Pengaruh Kualitas Data Terhadap Kualitas Clustering

Package yang diperlukan

library(MASS)
library(cluster)
library(mclust)
library(dplyr)
library(effectsize)
library(ggplot2)

Fungsi Pembangkit Data

generate_data <- function(n, sigma){

  n_per_cluster <- n / 3

  mu1 <- c(0, 0)
  mu2 <- c(5, 5)
  mu3 <- c(10, 0)

  Sigma <- matrix(
    c(sigma^2, 0,
      0, sigma^2),
    nrow = 2
  )

  cluster1 <- mvrnorm(
    n = n_per_cluster,
    mu = mu1,
    Sigma = Sigma
  )

  cluster2 <- mvrnorm(
    n = n_per_cluster,
    mu = mu2,
    Sigma = Sigma
  )

  cluster3 <- mvrnorm(
    n = n_per_cluster,
    mu = mu3,
    Sigma = Sigma
  )
  
  # Gabungkan menjadi satu dataset
  X <- rbind(
    cluster1,
    cluster2,
    cluster3
  )

  # Buat label cluster
  label_true <- c(
    rep(1, n_per_cluster),
    rep(2, n_per_cluster),
    rep(3, n_per_cluster)
  )

  # Simpan dalam fungsi list
  list(
    X = X,
    label_true = label_true
  )
}

Fungsi menghitung parameter alpha dan beta Silhoutte

compute_ab <- function(X, cluster_labels, D = NULL){

  if(is.null(D)){
    D <- as.matrix(dist(X))  # secara default menggunakan Euclidean Distance
  } else {
    D <- as.matrix(D)
  }
  
  n <- nrow(X)

  a <- numeric(n)
  b <- numeric(n)

  unique_clusters <- sort(unique(cluster_labels))

  
  for(i in 1:n){

    current_cluster <- cluster_labels[i]
    
    # Proses perhitungan parameter alpha
    same_cluster <- which(
      cluster_labels == current_cluster
    )

    same_cluster <- setdiff(
      same_cluster,
      i
    )

    if(length(same_cluster) > 0){

      a[i] <- mean(
        D[i, same_cluster]
      )

    } else {

      a[i] <- 0

    }

    # Proses perhitungan parameter beta
    other_clusters <- setdiff(
      unique_clusters,
      current_cluster
    )

    b_candidates <- c()

    for(cl in other_clusters){

      idx <- which(
        cluster_labels == cl
      )

      b_candidates <- c(
        b_candidates,
        mean(D[i, idx])
      )

    }

    b[i] <- min(b_candidates)

  }

  list(
    a = a,
    b = b
  )
}

Fungsi Setiap Replikasi Dalam Kombinasi Simulasi Tertentu

run_single_simulation <- function(
    n,
    sigma,
    k
){

  dat <- generate_data(
    n = n,
    sigma = sigma
  )

  X <- dat$X

  label_true <- dat$label_true

  km <- kmeans(
    X,
    centers = k,
    nstart = 25
  )

  label_pred <- km$cluster

  # Evaluasi ARI
  ari <- adjustedRandIndex(
    label_true,
    label_pred
  )

  # Evaluasi Silhoutte
  D <- dist(X)
  
  sil <- silhouette(
    label_pred,
    D
  )

  mean_sil <- mean(
    sil[, "sil_width"]
  )

  ab <- compute_ab(
    X,
    label_pred,
    D = D
  )

  mean_a <- mean(ab$a)

  sd_a <- sd(ab$a)

  mean_b <- mean(ab$b)

  sd_b <- sd(ab$b)

  # Buat dalam bentuk data frame
  data.frame(
    ARI = ari,
    Mean_Silhouette = mean_sil,
    Mean_a = mean_a,
    SD_a = sd_a,
    Mean_b = mean_b,
    SD_b = sd_b
  )
}

