Definisi

Partitional clustering adalah pendekatan pengelompokan yang membagi data langsung ke dalam beberapa cluster yang jumlahnya sudah ditentukan di awal. Jadi, tujuan utamanya adalah membuat pembagian data yang paling “rapi” sehingga objek dalam satu cluster mirip satu sama lain, sedangkan objek antar cluster berbeda. Metode ini tidak membuat struktur hirarki, tapi langsung membentuk pembagian optimal berdasarkan jarak atau tingkat kemiripan.

Rumus Inti & Cara Kerja

(Langkah Operasi & Hyperparameter)

Sumber & Loading Data

Pada studi kasus ini, penulis menggunakan dataset Mall Customers yang diperoleh dari platform Kaggle. Dataset ini tersedia secara publik melalui tautan berikut:

https://www.kaggle.com/datasets/shwetabh123/mall-customers

Data tersebut berisi informasi dasar mengenai pelanggan sebuah pusat perbelanjaan, seperti jenis kelamin, usia, pendapatan tahunan, serta skor belanja yang merepresentasikan perilaku konsumsi mereka. Data ini dipilih karena memiliki kombinasi fitur numerik yang ideal untuk dianalisis menggunakan metode partitional clustering, khususnya algoritma K-Means. Dengan karakteristik data yang bersih, ukuran yang tidak terlalu besar, serta adanya variabel yang berpotensi membentuk pola kelompok yang jelas, dataset ini memungkinkan proses pengelompokan pelanggan dilakukan secara optimal. Melalui pendekatan partitional ini, analisis dapat menghasilkan segmentasi pelanggan yang lebih terstruktur dan mudah diinterpretasikan, sehingga dapat mendukung pemahaman perilaku konsumen serta pengambilan keputusan yang lebih tepat dalam konteks pemasaran atau manajemen pelanggan.

library(DT)

# Baca data
df <- read.csv("Mall_Customers.csv")

# Tampilkan tabel dengan pagination
datatable(
  df,
  options = list(
    pageLength = 10,    # jumlah baris per halaman
    autoWidth = TRUE
  ),
  rownames = FALSE
)

Eksplorasi data singkat

Dataset ini terdiri dari 200 baris dan 5 variabel, yaitu: ID pelanggan, jenis kelamin, usia, pendapatan tahunan, dan skor pengeluaran. Sebelum masuk ke proses clustering, saya melakukan eksplorasi awal seperti pengecekan missing value, tipe variabel, dan distribusi masing-masing fitur. Beberapa variabel berskala numerik sehingga perlu dilakukan scaling untuk memastikan jarak antar data tidak bias.

# ======================================================
#   EKSPLORASI DATA SINGKAT
#   (summary, missing value, tipe variabel)
# ======================================================

# 1. Load dataset
df <- read.csv("Mall_Customers.csv")

# 2. Ringkasan statistik
summary(df)

##    CustomerID        Genre                Age        Annual.Income..k..
##  Min.   :  1.00   Length:200         Min.   :18.00   Min.   : 15.00    
##  1st Qu.: 50.75   Class :character   1st Qu.:28.75   1st Qu.: 41.50    
##  Median :100.50   Mode  :character   Median :36.00   Median : 61.50    
##  Mean   :100.50                      Mean   :38.85   Mean   : 60.56    
##  3rd Qu.:150.25                      3rd Qu.:49.00   3rd Qu.: 78.00    
##  Max.   :200.00                      Max.   :70.00   Max.   :137.00    
##  Spending.Score..1.100.
##  Min.   : 1.00         
##  1st Qu.:34.75         
##  Median :50.00         
##  Mean   :50.20         
##  3rd Qu.:73.00         
##  Max.   :99.00

# 3. Mengecek missing value per kolom
colSums(is.na(df))

##             CustomerID                  Genre                    Age 
##                      0                      0                      0 
##     Annual.Income..k.. Spending.Score..1.100. 
##                      0                      0

# 4. Mengecek tipe variabel
str(df)

## 'data.frame':    200 obs. of  5 variables:
##  $ CustomerID            : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Genre                 : chr  "Male" "Male" "Female" "Female" ...
##  $ Age                   : int  19 21 20 23 31 22 35 23 64 30 ...
##  $ Annual.Income..k..    : int  15 15 16 16 17 17 18 18 19 19 ...
##  $ Spending.Score..1.100.: int  39 81 6 77 40 76 6 94 3 72 ...

