##      2      1      1      1      1      3      1      2      1      2      2 
##  77589 105747  53971  40133  23248   4968  77872  56986  80931  44447  24728 
##      1      2      3      3      2      2      2      1      1      1      2 
##  52551  30541  15546  80653  98116  49689  62133  10550  86015  87576 103582 
##      3      2      2      1      1      1      2      3      1      3      2 
##  61118  72047  28535  19685  90544  56471  99374  40159  32661  49408  28999 
##      2      2      2      2      2      1      2      3      2      1      3 
##  17711  73171  47505   7789  12447  74556  95877   4298  25948  47534  65505 
##      2      2      2      3      2      1      1      2      1      2      1 
##  72884  68703  93017    756  13157  28676  64750  80650 102016  93955 104652 
##      1      1      1      1      1      2      1      1      1      1      3 
##  14600  27525  24934  78082    887  28360    914  92958  14405  45533  92684 
##      2      2      3      2      1      2      1      1      2      2      1 
##  81921  80734  96754  36234  83712  93439  63967   5799  91468  20874  84189 
##      1      1      1      1      1      2      1      1      2      2      1 
##  20474  14478  10943   1789  23506  93970  32638   5483  72383  41125  91154 
##      2      2      2      1      3      1      2      3      2      2      1 
##  22849  58127  38854   4961  77224  84796  73717   3004   8390  30774  47868 
##      2      1      2      2      1      1      1      1      2      2      1 
##  64790  91311  88178  15017  67101  50108  77784  33037  58460  82412  52243 
##      1      1      1      3      2      1      2      2      1      2      2 
##  54335  61595  72070  47332  25082  99710  58012  51396   2437  26219  91129 
##      1      2      1      3      2      2      1      2      2      1      2 
##  18771 102159  43025  41513  18671 100862  21556   2315  39113  70995  57334 
##      2      3      3      2      2      2      1      1      3      2      1 
##  55241  42775  77841  71112 104519  40332   4176  57247  61973  99134  72732 
##      2      2      1      2      1      3      2      1      2      2      2 
##  90266  20570  51114  78457  29278  39404  53042    352  65920  51260  24163 
##      1      2      3      1      3      3      3      1      2      2      2 
##  40818  32763  91819  61328   1191  98032  22660  59555  39396  95542  82243 
##      2      1      1      2      1      1      2      1      3      2      1 
##  30933  17832  40197   4588  89671   2304  21771  33442  68813 103715  99515 
##      3      2      2      2      2      1      2      1      2      1      3 
##  39150  45174  30536  29444  65839  92174  56987  57777  57766  32817  79173 
##      3      2      1      2      1      1      1      1      1      2      3 
##  20696  86160  51051  31566  50878   1003  80926  84909  70212  37984  87509 
##      2      1      3      2      2      1      2      1      1      1      1 
##  56785  14632  58085  53547  24226   9008  88320  74884  81626  51417  25681 
##      1      2      1      2      2      1      1      1      2      1      2 
##  39460  64935  48187  36573  54047 100649  17955  57137  