Desain Simulasi

# Ukuran sampel
sample_sizes <- c(
  45,
  180,
  450
)

# Tingkat noise
noise_levels <- c(
  0.5,
  1.5,
  3.0
)

# Jumlah klaster dalam algoritma k-means
k_values <- c(
  2,
  3,
  4
)

# Replikasi atau pengulangan
R <- 1000

Simulasi Monte Carlo

counter <- 1

# Banyaknya record dalam dataframe results
total_runs <-
  length(sample_sizes) *
  length(noise_levels) *
  length(k_values) *
  R

results_list <- vector("list", total_runs)  # alokasi sekali

for(n in sample_sizes){
  for(noise in noise_levels){
    for(k in k_values){
      for(rep in 1:R){

        temp <- run_single_simulation(n = n, sigma = noise, k = k)
        temp$n <- n
        temp$noise <- noise
        temp$k <- k
        temp$replication <- rep

        results_list[[counter]] <- temp  

        if(counter %% 100 == 0){
          cat("Progress:", counter, "/", total_runs, "\n")
        }

        counter <- counter + 1
      }
    }
  }
}

## Progress: 100 / 27000 
## Progress: 200 / 27000 
## Progress: 300 / 27000 
## Progress: 400 / 27000 
## Progress: 500 / 27000 
## Progress: 600 / 27000 
## Progress: 700 / 27000 
## Progress: 800 / 27000 
## Progress: 900 / 27000 
## Progress: 1000 / 27000 
## Progress: 1100 / 27000 
## Progress: 1200 / 27000 
## Progress: 1300 / 27000 
## Progress: 1400 / 27000 
## Progress: 1500 / 27000 
## Progress: 1600 / 27000 
## Progress: 1700 / 27000 
## Progress: 1800 / 27000 
## Progress: 1900 / 27000 
## Progress: 2000 / 27000 
## Progress: 2100 / 27000 
## Progress: 2200 / 27000 
## Progress: 2300 / 27000 
## Progress: 2400 / 27000 
## Progress: 2500 / 27000 
## Progress: 2600 / 27000 
## Progress: 2700 / 27000 
## Progress: 2800 / 27000 
## Progress: 2900 / 27000 
## Progress: 3000 / 27000 
## Progress: 3100 / 27000 
## Progress: 3200 / 27000 
## Progress: 3300 / 27000 
## Progress: 3400 / 27000 
## Progress: 3500 / 27000 
## Progress: 3600 / 27000 
## Progress: 3700 / 27000 
## Progress: 3800 / 27000 
## Progress: 3900 / 27000 
## Progress: 4000 / 27000 
## Progress: 4100 / 27000 
## Progress: 4200 / 27000 
## Progress: 4300 / 27000 
## Progress: 4400 / 27000 
## Progress: 4500 / 27000 
## Progress: 4600 / 27000 
## Progress: 4700 / 27000 
## Progress: 4800 / 27000 
## Progress: 4900 / 27000 
## Progress: 5000 / 27000 
## Progress: 5100 / 27000 
## Progress: 5200 / 27000 
## Progress: 5300 / 27000 
## Progress: 5400 / 27000 
## Progress: 5500 / 27000 
## Progress: 5600 / 27000 
## Progress: 5700 / 27000 
## Progress: 5800 / 27000 
## Progress: 5900 / 27000 
## Progress: 6000 / 27000 
## Progress: 6100 / 27000 
## Progress: 6200 / 27000 
## Progress: 6300 / 27000 
## Progress: 6400 / 27000 
## Progress: 6500 / 27000 
## Progress: 6600 / 27000 
## Progress: 6700 / 27000 
## Progress: 6800 / 27000 
## Progress: 6900 / 27000 