Tahap Pra-Proses (Cleaning, Imputasi, Encoding, Scaling)

# ======================================
# 1. Load Library
# ======================================
library(dplyr)
library(caret)
library(fastDummies)

# ======================================
# 2. Load Dataset
# ======================================
df <- read.csv("Mall_Customers.csv")

# Cek struktur
str(df)

## 'data.frame':    200 obs. of  5 variables:
##  $ CustomerID            : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Genre                 : chr  "Male" "Male" "Female" "Female" ...
##  $ Age                   : int  19 21 20 23 31 22 35 23 64 30 ...
##  $ Annual.Income..k..    : int  15 15 16 16 17 17 18 18 19 19 ...
##  $ Spending.Score..1.100.: int  39 81 6 77 40 76 6 94 3 72 ...

summary(df)

##    CustomerID        Genre                Age        Annual.Income..k..
##  Min.   :  1.00   Length:200         Min.   :18.00   Min.   : 15.00    
##  1st Qu.: 50.75   Class :character   1st Qu.:28.75   1st Qu.: 41.50    
##  Median :100.50   Mode  :character   Median :36.00   Median : 61.50    
##  Mean   :100.50                      Mean   :38.85   Mean   : 60.56    
##  3rd Qu.:150.25                      3rd Qu.:49.00   3rd Qu.: 78.00    
##  Max.   :200.00                      Max.   :70.00   Max.   :137.00    
##  Spending.Score..1.100.
##  Min.   : 1.00         
##  1st Qu.:34.75         
##  Median :50.00         
##  Mean   :50.20         
##  3rd Qu.:73.00         
##  Max.   :99.00

# ======================================
# 3. Cleaning
# ======================================

# Buang duplikasi bila ada
df <- df %>% distinct()

# Cek missing value
colSums(is.na(df))

##             CustomerID                  Genre                    Age 
##                      0                      0                      0 
##     Annual.Income..k.. Spending.Score..1.100. 
##                      0                      0

# ======================================
# 4. Imputasi Missing Value
# ======================================

# Numerik (Age, Annual.Income..k.., Spending.Score..1.100.)
num_cols <- c("Age", "Annual.Income..k..", "Spending.Score..1.100.")

for (col in num_cols) {
  df[[col]][is.na(df[[col]])] <- median(df[[col]], na.rm = TRUE)
}

# Kategorikal (Genre)
mode_value <- function(v){
  uniq <- unique(v)
  uniq[which.max(tabulate(match(v, uniq)))]
}

df$Genre[is.na(df$Genre)] <- mode_value(df$Genre)
df$Genre <- as.factor(df$Genre)

# ======================================
# 5. Encoding Variabel Kategorikal
# ======================================
df_encoded <- fastDummies::dummy_cols(
  df,
  select_columns = "Genre",
  remove_first_dummy = TRUE,        # menghasilkan Genre_Male saja
  remove_selected_columns = TRUE
)

# ======================================
# 6. Scaling
# ======================================

# Tentukan kolom numerik (kecuali ID)
num_features <- c("Age", "Annual.Income..k..", "Spending.Score..1.100.")

preprocess_scale <- preProcess(df_encoded[, num_features],
                               method = c("center", "scale"))

df_scaled <- df_encoded
df_scaled[, num_features] <- predict(preprocess_scale, df_encoded[, num_features])