36091  40269 102575 
##      3      1      3      3      1      1      2      2      3      3      2 
##  41194   5392  45030   9563  97416  32710  24790  70405  28650   2473  76085 
##      3      1      2      2      1      1      2      1      2      1      2 
##  52818  18937  43801  82422  50036  83098  31072  50814  10174  16021  13939 
##      3      2      1      1      1      1      2      3      1      2      2 
##  89105  68446 102808  57539  35544  42459  86615  12334  30092  13448   9046 
##      1      1      1      1      2      2      1      2      3      3      3 
##  95109  81997  10847  75796  58552  94933   9471  33714 105929   3649  80075 
##      2      2      3      2      3      2      2      1      1      1      1 
##  17521 105422  12530  15886  65768  94245  12893  81969 103367  37856  14610 
##      3      1      2      2      2      1      2      1      1      3      2 
##  48268  62339  48814  76991  78628  31389 107789  76202  73910  55791  54816 
##      2      2      1      1      1      2      2      2      1      1      3 
##    674  17674  61189  59857  26234  25855  68747   7103  86201  85279   1762 
##      2      1      2      1      3      3      1      3      1      1      1 
##  27251  69961  88698  63162  13344  83956  97921  79943   1607  43391  14303 
##      1      1      2      1      3      1      1      1      1      3      2 
##  67147  99873  61034  90361   9813 102375  99314  77391  68807  72042  90928 
##      2      2      2      1      1      1      2      2      1      2      1 
##  46339  10557  19807  91903  73691  46129  65308  28623  94953  27955   3302 
##      3      2      2      1      1      3      1      2      2      1      3 
##  55209  51897  96062   1847  11276  60972 104292   8412  46971  66737 104770 
##      1      1      2      1      2      3      3      2      3      1      2 
##  46355  18535   7111  72300  41939  85560 106988   3366  66984  87078  12083 
##      2      2      3      3      3      1      2      3      1      1      2 
##  56286  42481  96085  81623  42868  63521  51186  18970  64687  49957  81019 
##      2      3      1      3      2      2      1      2      1      2      1 
##  22312  64353  73796  66844  82487  20439  67538  29708   3288  98520  11159 
##      3      1      2      1      2      2      2      3      2      1      2 
##  72778 101252  27644  81147  57436  40703  12467  86872  65864  43474  38461 
##      1      2      1      1      1      2      2      1      1      3      2 
##  34622  45776  15127   5190 101849  13835  46988   4798  60389  10247  70345 
##      3      2      2      2      3      1      2      3      2      1      1 
##  23948  95993  53980  47840   4343  81107  27682  46776  58700  82762  43536 
##      1      1      1      2      2      1      1      3      2      1      1 
## 102986  26818  30856  16225  30552    528  90279  74686    663  96403  65228 
##      3      1      2      3      2      1      1      1      2      2      2 
## 101266  59056 105495  60043  86011  30481  66329 107917  28476  22232 
##      1      1      2      2      1      2      1      2      2      1
fcm_res$centers