## Progress: 7000 / 27000 
## Progress: 7100 / 27000 
## Progress: 7200 / 27000 
## Progress: 7300 / 27000 
## Progress: 7400 / 27000 
## Progress: 7500 / 27000 
## Progress: 7600 / 27000 
## Progress: 7700 / 27000 
## Progress: 7800 / 27000 
## Progress: 7900 / 27000 
## Progress: 8000 / 27000 
## Progress: 8100 / 27000 
## Progress: 8200 / 27000 
## Progress: 8300 / 27000 
## Progress: 8400 / 27000 
## Progress: 8500 / 27000 
## Progress: 8600 / 27000 
## Progress: 8700 / 27000 
## Progress: 8800 / 27000 
## Progress: 8900 / 27000 
## Progress: 9000 / 27000 
## Progress: 9100 / 27000 
## Progress: 9200 / 27000 
## Progress: 9300 / 27000 
## Progress: 9400 / 27000 
## Progress: 9500 / 27000 
## Progress: 9600 / 27000 
## Progress: 9700 / 27000 
## Progress: 9800 / 27000 
## Progress: 9900 / 27000 
## Progress: 10000 / 27000 
## Progress: 10100 / 27000 
## Progress: 10200 / 27000 
## Progress: 10300 / 27000 
## Progress: 10400 / 27000 
## Progress: 10500 / 27000 
## Progress: 10600 / 27000 
## Progress: 10700 / 27000 
## Progress: 10800 / 27000 
## Progress: 10900 / 27000 
## Progress: 11000 / 27000 
## Progress: 11100 / 27000 
## Progress: 11200 / 27000 
## Progress: 11300 / 27000 
## Progress: 11400 / 27000 
## Progress: 11500 / 27000 
## Progress: 11600 / 27000 
## Progress: 11700 / 27000 
## Progress: 11800 / 27000 
## Progress: 11900 / 27000 
## Progress: 12000 / 27000 
## Progress: 12100 / 27000 
## Progress: 12200 / 27000 
## Progress: 12300 / 27000 
## Progress: 12400 / 27000 
## Progress: 12500 / 27000 
## Progress: 12600 / 27000 
## Progress: 12700 / 27000 
## Progress: 12800 / 27000 
## Progress: 12900 / 27000 
## Progress: 13000 / 27000 
## Progress: 13100 / 27000 
## Progress: 13200 / 27000 
## Progress: 13300 / 27000 
## Progress: 13400 / 27000 
## Progress: 13500 / 27000 
## Progress: 13600 / 27000 
## Progress: 13700 / 27000 
## Progress: 13800 / 27000 
## Progress: 13900 / 27000 
## Progress: 14000 / 27000 
## Progress: 14100 / 27000 
## Progress: 14200 / 27000 
## Progress: 14300 / 27000 
## Progress: 14400 / 27000 
## Progress: 14500 / 27000 
## Progress: 14600 / 27000 
## Progress: 14700 / 27000 
## Progress: 14800 / 27000 
## Progress: 14900 / 27000 
## Progress: 15000 / 27000 
## Progress: 15100 / 27000 
## Progress: 15200 / 27000 
## Progress: 15300 / 27000 
## Progress: 15400 / 27000 
## Progress: 15500 / 27000 
## Progress: 15600 / 27000 
## Progress: 15700 / 27000 
## Progress: 15800 / 27000 
## Progress: 15900 / 27000 
## Progress: 16000 / 27000 
## Progress: 16100 / 27000 
## Progress: 16200 / 27000 
## Progress: 16300 / 27000 
## Progress: 16400 / 27000 
## Progress: 16500 / 27000 
## Progress: 16600 / 27000 
## Progress: 16700 / 27000 
## Progress: 16800 / 27000 
## Progress: 16900 / 27000 
## Progress: 17000 / 27000 