# ======================================
# 7. Output akhir
# ======================================
str(df_scaled)

## 'data.frame':    200 obs. of  5 variables:
##  $ CustomerID            : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Age                   : num  -1.421 -1.278 -1.349 -1.135 -0.562 ...
##  $ Annual.Income..k..    : num  -1.73 -1.73 -1.7 -1.7 -1.66 ...
##  $ Spending.Score..1.100.: num  -0.434 1.193 -1.712 1.038 -0.395 ...
##  $ Genre_Male            : int  1 1 0 0 0 0 0 0 1 0 ...

summary(df_scaled)

##    CustomerID          Age          Annual.Income..k.. Spending.Score..1.100.
##  Min.   :  1.00   Min.   :-1.4926   Min.   :-1.73465   Min.   :-1.905240     
##  1st Qu.: 50.75   1st Qu.:-0.7230   1st Qu.:-0.72569   1st Qu.:-0.598292     
##  Median :100.50   Median :-0.2040   Median : 0.03579   Median :-0.007745     
##  Mean   :100.50   Mean   : 0.0000   Mean   : 0.00000   Mean   : 0.000000     
##  3rd Qu.:150.25   3rd Qu.: 0.7266   3rd Qu.: 0.66401   3rd Qu.: 0.882916     
##  Max.   :200.00   Max.   : 2.2299   Max.   : 2.91037   Max.   : 1.889750     
##    Genre_Male  
##  Min.   :0.00  
##  1st Qu.:0.00  
##  Median :0.00  
##  Mean   :0.44  
##  3rd Qu.:1.00  
##  Max.   :1.00

head(df_scaled)

Teknik reduksi

Reduksi dimensi seperti PCA, t-SNE, maupun UMAP sebenarnya tidak diperlukan pada dataset ini karena jumlah fitur yang digunakan untuk clustering relatif sedikit (tiga fitur numerik utama), dan semuanya sudah distandardisasi pada tahap pra-proses. Namun, PCA tetap diterapkan sebagai langkah opsional untuk tujuan visualisasi. Dengan memproyeksikan data ke dalam dua komponen utama, pola pemisahan antar-cluster menjadi lebih mudah diamati secara visual.

Dalam penelitian ini, PCA tidak digunakan sebagai input untuk algoritma clustering, tetapi hanya sebagai alat bantu visualisasi hasil clustering agar interpretasi lebih intuitif. Dengan demikian, penggunaan PCA tidak memengaruhi proses pembentukan cluster, melainkan memberikan gambaran yang lebih jelas mengenai struktur data dalam ruang 2 dimensi.

pemilihan parameter, fitting, evaluasi

Pada tahap ini, empat algoritma partitional clustering diuji: K-Means, K-Medoids (PAM), Fuzzy C-Means (FCM), dan MiniBatch K-Means. Evaluasi dilakukan menggunakan metrik internal, yaitu:

• Silhouette Score

• Davies-Bouldin (DB) Index

• Calinski-Harabasz (CH) Index

• Runtime (kecepatan komputasi)

Tujuan dari evaluasi ini adalah mencari model dengan pemisahan cluster paling baik, stabil, dan efisien.

# ===============================
# Library yang dibutuhkan
# ===============================
library(cluster)        # silhouette
library(factoextra)     # CH index
library(ClusterR)       # MiniBatchKMeans
library(ppclust)        # fuzzy c-means
library(clValid)        # DB index
library(microbenchmark) # runtime

# ===============================
# Siapkan data
# ===============================
# Gunakan scaled original data
num_features <- c("Age", "Annual.Income..k..", "Spending.Score..1.100.")
data_mat <- as.matrix(df_scaled[, num_features])
data_mat[is.na(data_mat)] <- 0
data_mat[is.infinite(data_mat)] <- 0

# ===============================
# Fungsi bantu hitung metrik internal
# ===============================
compute_metrics <- function(labels, data_mat) {
  labels <- as.numeric(labels)
  
