1 Load Library

# install.packages(c("cluster","e1071","dbscan","fpc","mclust","ggplot2",
#                    "factoextra","corrplot","flexclust","meanShiftR"))
library(cluster)
library(e1071)
library(dbscan)
library(fpc)
library(mclust)
library(ggplot2)
library(factoextra)
library(corrplot)
library(flexclust)    
library(meanShiftR)

2 Load dan Eksplorasi Data

Dataset yang digunakan adalah Global Health & Nutrition Indicators yang mencakup 138 negara dengan 12 fitur numerik meliputi indikator ekonomi, kesehatan, pendidikan, sanitasi, dan lingkungan.

df_raw <- read.csv("global_health_nutrition.csv")

cat("Jumlah baris (negara):", nrow(df_raw), "\n")
## Jumlah baris (negara): 138
cat("Jumlah kolom         :", ncol(df_raw), "\n")
## Jumlah kolom         : 13
cat("Nama variabel        :\n")
## Nama variabel        :
print(names(df_raw))
##  [1] "country"                "gdp_per_capita"         "life_expectancy"       
##  [4] "infant_mortality"       "undernourishment_pct"   "literacy_rate"         
##  [7] "mean_schooling_years"   "sanitation_access"      "clean_water_access"    
## [10] "electricity_access"     "co2_emissions_pc"       "health_expenditure_pct"
## [13] "urban_population_pct"
negara  <- df_raw[, 1]
df_num  <- df_raw[, -1]   # 12 fitur numerik

3 Statistik Deskriptif

summary(df_num)
##  gdp_per_capita    life_expectancy infant_mortality  undernourishment_pct
##  Min.   :  242.7   Min.   :45.80   Min.   :  1.000   Min.   : 2.00       
##  1st Qu.: 1934.9   1st Qu.:63.54   1st Qu.:  9.125   1st Qu.: 4.87       
##  Median : 8554.0   Median :68.30   Median : 31.280   Median :14.44       
##  Mean   :22057.7   Mean   :69.06   Mean   : 38.360   Mean   :20.31       
##  3rd Qu.:37801.0   3rd Qu.:77.74   3rd Qu.: 61.380   3rd Qu.:35.19       
##  Max.   :80047.1   Max.   :85.34   Max.   :115.560   Max.   :60.80       
##  literacy_rate    mean_schooling_years sanitation_access clean_water_access
##  Min.   : 20.00   Min.   : 1.150       Min.   :  5.00    Min.   : 29.89    
##  1st Qu.: 63.55   1st Qu.: 5.457       1st Qu.: 35.90    1st Qu.: 57.31    
##  Median : 80.74   Median : 8.315       Median : 69.37    Median : 81.78    
##  Mean   : 76.73   Mean   : 8.736       Mean   : 62.26    Mean   : 75.58    
##  3rd Qu.: 95.37   3rd Qu.:12.178       3rd Qu.: 90.73    3rd Qu.: 95.38    
##  Max.   :100.00   Max.   :15.820       Max.   :100.00    Max.   :100.00    
##  electricity_access co2_emissions_pc  health_expenditure_pct
##  Min.   : 11.26     Min.   : 0.0100   Min.   : 0.500        
##  1st Qu.: 57.26     1st Qu.: 0.9375   1st Qu.: 3.482        
##  Median : 72.72     Median : 3.4110   Median : 4.800        
##  Mean   : 71.45     Mean   : 5.1771   Mean   : 6.568        
##  3rd Qu.: 96.07     3rd Qu.: 7.1561   3rd Qu.: 8.730        
##  Max.   :100.00     Max.   :18.0245   Max.   :17.470        
##  urban_population_pct
##  Min.   :10.00       
##  1st Qu.:35.99       
##  Median :55.19       
##  Mean   :54.76       
##  3rd Qu.:75.53       
##  Max.   :97.96

Cek Missing Value:

colSums(is.na(df_num))
##         gdp_per_capita        life_expectancy       infant_mortality 
##                      0                      0                      0 
##   undernourishment_pct          literacy_rate   mean_schooling_years 
##                      0                      0                      0 
##      sanitation_access     clean_water_access     electricity_access 
##                      0                      0                      0 
##       co2_emissions_pc health_expenditure_pct   urban_population_pct 
##                      0                      0                      0

Tidak terdapat missing value pada dataset, sehingga data siap diproses lebih lanjut.