## Progress: 17100 / 27000 
## Progress: 17200 / 27000 
## Progress: 17300 / 27000 
## Progress: 17400 / 27000 
## Progress: 17500 / 27000 
## Progress: 17600 / 27000 
## Progress: 17700 / 27000 
## Progress: 17800 / 27000 
## Progress: 17900 / 27000 
## Progress: 18000 / 27000 
## Progress: 18100 / 27000 
## Progress: 18200 / 27000 
## Progress: 18300 / 27000 
## Progress: 18400 / 27000 
## Progress: 18500 / 27000 
## Progress: 18600 / 27000 
## Progress: 18700 / 27000 
## Progress: 18800 / 27000 
## Progress: 18900 / 27000 
## Progress: 19000 / 27000 
## Progress: 19100 / 27000 
## Progress: 19200 / 27000 
## Progress: 19300 / 27000 
## Progress: 19400 / 27000 
## Progress: 19500 / 27000 
## Progress: 19600 / 27000 
## Progress: 19700 / 27000 
## Progress: 19800 / 27000 
## Progress: 19900 / 27000 
## Progress: 20000 / 27000 
## Progress: 20100 / 27000 
## Progress: 20200 / 27000 
## Progress: 20300 / 27000 
## Progress: 20400 / 27000 
## Progress: 20500 / 27000 
## Progress: 20600 / 27000 
## Progress: 20700 / 27000 
## Progress: 20800 / 27000 
## Progress: 20900 / 27000 
## Progress: 21000 / 27000 
## Progress: 21100 / 27000 
## Progress: 21200 / 27000 
## Progress: 21300 / 27000 
## Progress: 21400 / 27000 
## Progress: 21500 / 27000 
## Progress: 21600 / 27000 
## Progress: 21700 / 27000 
## Progress: 21800 / 27000 
## Progress: 21900 / 27000 
## Progress: 22000 / 27000 
## Progress: 22100 / 27000 
## Progress: 22200 / 27000 
## Progress: 22300 / 27000 
## Progress: 22400 / 27000 
## Progress: 22500 / 27000 
## Progress: 22600 / 27000 
## Progress: 22700 / 27000 
## Progress: 22800 / 27000 
## Progress: 22900 / 27000 
## Progress: 23000 / 27000 
## Progress: 23100 / 27000 
## Progress: 23200 / 27000 
## Progress: 23300 / 27000 
## Progress: 23400 / 27000 
## Progress: 23500 / 27000 
## Progress: 23600 / 27000 
## Progress: 23700 / 27000 
## Progress: 23800 / 27000 
## Progress: 23900 / 27000 
## Progress: 24000 / 27000 
## Progress: 24100 / 27000 
## Progress: 24200 / 27000 
## Progress: 24300 / 27000 
## Progress: 24400 / 27000 
## Progress: 24500 / 27000 
## Progress: 24600 / 27000 
## Progress: 24700 / 27000 
## Progress: 24800 / 27000 
## Progress: 24900 / 27000 
## Progress: 25000 / 27000 
## Progress: 25100 / 27000 
## Progress: 25200 / 27000 
## Progress: 25300 / 27000 
## Progress: 25400 / 27000 
## Progress: 25500 / 27000 
## Progress: 25600 / 27000 
## Progress: 25700 / 27000 
## Progress: 25800 / 27000 
## Progress: 25900 / 27000 
## Progress: 26000 / 27000 
## Progress: 26100 / 27000 
## Progress: 26200 / 27000 
## Progress: 26300 / 27000 
## Progress: 26400 / 27000 
## Progress: 26500 / 27000 
## Progress: 26600 / 27000 
## Progress: 26700 / 27000 
## Progress: 26800 / 27000 
## Progress: 26900 / 27000 
## Progress: 27000 / 27000