##         PM2.5        PM10          NO          NO2         NOx        NH3
## 1 -0.42688785 -0.39849245 -0.34463029 -0.392531445 -0.36695628 -0.2344292
## 2 -0.01677294 -0.01535908 -0.06614412 -0.006638347 -0.06941096 -0.0129972
## 3  1.21842644  1.16368550  1.16182025  1.014801479  1.20587769  0.6198301
##            CO          SO2          O3     Benzene     Toluene       Xylene
## 1 -0.12719077 -0.194219091 -0.07501770 -0.18290465 -0.20918853 -0.085969234
## 2 -0.03907261  0.001858873  0.03517847 -0.02168255 -0.03635418 -0.002085232
## 3  0.30393242  0.346965935 -0.05612896  0.49149758  0.58922724  0.187923620
##           AQI
## 1 -0.51487191
## 2  0.01804683
## 3  1.26424424
fcm_res$membership
##                 1         2           3
## 51663  0.01238009 0.9859554 0.001664465
## 57870  0.65384966 0.2879619 0.058188489
## 2986   0.60636712 0.3287348 0.064898076
## 29925  0.42836908 0.4391820 0.132448873
## 95246  0.11197491 0.8727289 0.015296225
## 103065 0.32529466 0.3343285 0.340376819
## 68293  0.01238009 0.9859554 0.001664465
## 62555  0.71108309 0.2543018 0.034615136
## 45404  0.49040740 0.4584658 0.051126819
## 65161  0.55140634 0.3847708 0.063822871
## 46435  0.71739709 0.2529269 0.029676042
## 104474 0.34108998 0.5946465 0.064263523
## 9642   0.61326759 0.3586307 0.028101716
## 59134  0.59821668 0.3246570 0.077126356
## 52132  0.01238009 0.9859554 0.001664465
## 96849  0.69536698 0.2597494 0.044883598
## 14183  0.01238009 0.9859554 0.001664465
## 15180  0.57136538 0.3587748 0.069859860
## 27168  0.28669545 0.4581322 0.255172316
## 89709  0.52597092 0.4129495 0.061079531
## 9097   0.29070978 0.5850753 0.124214974
## 30538  0.44694724 0.4532219 0.099830885
## 56219  0.01238009 0.9859554 0.001664465
## 94517  0.45488163 0.4618324 0.083286011
## 7989   0.27461235 0.4876377 0.237749943
## 13536  0.56318500 0.3667012 0.070113763
## 90077  0.26568345 0.3240395 0.410277083
## 6216   0.54880465 0.3625240 0.088671371
## 83519  0.53844848 0.3822484 0.079303088
## 29394  0.29515635 0.5352460 0.169597622
## 53241  0.52398200 0.4000635 0.075954509
## 28825  0.45098032 0.4939590 0.055060660
## 106773 0.38705341 0.4976656 0.115280988
## 41     0.45066955 0.4445843 0.104746162
## 14426  0.01238009 0.9859554 0.001664465
## 105695 0.33081738 0.5361231 0.133059526
## 72820  0.59842801 0.3286461 0.072925910
## 51656  0.01238009 0.9859554 0.001664465
## 94038  0.58278614 0.3360466 0.081167300
## 58527  0.56133180 0.3776652 0.061003038
## 77009  0.59155721 0.3187563 0.089686471
## 43042  0.17887477 0.2301958 0.590929408
## 77837  0.43409697 0.4845653 0.081337744
## 6134   0.43791494 0.4286896 0.133395407
## 33523  0.19667215 0.2687421 0.534585781
## 21812  0.33697509 0.6319445 0.031080427
## 39895  0.73410659 0.2446918 0.021201627
## 9640   0.64381169 0.3116201 0.044568228
## 85278  0.60104223 0.3122200 0.086737775
## 9326   0.11184532 0.8730080 0.015146721
## 26510  0.27372555 0.3017567 0.424517743
## 20960  0.11197491 0.8727289 0.015296225
## 14403  0.01238009 0.9859554 0.001664465
## 64502  0.64753172 0.2879213 0.064546974
## 71503  0.11197491 0.8727289 0.015296225
## 45221  0.45098032 0.4939590 0.055060660
## 94335  0.46111074 0.4076440 0.131245214
## 92372  0.48726809 0.4653913 0.047340645
## 