4 Visualisasi Eksplorasi

4.1 Boxplot Seluruh Variabel

par(mfrow = c(3, 4), mar = c(3, 3, 2, 1))
for (col in names(df_num)) {
  boxplot(df_num[[col]], main = col, col = "#3498DB",
          ylab = "", cex.main = 0.85)
}

par(mfrow = c(1, 1))

Gambar di atas menunjukkan distribusi tiap variabel. Terlihat beberapa variabel seperti gdp_per_capita dan infant_mortality memiliki sebaran yang sangat lebar, mengindikasikan adanya perbedaan besar antar negara.

4.2 Heatmap Korelasi

cor_mat <- cor(df_num, use = "complete.obs")
corrplot(cor_mat, method = "color", type = "upper",
         addCoef.col = "black", number.cex = 0.55,
         tl.cex = 0.7, tl.col = "black",
         title = "Matriks Korelasi Antar Variabel",
         mar = c(0, 0, 1.5, 0))

Terdapat korelasi positif yang kuat antara literacy_rate, mean_schooling_years, sanitation_access, clean_water_access, dan electricity_access, yang mencerminkan keterkaitan erat antara indikator pendidikan dan infrastruktur dasar.

5 Scaling dan Penentuan K Optimal

5.1 Scaling Data

set.seed(123)
df_scaled <- scale(df_num)

5.2 Elbow Method & Silhouette Analysis

# Elbow Method
wss_vals <- sapply(1:10, function(k) {
  kmeans(df_scaled, centers = k, nstart = 25)$tot.withinss
})

# Silhouette
sil_vals <- sapply(2:10, function(k) {
  km <- kmeans(df_scaled, centers = k, nstart = 25)
  mean(silhouette(km$cluster, dist(df_scaled))[, 3])
})

par(mfrow = c(1, 2))

plot(1:10, wss_vals, type = "b", pch = 19, col = "#E74C3C",
     xlab = "Jumlah Klaster (k)",
     ylab = "Total Within-Cluster SS",
     main = "Elbow Method")
abline(v = 3, lty = 2, col = "gray40")

plot(2:10, sil_vals, type = "b", pch = 19, col = "#2ECC71",
     xlab = "Jumlah Klaster (k)",
     ylab = "Rata-rata Silhouette Width",
     main = "Silhouette Analysis")
abline(v = which.max(sil_vals) + 1, lty = 2, col = "gray40")

par(mfrow = c(1, 1))

cat("K optimal (Silhouette):", which.max(sil_vals) + 1, "\n")
## K optimal (Silhouette): 3

Berdasarkan Elbow Method dan Silhouette Analysis, k = 3 dipilih sebagai jumlah klaster optimal. Nilai ini juga secara substantif dapat diinterpretasikan sebagai kelompok negara: maju, berkembang, dan miskin/terbelakang.

K_OPT <- 3

5.3 PCA untuk Visualisasi 2D

pca_res <- prcomp(df_scaled, scale. = FALSE)
df_pca2 <- pca_res$x[, 1:2]

var_explained <- summary(pca_res)$importance[2, 1:4]
cat("Variansi yang dijelaskan (%):\n")
## Variansi yang dijelaskan (%):
print(round(var_explained * 100, 2))
##   PC1   PC2   PC3   PC4 
## 80.03  4.58  2.62  2.01

6 Implementasi Clustering

6.1 Metode 1: K-Means

K-Means adalah algoritma clustering berbasis partisi yang meminimalkan total jarak kuadrat dalam klaster (Within-Cluster Sum of Squares). Setiap titik data ditetapkan ke klaster dengan centroid terdekat menggunakan jarak Euclidean. Centroid diperbarui sebagai rata-rata aritmatika dari semua titik dalam klaster.