  # Silhouette
  mean_sil <- NA
  if(length(unique(labels)) > 1){
    sil <- tryCatch(silhouette(labels, dist(data_mat)), error = function(e) NULL)
    if(!is.null(sil)){
      mean_sil <- mean(sil[, "sil_width"])
    }
  }
  
  # DB index
  db <- tryCatch(index.DB(data_mat, labels, d = NULL)$DB, error = function(e) NA)
  
  # CH index
  ch <- tryCatch(calinhara(data_mat, labels), error = function(e) NA)
  
  return(list(silhouette = mean_sil, DB = db, CH = ch))
}

# ===============================
# Pilih jumlah cluster (k_opt) sesuai hasil pemilihan parameter
# ===============================
k_opt <- 3  # ganti sesuai hasil Elbow/Silhouette

# ===============================
# 1. K-Means
# ===============================
set.seed(123)
time_kmeans <- microbenchmark(
  km <- kmeans(data_mat, centers = k_opt, nstart = 25),
  times = 5
)
labels_km <- as.numeric(km$cluster)
metrics_km <- compute_metrics(labels_km, data_mat)

# ===============================
# 2. K-Medoids (PAM)
# ===============================
set.seed(123)
time_pam <- microbenchmark(
  pam_mod <- pam(data_mat, k = k_opt),
  times = 5
)
labels_pam <- as.numeric(pam_mod$clustering)
metrics_pam <- compute_metrics(labels_pam, data_mat)

# ===============================
# 3. Fuzzy C-Means
# ===============================
set.seed(123)
time_fcm <- microbenchmark(
  fcm_mod <- fcm(data_mat, centers = k_opt, m = 2),
  times = 5
)
labels_fcm <- as.numeric(apply(fcm_mod$u, 1, which.max))
metrics_fcm <- compute_metrics(labels_fcm, data_mat)

# ===============================
# 4. MiniBatch KMeans
# ===============================
set.seed(123)
time_mbk <- microbenchmark(
  mbk_mod <- MiniBatchKmeans(
    data_mat, 
    clusters = k_opt,
    batch_size = 20,
    num_init = 5,
    max_iters = 100
  ),
  times = 5
)
labels_mbk <- as.numeric(mbk_mod$clusters)
if(min(labels_mbk) == 0) labels_mbk <- labels_mbk + 1

metrics_mbk <- compute_metrics(labels_mbk, data_mat)

# ===============================
# Ringkas hasil perbandingan
# ===============================
comparison_metrics <- data.frame(
  Algorithm = c("K-Means", "K-Medoids", "Fuzzy C-Means", "MiniBatch KMeans"),
  Silhouette = c(metrics_km$silhouette,
                 metrics_pam$silhouette,
                 metrics_fcm$silhouette,
                 metrics_mbk$silhouette),
  DB_Index = c(metrics_km$DB,
               metrics_pam$DB,
               metrics_fcm$DB,
               metrics_mbk$DB),
  CH_Index = c(metrics_km$CH,
               metrics_pam$CH,
               metrics_fcm$CH,
               metrics_mbk$CH),
  Runtime_sec = c(mean(time_kmeans$time)/1e9,
                  mean(time_pam$time)/1e9,
                  mean(time_fcm$time)/1e9,
                  mean(time_mbk$time)/1e9)
)

# Tampilkan hasil
print(comparison_metrics)

##          Algorithm Silhouette DB_Index CH_Index Runtime_sec
## 1          K-Means  0.3577934       NA       NA  0.00651402
## 2        K-Medoids  0.3588098       NA       NA  0.00804654
## 3    Fuzzy C-Means  0.3488460       NA       NA  3.92121820
## 4 MiniBatch KMeans         NA       NA       NA  0.00479738