77585  0.56424199 0.3956195 0.040138547
## 80686  0.46952308 0.4316791 0.098797848
## 70563  0.57900475 0.3316993 0.089295975
## 32606  0.51763958 0.4158436 0.066516845
## 16152  0.46189558 0.4707008 0.067403605
## 25559  0.11908024 0.1744412 0.706478586
## 14215  0.01238009 0.9859554 0.001664465
## 14287  0.01238009 0.9859554 0.001664465
## 23194  0.39685850 0.5632398 0.039901676
## 90094  0.60321846 0.3435694 0.053212132
## 34976  0.50776331 0.4585911 0.033645567
## 14491  0.01238009 0.9859554 0.001664465
## 82949  0.69378786 0.2563025 0.049909629
## 77584  0.47004692 0.4863746 0.043578488
## 40503  0.18117292 0.2272884 0.591538721
## 34724  0.17070735 0.2454258 0.583866863
## 103662 0.67387771 0.2804500 0.045672311
## 86013  0.59353688 0.3274975 0.078965658
## 17369  0.63788918 0.2929193 0.069191497
## 31542  0.07570732 0.9147786 0.009514065
## 102537 0.17680267 0.2612515 0.561945813
## 59106  0.64713251 0.2973163 0.055551171
## 86605  0.54896122 0.3838890 0.067149778
## 40632  0.53698295 0.3797413 0.083275761
## 96111  0.37320883 0.3909666 0.235824584
## 43204  0.23305588 0.4323007 0.334643409
## 37544  0.35629955 0.5154363 0.128264127
## 99289  0.39591729 0.5419812 0.062101554
## 84427  0.41776553 0.3996270 0.182607495
## 76820  0.58789529 0.3640842 0.048020542
## 82115  0.56624174 0.4011443 0.032613963
## 44196  0.59489455 0.3309997 0.074105713
## 92337  0.51407493 0.4191004 0.066824647
## 44983  0.26586598 0.7098222 0.024311841
## 91438  0.31786153 0.4229829 0.259155558
## 36717  0.73495372 0.2477686 0.017277634
## 28078  0.42578980 0.4038407 0.170369502
## 69369  0.58649660 0.3340509 0.079452457
## 91564  0.01238009 0.9859554 0.001664465
## 43406  0.22178441 0.2904598 0.487755805
## 41488  0.36084285 0.4797313 0.159425826
## 47485  0.24511038 0.3828684 0.372021260
## 63528  0.59588875 0.3362170 0.067894270
## 14536  0.01238009 0.9859554 0.001664465
## 83069  0.29768818 0.3478697 0.354442145
## 51465  0.58972722 0.3301484 0.080124368
## 26503  0.25486235 0.3695802 0.375557416
## 103319 0.45632541 0.4317256 0.111949029
## 88299  0.46352760 0.4765217 0.059950745
## 32953  0.13188364 0.2249985 0.643117865
## 413    0.28741667 0.3673283 0.345255068
## 10762  0.34252049 0.3688594 0.288620098
## 48182  0.16082564 0.2095341 0.629640257
## 30571  0.30336004 0.5020399 0.194600035
## 42521  0.27142989 0.3705629 0.358007227
## 74522  0.72988203 0.2316526 0.038465388
## 14745  0.34772614 0.6106338 0.041640028
## 25946  0.34380568 0.5440918 0.112102509
## 80340  0.42467230 0.4805773 0.094750374
## 43928  0.14266131 0.1982518 0.659086921
## 6601   0.21977761 0.2832378 0.496984600
## 57701  0.67932567 0.2792512 0.041423118
## 53518  0.01238009 0.9859554 0.001664465
## 72326  0.37687894 0.4757259 0.147395140
## 52353  0.30257773 0.3339644 0.363457869
## 66154  0.68950412 0.2658194 0.044676468
## 47802  0.68776422 0.2763545 0.035881308
## 31517  0.01061084 0.9879975 0.001391709
## 66075  0.48040237 0.4095329 0.110064763
## 32263  0.35138908 0.4953610 0.153249953
## 95989  0.35857036 0.6049161 0.036513549
## 69161  0.67114265 0.2704547 0.058402640
## 81118  0.64084455 0.3207274 0.038428097
## 56157  0.47973517 0.4685166 0.051748243
## 19392  0.24788171 0.5236845 0.228433815
## 46137  0.25435419 0.4781693 0.267476497
## 67747  0.37180096 0.5828934 0.045305611
## 2286   0.65198050 0.2966923 0.051327226
## 59970  0.65494215 0.3079515 0.037106318
## 84298  0.65619697 0.2873427 0.056460301
## 54661  0.57287839 0.3639325 0.063189061
## 32281  0.68965458 0.2715119 0.038833498
## 107575 0.72381719 0.2421251 0.034057692
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## 86201  0.62870660 0.3044646 0.066828815