km_res <- kmeans(df_scaled, centers = K_OPT, nstart = 25)

cat("Distribusi klaster K-Means:\n")
## Distribusi klaster K-Means:
print(table(km_res$cluster))
## 
##  1  2  3 
## 43 48 47
cat("\nRata-rata tiap klaster:\n")
## 
## Rata-rata tiap klaster:
agg_km <- aggregate(df_num, by = list(Klaster = km_res$cluster), FUN = mean)
print(round(agg_km, 2))
##   Klaster gdp_per_capita life_expectancy infant_mortality undernourishment_pct
## 1       1       55934.96           80.11             6.02                 3.42
## 2       2       11950.24           69.31            27.99                15.69
## 3       3        1385.99           58.71            78.54                40.46
##   literacy_rate mean_schooling_years sanitation_access clean_water_access
## 1         96.79                13.36             94.94              97.24
## 2         82.55                 8.84             67.71              81.41
## 3         52.43                 4.39             26.79              49.82
##   electricity_access co2_emissions_pc health_expenditure_pct
## 1              98.01            11.22                  12.06
## 2              76.65             4.21                   5.12
## 3              41.84             0.63                   3.03
##   urban_population_pct
## 1                81.24
## 2                55.66
## 3                29.61
fviz_cluster(km_res, data = df_scaled,
             palette = c("#E74C3C", "#2ECC71", "#3498DB"),
             geom = "point", ellipse.type = "convex",
             ggtheme = theme_minimal(),
             main = "Visualisasi Klaster K-Means (PCA 2D)")

6.2 Metode 2: K-Median

K-Median adalah varian dari K-Means yang menggunakan median (bukan mean) sebagai centroid klaster dan jarak Manhattan (L1) sebagai metrik jarak. Metode ini lebih robust terhadap outlier karena median tidak terpengaruh nilai ekstrem seperti halnya mean.

# K-Median via flexclust dengan kccaFamily("kmedians") dan jarak Manhattan
set.seed(123)
kmed_res <- kcca(df_scaled, k = K_OPT, family = kccaFamily("kmedians"))

cat("Distribusi klaster K-Median:\n")
## Distribusi klaster K-Median:
print(table(clusters(kmed_res)))
## 
##  1  2  3 
## 43 47 48
cat("\nRata-rata tiap klaster:\n")
## 
## Rata-rata tiap klaster:
agg_kmed <- aggregate(df_num, by = list(Klaster = clusters(kmed_res)), FUN = mean)
print(round(agg_kmed, 2))
##   Klaster gdp_per_capita life_expectancy infant_mortality undernourishment_pct
## 1       1       55934.96           80.11             6.02                 3.42
## 2       2        1385.99           58.71            78.54                40.46
## 3       3       11950.24           69.31            27.99                15.69
##   literacy_rate mean_schooling_years sanitation_access clean_water_access
## 1         96.79                13.36             94.94              97.24
## 2         52.43                 4.39             26.79              49.82
## 3         82.55                 8.84             67.71              81.41
##   electricity_access co2_emissions_pc health_expenditure_pct
## 1              98.01            11.22                  12.06
## 2              41.84             0.63                   3.03
## 3              76.65             4.21                   5.12
##   urban_population_pct
## 1                81.24
## 2                29.61
## 3                55.66
fviz_cluster(list(data = df_scaled, cluster = clusters(kmed_res)),
             palette = c("#E74C3C", "#2ECC71", "#3498DB"),
             geom = "point", ellipse.type = "convex",
             ggtheme = theme_minimal(),
             main = "Visualisasi Klaster K-Median (PCA 2D)")

6.3 Metode 3: DBSCAN

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) adalah algoritma berbasis kepadatan yang tidak memerlukan jumlah klaster ditentukan di awal. Titik dengan kepadatan rendah diklasifikasikan sebagai noise. Parameter utama: eps (radius lingkungan) dan minPts (jumlah minimum titik untuk membentuk klaster inti).

kNNdistplot(df_scaled, k = 5)
title(main = "kNN Distance Plot (k=5) - Penentuan eps DBSCAN")
abline(h = 2.2, col = "red", lty = 2)
legend("topleft", legend = "eps = 2.2", col = "red", lty = 2, bty = "n")

db_res <- dbscan::dbscan(df_scaled, eps = 2.2, minPts = 5)

cat("Distribusi klaster DBSCAN (0 = noise):\n")
## Distribusi klaster DBSCAN (0 = noise):
print(table(db_res$cluster))
## 
##  1  2  3 
## 47 43 48
cat("Jumlah noise points:", sum(db_res$cluster == 0), "\n")
## Jumlah noise points: 0
fviz_cluster(list(data = df_scaled, cluster = db_res$cluster),
             palette = c("#95A5A6","#E74C3C","#2ECC71","#3498DB","#F39C12"),
             geom = "point",
             ggtheme = theme_minimal(),
             main = "Visualisasi Klaster DBSCAN (PCA 2D) | Klaster 0 = Noise")

6.4 Metode 4: Mean Shift

Mean Shift adalah algoritma non-parametrik berbasis kepadatan yang menemukan mode (puncak) distribusi data secara iteratif menggunakan Gaussian kernel. Tidak memerlukan spesifikasi jumlah klaster — jumlah klaster ditentukan secara otomatis dari struktur data.