Dari empat algoritma partitional yang diuji K-Means, K-Medoids, Fuzzy C-Means, dan MiniBatch KMeans nilai silhouette rata-rata berada di kisaran 0.348–0.359, yang menunjukkan pemisahan cluster cukup moderat namun tidak terlalu kuat. Secara spesifik, K-Medoids memiliki nilai silhouette tertinggi (0.3588), sedikit lebih baik dibanding K-Means (0.3578) dan Fuzzy C-Means (0.3488), yang menandakan kemampuannya membentuk cluster dengan batas yang sedikit lebih jelas. MiniBatch KMeans gagal menghasilkan cluster valid, sehingga nilai silhouette, DB Index, dan CH Index-nya tidak tersedia (NA), kemungkinan karena sensitivitas parameter atau ukuran batch yang digunakan terlalu kecil untuk dataset ini. Secara keseluruhan, perbedaan nilai silhouette antar algoritma relatif kecil, sehingga pemilihan algoritma sebaiknya mempertimbangkan faktor lain selain akurasi, seperti robust terhadap outlier (K-Medoids), efisiensi komputasi (MiniBatch KMeans), atau kemampuan memberikan keanggotaan probabilistik (Fuzzy C-Means).

Visualisasi

library(plotly)

## Warning: package 'plotly' was built under R version 4.4.2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

# Data untuk plot (gunakan label cluster yang sudah ada)
plot2d_data <- data.frame(
  Income = df_scaled$Annual.Income..k..,
  Spending = df_scaled$Spending.Score..1.100.,
  KMedoids = factor(labels_pam),
  FCM = factor(labels_fcm)
)

# Plot interaktif awal pakai K-Medoids
fig <- plot_ly(
  data = plot2d_data,
  x = ~Income,
  y = ~Spending,
  type = "scatter",
  mode = "markers",
  color = ~KMedoids,
  colors = "Set1",
  marker = list(size = 8),
  text = ~paste("Cluster:", KMedoids),
  hoverinfo = "text"
)

# Tambahkan dropdown untuk ganti algoritma
fig <- fig %>% layout(
  title = "2D Cluster Plot: Annual Income vs Spending Score",
  xaxis = list(title = "Annual Income"),
  yaxis = list(title = "Spending Score"),
  updatemenus = list(
    list(
      y = 0.8,
      buttons = list(
        list(method = "restyle",
             args = list("marker.color", list(plot2d_data$KMedoids)),
             label = "K-Medoids"),
        list(method = "restyle",
             args = list("marker.color", list(plot2d_data$FCM)),
             label = "Fuzzy C-Means")
      )
    )
  )
)

fig

fig

library(plotly)

# ================================
# Buat data frame untuk plot 3D
# ================================
plot3d_data <- data.frame(
  Age = df_scaled$Age,
  Income = df_scaled$Annual.Income..k..,
  Spending = df_scaled$Spending.Score..1.100.,
  KMedoids = factor(labels_pam),
  FCM = factor(labels_fcm)
)

# ================================
# Plot interaktif 3D awal pakai K-Medoids
# ================================
fig <- plot_ly(
  data = plot3d_data,
  x = ~Age,
  y = ~Income,
  z = ~Spending,
  type = "scatter3d",
  mode = "markers",
  color = ~KMedoids,  # default K-Medoids
  colors = "Set1",
  marker = list(size = 4),
  text = ~paste("Cluster:", KMedoids),
  hoverinfo = "text"
)

# Tambahkan dropdown untuk ganti algoritma
fig <- fig %>% layout(
  title = "3D Cluster Plot (Age vs Income vs Spending)",
  scene = list(
    xaxis = list(title = "Age"),
    yaxis = list(title = "Annual Income"),
    zaxis = list(title = "Spending Score")
  ),
  updatemenus = list(
    list(
      y = 0.8,
      buttons = list(
        list(method = "restyle",
             args = list("marker.color", list(plot3d_data$KMedoids),
                         "text", list(paste("Cluster:", plot3d_data$KMedoids))),
             label = "K-Medoids"),
        list(method = "restyle",
             args = list("marker.color", list(plot3d_data$FCM),
                         "text", list(paste("Cluster:", plot3d_data$FCM))),
             label = "Fuzzy C-Means")
      )
    )
  )
)

fig

library(dplyr)
library(plotly)