## 85279  0.59690333 0.3138754 0.089221220
## 1762   0.48893842 0.4162514 0.094810218
## 27251  0.69506473 0.2602888 0.044646457
## 69961  0.62428676 0.3160114 0.059701814
## 88698  0.36921215 0.4562014 0.174586459
## 63162  0.65876359 0.2969985 0.044237954
## 13344  0.20206376 0.2518028 0.546133412
## 83956  0.60471525 0.3277374 0.067547391
## 97921  0.68928820 0.2645071 0.046204717
## 79943  0.65696012 0.2875131 0.055526814
## 1607   0.51449340 0.3871859 0.098320722
## 43391  0.21544071 0.2887677 0.495791631
## 14303  0.01238009 0.9859554 0.001664465
## 67147  0.37180096 0.5828934 0.045305611
## 99873  0.24281215 0.4693416 0.287846244
## 61034  0.01238009 0.9859554 0.001664465
## 90361  0.61918536 0.3233599 0.057454792
## 9813   0.63731032 0.3367185 0.025971202
## 102375 0.57376491 0.3846872 0.041547931
## 99314  0.01238009 0.9859554 0.001664465
## 77391  0.36905267 0.4808867 0.150060600
## 68807  0.49475454 0.4280797 0.077165716
## 72042  0.39261418 0.5290069 0.078378949
## 90928  0.46108750 0.4534242 0.085488337
## 46339  0.10330836 0.1623429 0.734348750
## 10557  0.32676773 0.3639710 0.309261277
## 19807  0.21211598 0.4600826 0.327801404
## 91903  0.63981390 0.3053997 0.054786436
## 73691  0.64647084 0.2856802 0.067848994
## 46129  0.21957250 0.3358713 0.444556223
## 65308  0.73840673 0.2309866 0.030606663
## 28623  0.01238009 0.9859554 0.001664465
## 94953  0.36124923 0.3648776 0.273873158
## 27955  0.52384511 0.3981239 0.078031018
## 3302   0.24732246 0.2925965 0.460081038
## 55209  0.53309009 0.4241113 0.042798575
## 51897  0.40828587 0.3986502 0.193063949
## 96062  0.39100662 0.4660011 0.142992271
## 1847   0.46626907 0.4367465 0.096984454
## 11276  0.32371553 0.5799059 0.096378582
## 60972  0.26587827 0.3444241 0.389697649
## 104292 0.16201014 0.2595909 0.578398931
## 8412   0.35619526 0.3817551 0.262049642
## 46971  0.27019017 0.3605890 0.369220801
## 66737  0.65431243 0.2874817 0.058205870
## 104770 0.47054308 0.4893954 0.040061535
## 46355  0.24603381 0.4023084 0.351657802
## 18535  0.29850561 0.6427811 0.058713244
## 7111   0.20907182 0.2539805 0.536947702
## 72300  0.19255594 0.2997790 0.507665079
## 41939  0.17240309 0.2283217 0.599275200
## 85560  0.60711210 0.3097115 0.083176423
## 106988 0.36413513 0.4503231 0.185541730
## 3366   0.20177910 0.2641562 0.534064667
## 66984  0.66977061 0.2871932 0.043036152
## 87078  0.50495706 0.3873803 0.107662649
## 12083  0.01238009 0.9859554 0.001664465
## 56286  0.01238009 0.9859554 0.001664465
## 42481  0.23624547 0.2891339 0.474620621
## 96085  0.64096299 0.3071665 0.051870510
## 81623  0.22624838 0.2894312 0.484320449
## 42868  0.28609834 0.4992933 0.214608346
## 63521  0.46137601 0.4646380 0.073985988
## 51186  0.79191894 0.1872122 0.020868821
## 18970  0.29012615 