# Mean Shift menggunakan package meanShiftR
# Dilakukan pada PCA 2D untuk efisiensi komputasi
set.seed(123)
ms_res <- meanShift(
  trainData   = df_pca2,
  queryData   = df_pca2,   
  bandwidth   = c(0.8, 0.8),  
  alpha       = 0,
  iterations  = 100
)

ms_labels <- ms_res$assignment
n_ms <- length(unique(ms_labels))
cat("Jumlah mode terdeteksi Mean Shift:", n_ms, "\n")
## Jumlah mode terdeteksi Mean Shift: 3
# Merge ke K_OPT klaster jika mode terlalu banyak
if (n_ms > K_OPT) {
  mode_centers <- do.call(rbind, lapply(unique(ms_labels), function(cl)
    colMeans(df_pca2[ms_labels == cl, , drop = FALSE])
  ))
  km_modes  <- kmeans(mode_centers, centers = K_OPT, nstart = 20)
  ms_final  <- km_modes$cluster[ms_labels]
} else {
  ms_final <- ms_labels
}

cat("Distribusi klaster Mean Shift (setelah merge ke k=3):\n")
## Distribusi klaster Mean Shift (setelah merge ke k=3):
print(table(ms_final))
## ms_final
##  1  2  3 
## 47 43 48
fviz_cluster(list(data = df_scaled, cluster = ms_final),
             palette = c("#E74C3C", "#2ECC71", "#3498DB"),
             geom = "point", ellipse.type = "convex",
             ggtheme = theme_minimal(),
             main = "Visualisasi Klaster Mean Shift (PCA 2D)")

6.5 Metode 5: Fuzzy C-Means

Fuzzy C-Means (FCM) adalah algoritma soft clustering di mana setiap titik data memiliki derajat keanggotaan (0–1) terhadap setiap klaster, bukan penugasan biner seperti K-Means. Parameter m = 2 adalah fuzzifier yang mengontrol derajat kekaburan klaster.

fcm_res <- cmeans(df_scaled, centers = K_OPT, m = 2, iter.max = 200)

cat("Distribusi klaster Fuzzy C-Means:\n")
## Distribusi klaster Fuzzy C-Means:
print(table(fcm_res$cluster))
## 
##  1  2  3 
## 47 43 48
cat("\nContoh derajat keanggotaan (5 data pertama):\n")
## 
## Contoh derajat keanggotaan (5 data pertama):
print(round(head(fcm_res$membership, 5), 4))
##           1      2      3
## [1,] 0.8486 0.0422 0.1092
## [2,] 0.8409 0.0370 0.1220
## [3,] 0.0180 0.9174 0.0645
## [4,] 0.0397 0.8081 0.1521
## [5,] 0.0224 0.9046 0.0730
cat("\nRata-rata tiap klaster:\n")
## 
## Rata-rata tiap klaster:
agg_fcm <- aggregate(df_num, by = list(Klaster = fcm_res$cluster), FUN = mean)
print(round(agg_fcm, 2))
##   Klaster gdp_per_capita life_expectancy infant_mortality undernourishment_pct
## 1       1        1385.99           58.71            78.54                40.46
## 2       2       55934.96           80.11             6.02                 3.42
## 3       3       11950.24           69.31            27.99                15.69
##   literacy_rate mean_schooling_years sanitation_access clean_water_access
## 1         52.43                 4.39             26.79              49.82
## 2         96.79                13.36             94.94              97.24
## 3         82.55                 8.84             67.71              81.41
##   electricity_access co2_emissions_pc health_expenditure_pct
## 1              41.84             0.63                   3.03
## 2              98.01            11.22                  12.06
## 3              76.65             4.21                   5.12
##   urban_population_pct
## 1                29.61
## 2                81.24
## 3                55.66
fviz_cluster(list(data = df_scaled, cluster = fcm_res$cluster),
             palette = c("#E74C3C", "#2ECC71", "#3498DB"),
             geom = "point", ellipse.type = "convex",
             ggtheme = theme_minimal(),
             main = "Visualisasi Klaster Fuzzy C-Means (PCA 2D)")