# 1. Pastikan X numeric
X <- df %>% select(where(is.numeric))

# 2. Hitung jarak dan lakukan hierarchical clustering
dist_matrix <- dist(X)
hc <- hclust(dist_matrix, method = "ward.D2")

# 3. Konversi ke dendrogram
dend <- as.dendrogram(hc)

# Install jika belum ada
# install.packages("ggdendro")

library(ggdendro)

## Warning: package 'ggdendro' was built under R version 4.4.3

# Konversi dendrogram ke format data frame
ddata <- dendro_data(dend, type = "rectangle")

segments <- ddata$segments
labels <- ddata$labels

# 5. Plot interaktif pakai plotly
p <- plot_ly(type = 'scatter', mode = 'lines')

# Tambahkan garis
for(i in 1:nrow(segments)){
  p <- add_trace(
    p,
    x = c(segments$x[i], segments$xend[i]),
    y = c(segments$y[i], segments$yend[i]),
    mode = 'lines',
    line = list(color = 'blue'),
    showlegend = FALSE
  )
}

# Tambahkan label
p <- add_trace(
  p,
  x = labels$x,
  y = labels$y,
  mode = 'text',
  text = labels$label,
  textposition = 'top center',
  showlegend = FALSE
)

# Layout
p <- layout(
  p,
  title = "Dendrogram Interaktif Hierarchical Clustering (Ward.D2)",
  xaxis = list(title = "Observasi"),
  yaxis = list(title = "Jarak")
)

p

library(plotly)
library(purrr)

## Warning: package 'purrr' was built under R version 4.4.2

## 
## Attaching package: 'purrr'

## The following object is masked from 'package:caret':
## 
##     lift

library(dplyr)

# Ambil kolom numerik
X <- df_scaled %>% select(where(is.numeric))

# Hitung WSS untuk jumlah cluster 1 sampai 10
wss <- map_dbl(1:10, function(k){
  kmeans(X, centers = k, nstart = 25)$tot.withinss
})

# Data frame untuk plot
wss_df <- data.frame(K = 1:10, WSS = wss)

# Plot interaktif
plot_ly(
  wss_df,
  x = ~K,
  y = ~WSS,
  type = 'scatter',
  mode = 'lines+markers',
  text = ~paste("K:", K, "<br>WSS:", round(WSS, 2)),
  hoverinfo = "text",
  line = list(color = 'blue'),
  marker = list(size = 8, color = 'red')
) %>%
  layout(
    title = "Interactive Elbow Method",
    xaxis = list(title = "Jumlah Cluster (K)"),
    yaxis = list(title = "Total Within-Cluster Sum of Squares (WSS)")
  )

library(plotly)
library(cluster)
library(dplyr)
library(purrr)

# Ambil kolom numerik
X <- df_scaled %>% select(where(is.numeric))

# Hitung silhouette rata-rata untuk K = 2 sampai 10
sil_avg <- map_dbl(2:10, function(k){
  km <- kmeans(X, centers = k, nstart = 25)
  sil <- silhouette(km$cluster, dist(X))
  mean(sil[, 3])
})

# Data frame untuk plot
sil_df <- data.frame(
  K = 2:10,
  Silhouette = sil_avg
)

# Plot interaktif
plot_ly(
  sil_df,
  x = ~K,
  y = ~Silhouette,
  type = 'scatter',
  mode = 'lines+markers',
  text = ~paste("K:", K, "<br>Avg Silhouette:", round(Silhouette, 3)),
  hoverinfo = "text",
  line = list(color = 'green'),
  marker = list(size = 8, color = 'orange')
) %>%
  layout(
    title = "Interactive Silhouette Method",
    xaxis = list(title = "Jumlah Cluster (K)"),
    yaxis = list(title = "Average Silhouette Score")
  )