0.6151603 0.094713597
## 64687  0.53969336 0.3965773 0.063729364
## 49957  0.27390638 0.4074884 0.318605246
## 81019  0.64902705 0.2993893 0.051583626
## 22312  0.26078588 0.3557397 0.383474443
## 64353  0.56536736 0.3648847 0.069747965
## 73796  0.33507625 0.4698170 0.195106794
## 66844  0.62459028 0.3205240 0.054885683
## 82487  0.37426149 0.5389001 0.086838361
## 20439  0.01238009 0.9859554 0.001664465
## 67538  0.37180096 0.5828934 0.045305611
## 29708  0.13798671 0.1998714 0.662141894
## 3288   0.37279411 0.4525574 0.174648452
## 98520  0.63572713 0.2949754 0.069297466
## 11159  0.01238009 0.9859554 0.001664465
## 72778  0.47727919 0.4105856 0.112135205
## 101252 0.38941234 0.4685995 0.141988154
## 27644  0.64277990 0.2961591 0.061061028
## 81147  0.59555215 0.3184158 0.086032003
## 57436  0.67657989 0.2757239 0.047696215
## 40703  0.40526533 0.4867564 0.107978258
## 12467  0.01238009 0.9859554 0.001664465
## 86872  0.46514743 0.4158915 0.118961052
## 65864  0.72286730 0.2442111 0.032921614
## 43474  0.20561426 0.3670075 0.427378242
## 38461  0.31765306 0.3598735 0.322473476
## 34622  0.20705744 0.3023158 0.490626734
## 45776  0.20820479 0.4446875 0.347107740
## 15127  0.32624748 0.3975520 0.276200550
## 5190   0.38442984 0.4210736 0.194496554
## 101849 0.24813773 0.3588021 0.393060175
## 13835  0.70653469 0.2549167 0.038548649
## 46988  0.27067736 0.4652365 0.264086136
## 4798   0.21300954 0.2835349 0.503455568
## 60389  0.45695657 0.4915657 0.051477764
## 10247  0.72579108 0.2514189 0.022790032
## 70345  0.57617796 0.3384645 0.085357535
## 23948  0.62636883 0.3282201 0.045411089
## 95993  0.48722988 0.4368874 0.075882723
## 53980  0.73306550 0.2391460 0.027788514
## 47840  0.39519592 0.4239202 0.180883875
## 4343   0.32331953 0.3415524 0.335128068
## 81107  0.64707112 0.3008469 0.052081939
## 27682  0.68150939 0.2652777 0.053212865
## 46776  0.27075143 0.3404115 0.388837028
## 58700  0.01238009 0.9859554 0.001664465
## 82762  0.64365330 0.3197576 0.036589111
## 43536  0.57591489 0.3452121 0.078873046
## 102986 0.31801331 0.3305716 0.351415108
## 26818  0.56576525 0.3594562 0.074778512
## 30856  0.42168270 0.4455203 0.132797026
## 16225  0.21147986 0.3076720 0.480848117
## 30552  0.40347627 0.5191043 0.077419431
## 528    0.52627884 0.3843093 0.089411837
## 90279  0.67072448 0.2756639 0.053611627
## 74686  0.62551640 0.3009091 0.073574456
## 663    0.01238009 0.9859554 0.001664465
## 96403  0.45450454 0.5112315 0.034263965
## 65228  0.32728827 0.6053021 0.067409656
## 101266 0.62773691 0.3211063 0.051156833
## 59056  0.59798356 0.3256124 0.076404017
## 105495 0.33059624 0.3358948 0.333508959
## 60043  0.33437538 0.4956896 0.169935034
## 86011  0.58253232 0.3371441 0.080323533
## 30481  0.31115649 0.4757809 0.213062626
## 66329  0.70210420 0.2636330 0.034262762
## 107917 0.44006086 0.4559084 0.104030742
## 28476  0.01238009 0.9859554 0.001664465
## 22232  0.75050800 0.2257358 0.023756155

metriks

# 1. silhouette (-1 to 1) higher is better
mean(silhouette(km_res$cluster, dist(data_scaled))[,3])
## [1] 0.1960999
mean(silhouette(kmed_res@cluster, dist(data_scaled))[,3])
## [1] -0.01226353
mean(silhouette(db_res$cluster, dist(data_scaled))[,3])
## [1] -0.1356254