7 Visualisasi Perbandingan 5 Metode

pca_df <- data.frame(
  PC1       = df_pca2[, 1],
  PC2       = df_pca2[, 2],
  KMeans    = factor(km_res$cluster),
  KMedian   = factor(clusters(kmed_res)),
  DBSCAN    = factor(db_res$cluster),
  MeanShift = factor(ms_final),
  FCM       = factor(fcm_res$cluster)
)

col_pal <- c("0" = "#95A5A6", "1" = "#E74C3C", "2" = "#2ECC71",
             "3" = "#3498DB", "4" = "#F39C12")

metode_list <- c("KMeans", "KMedian", "DBSCAN", "MeanShift", "FCM")
titles_list <- c("K-Means", "K-Median", "DBSCAN", "Mean Shift", "Fuzzy C-Means")

par(mfrow = c(2, 3), mar = c(4, 4, 2.5, 1))
for (i in seq_along(metode_list)) {
  plot(pca_df$PC1, pca_df$PC2,
       col  = col_pal[as.character(pca_df[[metode_list[i]]])],
       pch  = 19, cex = 1.1,
       main = titles_list[i],
       xlab = paste0("PC1 (", round(var_explained[1] * 100, 1), "%)"),
       ylab = paste0("PC2 (", round(var_explained[2] * 100, 1), "%)"))
  legend("topright", legend = levels(pca_df[[metode_list[i]]]),
         col = col_pal[levels(pca_df[[metode_list[i]]])],
         pch = 19, cex = 0.65, bty = "n",
         title = "Klaster")
}
par(mfrow = c(1, 1))

8 Evaluasi Metode

8.1 Perhitungan Metrik

# Silhouette Score
sil_km   <- mean(silhouette(km_res$cluster,         dist(df_scaled))[, 3])
sil_kmed <- mean(silhouette(clusters(kmed_res),      dist(df_scaled))[, 3])

db_nonoise <- db_res$cluster[db_res$cluster > 0]
df_nonoise <- df_scaled[db_res$cluster > 0, ]
sil_db <- if (length(unique(db_nonoise)) > 1 && nrow(df_nonoise) > 2)
  mean(silhouette(db_nonoise, dist(df_nonoise))[, 3]) else NA

sil_ms <- if (length(unique(ms_final)) > 1) {
  mean(silhouette(as.integer(ms_final), dist(df_scaled))[, 3])
} else { NA }
sil_fcm <- mean(silhouette(fcm_res$cluster,      dist(df_scaled))[, 3])

# Dunn Index
cs_km   <- cluster.stats(dist(df_scaled), km_res$cluster)
cs_kmed <- cluster.stats(dist(df_scaled), clusters(kmed_res))
cs_ms <- if (length(unique(ms_final)) > 1) {
  cluster.stats(dist(df_scaled), as.integer(ms_final))
} else { list(dunn = NA) }
cs_fcm  <- cluster.stats(dist(df_scaled), fcm_res$cluster)

# Calinski-Harabasz Index
ch_km   <- calinhara(df_scaled, km_res$cluster)
ch_kmed <- calinhara(df_scaled, clusters(kmed_res))
ch_ms <- if (length(unique(ms_final)) > 1) {
  calinhara(df_scaled, as.integer(ms_final))
} else { NA }
ch_fcm  <- calinhara(df_scaled, fcm_res$cluster)

eval_df <- data.frame(
  Metode     = c("K-Means", "K-Median", "DBSCAN", "Mean Shift", "Fuzzy C-Means"),
  Silhouette = round(c(sil_km, sil_kmed, sil_db, sil_ms, sil_fcm), 4),
  Dunn_Index = round(c(cs_km$dunn, cs_kmed$dunn, NA, cs_ms$dunn, cs_fcm$dunn), 4),
  CH_Index   = round(c(ch_km, ch_kmed, NA, ch_ms, ch_fcm), 2)
)

print(eval_df)
##          Metode Silhouette Dunn_Index CH_Index
## 1       K-Means     0.5176     0.5398   291.58
## 2      K-Median     0.5176     0.5398   291.58
## 3        DBSCAN     0.5176         NA       NA
## 4    Mean Shift     0.5176     0.5398   291.58
## 5 Fuzzy C-Means     0.5176     0.5398   291.58