# Gabungkan setelah loop selesai
results <- do.call(rbind, results_list)

Data Hasil Simulasi

# 5 data teratas
head(results, 5)

##    ARI Mean_Silhouette   Mean_a     SD_a   Mean_b     SD_b  n noise k
## 1 0.56       0.6343822 3.001019 1.332255 8.364889 1.127164 45   0.5 2
## 2 0.56       0.6490691 3.038576 1.674560 8.900508 1.280366 45   0.5 2
## 3 0.56       0.6407476 3.097378 1.658248 8.887228 1.316755 45   0.5 2
## 4 0.56       0.6434983 3.028490 1.414859 8.741211 1.331052 45   0.5 2
## 5 0.56       0.6455947 2.985892 1.566584 8.665588 1.351188 45   0.5 2
##   replication
## 1           1
## 2           2
## 3           3
## 4           4
## 5           5

# Lima Data Terakhir
tail(results, 5)

##             ARI Mean_Silhouette   Mean_a     SD_a   Mean_b     SD_b   n noise k
## 26996 0.4681075       0.3661214 4.297360 1.226547 7.081494 2.034390 450     3 4
## 26997 0.4423655       0.3577192 4.286901 1.090775 6.923746 1.913432 450     3 4
## 26998 0.3798746       0.3589400 4.075811 1.108540 6.556188 1.697817 450     3 4
## 26999 0.4406424       0.3606018 4.194952 1.087018 6.839994 1.837484 450     3 4
## 27000 0.4609846       0.3653984 4.299116 1.065736 7.074528 1.856457 450     3 4
##       replication
## 26996         996
## 26997         997
## 26998         998
## 26999         999
## 27000        1000

Data Ringkasan Kombinasi

summary_results <-
  results %>%
  group_by(
    n,
    noise,
    k
  ) %>%
  summarise(
    Mean_ARI =
      mean(ARI),

    SD_ARI =
      sd(ARI),

    `Mean_mean(Silhouette)` =
      mean(Mean_Silhouette),

    `Mean_mean(a)` =
      mean(Mean_a),

    `Mean_mean(b)` =
      mean(Mean_b),

    .groups = "drop"
  )

readr::write_excel_csv(summary_results, file = "C:/Users/LENOVO/Documents/Output R/Ringkasan Kombinasi Perlakuan.csv")
summary_results

## # A tibble: 27 × 8
##        n noise     k Mean_ARI SD_ARI `Mean_mean(Silhouette)` `Mean_mean(a)`
##    <dbl> <dbl> <dbl>    <dbl>  <dbl>                   <dbl>          <dbl>
##  1    45   0.5     2    0.56  0                        0.643          2.99 
##  2    45   0.5     3    1     0                        0.873          0.886
##  3    45   0.5     4    0.877 0.0187                   0.725          0.797
##  4    45   1.5     2    0.519 0.0422                   0.512          4.18 
##  5    45   1.5     3    0.958 0.0544                   0.613          2.64 
##  6    45   1.5     4    0.824 0.0551                   0.537          2.36 
##  7    45   3       2    0.368 0.0773                   0.410          5.84 
##  8    45   3       3    0.528 0.135                    0.422          4.63 
##  9    45   3       4    0.432 0.109                    0.403          4.04 
## 10   180   0.5     2    0.569 0                        0.646          2.96 
## # ℹ 17 more rows
## # ℹ 1 more variable: `Mean_mean(b)` <dbl>

ANOVA dan Asumsinya

1. ANOVA ARI

anova_ari <- aov(
  ARI ~
    factor(n) *
    factor(noise) *
    factor(k),
  data = results
)

cat("Hasil ANOVA ARI: \n")

## Hasil ANOVA ARI:

summary(anova_ari)

##                                      Df Sum Sq Mean Sq   F value Pr(>F)    
## factor(n)                             2    0.3     0.2     76.67 <2e-16 ***
## factor(noise)                         2  696.0   348.0 161044.61 <2e-16 ***
## factor(k)                             2  572.6   286.3 132506.54 <2e-16 ***
## factor(n):factor(noise)               4    0.2     0.1     27.54 <2e-16 ***
## factor(n):factor(k)                   4    0.1     0.0     10.20  3e-08 ***
## factor(noise):factor(k)               4   78.6    19.7   9095.19 <2e-16 ***
## factor(n):factor(noise):factor(k)     8    0.4     0.1     23.62 <2e-16 ***
## Residuals                         26973   58.3     0.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\n ", rep("=",80), "\n Partial eta squared: \n", sep = "")

## 
##  ================================================================================
##  Partial eta squared:

eta_squared(anova_ari, partial = TRUE)

## # Effect Size for ANOVA (Type I)
## 
## Parameter                         | Eta2 (partial) |       95% CI
## -----------------------------------------------------------------
## factor(n)                         |       5.65e-03 | [0.00, 1.00]
## factor(noise)                     |           0.92 | [0.92, 1.00]
## factor(k)                         |           0.91 | [0.91, 1.00]
## factor(n):factor(noise)           |       4.07e-03 | [0.00, 1.00]
## factor(n):factor(k)               |       1.51e-03 | [0.00, 1.00]
## factor(noise):factor(k)           |           0.57 | [0.57, 1.00]
## factor(n):factor(noise):factor(k) |       6.96e-03 | [0.01, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