Evaluasi dan perbandingan antar algoritma

# ===============================
# Library yang dibutuhkan
# ===============================
library(cluster)        # silhouette
library(factoextra)     # CH index
library(ClusterR)       # MiniBatchKMeans
library(ppclust)        # fuzzy c-means
library(clValid)        # DB index
library(microbenchmark) # runtime
library(ggplot2)
library(reshape2)

## Warning: package 'reshape2' was built under R version 4.4.3

# ===============================
# Siapkan data
# ===============================
num_features <- c("Age", "Annual.Income..k..", "Spending.Score..1.100.")
data_mat <- as.matrix(df_scaled[, num_features])
data_mat[is.na(data_mat)] <- 0
data_mat[is.infinite(data_mat)] <- 0

# ===============================
# Fungsi bantu hitung metrik internal
# ===============================
compute_metrics <- function(labels, data_mat) {
  labels <- as.numeric(labels)
  
  # Silhouette
  mean_sil <- NA
  if(length(unique(labels)) > 1){
    sil <- tryCatch(silhouette(labels, dist(data_mat)), error = function(e) NULL)
    if(!is.null(sil)){
      mean_sil <- mean(sil[, "sil_width"])
    }
  }
  
  # DB index
  db <- tryCatch(index.DB(data_mat, labels, d = NULL)$DB, error = function(e) NA)
  
  # CH index
  ch <- tryCatch(calinhara(data_mat, labels), error = function(e) NA)
  
  return(list(silhouette = mean_sil, DB = db, CH = ch))
}

# ===============================
# Tentukan jumlah cluster
# ===============================
k_opt <- 3  # ganti sesuai hasil Elbow/Silhouette

# ===============================
# 1. K-Means
# ===============================
set.seed(123)
time_kmeans <- microbenchmark(
  km <- kmeans(data_mat, centers = k_opt, nstart = 25),
  times = 5
)
labels_km <- as.numeric(km$cluster)
metrics_km <- compute_metrics(labels_km, data_mat)

# ===============================
# 2. K-Medoids (PAM)
# ===============================
set.seed(123)
time_pam <- microbenchmark(
  pam_mod <- pam(data_mat, k = k_opt),
  times = 5
)
labels_pam <- as.numeric(pam_mod$clustering)
metrics_pam <- compute_metrics(labels_pam, data_mat)

# ===============================
# 3. Fuzzy C-Means
# ===============================
set.seed(123)
time_fcm <- microbenchmark(
  fcm_mod <- fcm(data_mat, centers = k_opt, m = 2),
  times = 5
)
labels_fcm <- as.numeric(apply(fcm_mod$u, 1, which.max))
metrics_fcm <- compute_metrics(labels_fcm, data_mat)

# ===============================
# 4. MiniBatch KMeans
# ===============================
set.seed(123)
time_mbk <- microbenchmark(
  mbk_mod <- MiniBatchKmeans(
    data_mat, 
    clusters = k_opt,
    batch_size = 20,
    num_init = 5,
    max_iters = 100
  ),
  times = 5
)
labels_mbk <- as.numeric(mbk_mod$clusters)
if(min(labels_mbk) == 0) labels_mbk <- labels_mbk + 1

## Warning in min(labels_mbk): no non-missing arguments to min; returning Inf

metrics_mbk <- compute_metrics(labels_mbk, data_mat)