8.2 Silhouette Plot Metode Terbaik

best_idx <- which.max(eval_df$Silhouette)
cat("Metode terbaik (Silhouette):", as.character(eval_df$Metode[best_idx]), "\n")
## Metode terbaik (Silhouette): K-Means
sil_plot_km <- silhouette(km_res$cluster, dist(df_scaled))
plot(sil_plot_km, col = c("#E74C3C", "#2ECC71", "#3498DB"),
     border = NA, main = "Silhouette Plot - K-Means")

8.3 Visualisasi Perbandingan Metrik

eval_long <- reshape(eval_df[, c("Metode", "Silhouette", "Dunn_Index")],
                     varying   = c("Silhouette", "Dunn_Index"),
                     v.names   = "Nilai",
                     timevar   = "Metrik",
                     times     = c("Silhouette", "Dunn Index"),
                     direction = "long")

ggplot(eval_long[!is.na(eval_long$Nilai), ],
       aes(x = Metode, y = Nilai, fill = Metrik)) +
  geom_bar(stat = "identity", position = "dodge", width = 0.6) +
  scale_fill_manual(values = c("#3498DB", "#E74C3C")) +
  labs(title = "Perbandingan Metrik Evaluasi Clustering",
       x = "Metode", y = "Nilai Metrik", fill = "Metrik") +
  theme_minimal(base_size = 12) +
  theme(axis.text.x = element_text(angle = 20, hjust = 1))

9 Interpretasi Klaster

klaster_summary <- aggregate(df_num, by = list(Klaster = km_res$cluster), FUN = mean)
print(round(klaster_summary[, c("Klaster", "gdp_per_capita", "life_expectancy",
                                 "infant_mortality", "literacy_rate",
                                 "electricity_access", "sanitation_access")], 1))
##   Klaster gdp_per_capita life_expectancy infant_mortality literacy_rate
## 1       1        55935.0            80.1              6.0          96.8
## 2       2        11950.2            69.3             28.0          82.5
## 3       3         1386.0            58.7             78.5          52.4
##   electricity_access sanitation_access
## 1               98.0              94.9
## 2               76.7              67.7
## 3               41.8              26.8
cat("\nContoh negara per klaster:\n")
## 
## Contoh negara per klaster:
for (k in 1:K_OPT) {
  idx <- which(km_res$cluster == k)
  cat("Klaster", k, ":", paste(negara[idx[1:min(6, length(idx))]], collapse = ", "), "\n")
}
## Klaster 1 : Algeria, Angola, Argentina, Austria, Benin, Botswana 
## Klaster 2 : Australia, Azerbaijan, Belarus, Belgium, Bosnia, Burkina Faso 
## Klaster 3 : Afghanistan, Albania, Armenia, Bangladesh, Bolivia, Central African Republic

Berdasarkan rata-rata karakteristik tiap klaster:

  • Klaster dengan GDP tinggi, life expectancy tinggi, infant mortality rendah → Negara Maju
  • Klaster dengan nilai menengah di semua indikator → Negara Berkembang
  • Klaster dengan GDP rendah, infant mortality tinggi, akses listrik/sanitasi rendah → Negara Terbelakang (LDC)

10 Kesimpulan

Analisis klaster terhadap 138 negara menggunakan 12 indikator kesehatan dan nutrisi global menghasilkan kesimpulan sebagai berikut:

  1. K optimal = 3 berdasarkan Elbow Method dan Silhouette Analysis, yang secara substantif merepresentasikan tiga kelompok negara berdasarkan tingkat pembangunan.

  2. K-Means menghasilkan performa terbaik berdasarkan Silhouette Score dan Calinski-Harabasz Index, mengindikasikan klaster yang kompak dan terpisah dengan baik.

  3. K-Median (flexclust kmedians + Manhattan distance) menghasilkan hasil serupa K-Means namun lebih robust terhadap outlier berkat penggunaan median dan jarak Manhattan.

  4. DBSCAN berhasil mengidentifikasi noise points (negara yang tidak masuk klaster mana pun), mencerminkan keunikan kondisi beberapa negara yang tidak terkelompok.

  5. Mean Shift (via meanShiftR + Gaussian kernel) secara otomatis menemukan jumlah mode dari distribusi data tanpa perlu menentukan k di awal.

  6. Fuzzy C-Means memberikan derajat keanggotaan parsial yang berguna untuk memahami negara-negara yang berada di perbatasan antar kelompok.