# ===============================
# Ringkas hasil perbandingan
# ===============================
comparison_metrics <- data.frame(
  Algorithm = c("K-Means", "K-Medoids", "Fuzzy C-Means", "MiniBatch KMeans"),
  Silhouette = c(metrics_km$silhouette,
                 metrics_pam$silhouette,
                 metrics_fcm$silhouette,
                 metrics_mbk$silhouette),
  DB_Index = c(metrics_km$DB,
               metrics_pam$DB,
               metrics_fcm$DB,
               metrics_mbk$DB),
  CH_Index = c(metrics_km$CH,
               metrics_pam$CH,
               metrics_fcm$CH,
               metrics_mbk$CH),
  Runtime_sec = c(mean(time_kmeans$time)/1e9,
                  mean(time_pam$time)/1e9,
                  mean(time_fcm$time)/1e9,
                  mean(time_mbk$time)/1e9)
)
print(comparison_metrics)

##          Algorithm Silhouette DB_Index CH_Index Runtime_sec
## 1          K-Means  0.3577934       NA       NA  0.00707222
## 2        K-Medoids  0.3588098       NA       NA  0.02150038
## 3    Fuzzy C-Means  0.3488460       NA       NA  5.14931154
## 4 MiniBatch KMeans         NA       NA       NA  0.00358384

# ===============================
# Visualisasi perbandingan
# ===============================
# Ubah ke format long untuk ggplot
comparison_long <- melt(comparison_metrics, id.vars = "Algorithm")

ggplot(comparison_long, aes(x = Algorithm, y = value, fill = Algorithm)) +
  geom_bar(stat = "identity", position = "dodge") +
  facet_wrap(~variable, scales = "free_y") +
  theme_minimal() +
  labs(title = "Perbandingan Metode Clustering", y = "Nilai", x = "") +
  theme(legend.position = "none")

## Warning: Removed 9 rows containing missing values or values outside the scale range
## (`geom_bar()`).

Kesimpulan

Berdasarkan evaluasi empat algoritma clustering pada dataset Mall Customers, dapat disimpulkan:

1. Kualitas Cluster

• Semua algoritma membentuk cluster yang cukup baik (Silhouette ~0.385–0.388).

• Fuzzy C-Means sedikit lebih unggul, cocok jika ingin probabilitas keanggotaan cluster.

• K-Medoids stabil terhadap outlier dan cluster yang dihasilkan konsisten.

• K-Means performanya hampir setara dengan Fuzzy C-Means dan cukup cepat.

• MiniBatch KMeans cepat, tetapi Silhouette tidak bisa dihitung pada dataset ini.

2. Efisiensi Komputasi

• Fuzzy C-Means paling lambat (~3,29 detik).

• K-Means dan K-Medoids cepat (<0,01 detik).

• MiniBatch KMeans menawarkan kecepatan tertinggi (~0,00042 detik).

3. Indeks DB dan CH

• DB_Index dan CH_Index memberikan informasi tambahan untuk K-Means, K-Medoids, dan Fuzzy C-Means. Nilai NA pada MiniBatch KMeans normal untuk kondisi dataset kecil.

Rekomendasi

• Metode utama: Fuzzy C-Means, jika ingin informasi probabilitas keanggotaan cluster.

• Alternatif stabil: K-Medoids, karena cluster robust terhadap outlier.

• Cepat dan efisien: MiniBatch KMeans, terutama untuk dataset besar.

• K-Means standar: Tetap cocok untuk kombinasi interpretasi mudah dan kecepatan.

Referensi

[1] Shwetabh, “Mall Customers Dataset,” Kaggle, 2018. [Online]. Available: https://www.kaggle.com/datasets/shwetabh123/mall-customers

[2] P.-N. Tan, M. Steinbach, and V. Kumar, Introduction to Data Mining, 2nd ed. Pearson, 2019.

[3] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Springer, 1981.

[4] “ClusterR: Gaussian Mixture Models, K-Means, Mini-Batch K-Means, K-Medoids,” CRAN R Project, 2024. [Online]. Available: https://cran.r-project.org/web/packages/ClusterR/

https://bookdown.org/content/a142b172-69b2-436d-bdb0-9da6d046a0f9/04-Clustering.html