Uji Asumsi ANOVA ARI

plot(anova_ari)

2. Silhoutte

anova_sil <- aov(
  Mean_Silhouette ~
    factor(n) *
    factor(noise) *
    factor(k),
  data = results
)

cat("Hasil ANOVA Silhoutte: \n")

## Hasil ANOVA Silhoutte:

summary(anova_sil)

##                                      Df Sum Sq Mean Sq   F value Pr(>F)    
## factor(n)                             2    1.3    0.63   1604.49 <2e-16 ***
## factor(noise)                         2  536.3  268.13 678998.89 <2e-16 ***
## factor(k)                             2   70.2   35.10  88889.59 <2e-16 ***
## factor(n):factor(noise)               4    0.2    0.05    123.65 <2e-16 ***
## factor(n):factor(k)                   4    0.8    0.20    508.60 <2e-16 ***
## factor(noise):factor(k)               4   35.4    8.85  22419.64 <2e-16 ***
## factor(n):factor(noise):factor(k)     8    0.0    0.01     13.35 <2e-16 ***
## Residuals                         26973   10.7    0.00                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\n ", rep("=",80), "\n Partial eta squared: \n", sep = "")

## 
##  ================================================================================
##  Partial eta squared:

eta_squared(anova_sil, partial = TRUE)

## # Effect Size for ANOVA (Type I)
## 
## Parameter                         | Eta2 (partial) |       95% CI
## -----------------------------------------------------------------
## factor(n)                         |           0.11 | [0.10, 1.00]
## factor(noise)                     |           0.98 | [0.98, 1.00]
## factor(k)                         |           0.87 | [0.87, 1.00]
## factor(n):factor(noise)           |           0.02 | [0.02, 1.00]
## factor(n):factor(k)               |           0.07 | [0.07, 1.00]
## factor(noise):factor(k)           |           0.77 | [0.77, 1.00]
## factor(n):factor(noise):factor(k) |       3.94e-03 | [0.00, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

Uji Asumsi ANOVA Silhoutte

plot(anova_sil)

Plot

# Mengubah tipe data beberapa variabel sehingga dapat divisualisasikan
results <- results %>%
  mutate(
    n = factor(n),
    noise = factor(noise),
    k = factor(k)
  )

Box-plot dan lince chart pengaruh ukuran sampel terhadap ARI dan Silhoutte

Boxplot

ggplot(results,
       aes(x = n,
           y = ARI)) +
  geom_boxplot() +
  labs(
    x = "Ukuran Sampel",
    y = "ARI",
    title = "Distribusi ARI Berdasarkan Ukuran Sampel"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/1.png", width = 8, height = 6, dpi = 300)

Silhoutte

ggplot(results,
       aes(x = n,
           y = Mean_Silhouette)) +
  geom_boxplot() +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(Silhouette)),
    title = "Distribusi Mean Silhouette Berdasarkan Ukuran Sampel"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/2.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(n) %>%
  summarise(
    Mean_ARI = mean(ARI)
  ) %>%
  ggplot(
    aes(
      x = n,
      y = Mean_ARI,
      group = 1
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(ARI)),
    title = "Rata-rata ARI Berdasarkan Ukuran Sampel"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/3.png", width = 8, height = 6, dpi = 300)

Silhouette

results %>%
  group_by(n) %>%
  summarise(
    Mean_mean_Silhoutte = mean(Mean_Silhouette)
  ) %>%
  ggplot(
    aes(
      x = n,
      y = Mean_mean_Silhoutte,
      group = 1
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(bar(Silhouette))),
    title = expression(bold(paste(bar(bar(Silhouette))," Berdasarkan Ukuran Sampel")))
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5))

ggsave("C:/Users/LENOVO/Documents/Output R/4.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(n) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b)
  )

## # A tibble: 3 × 3
##   n     Mean_mean_a Mean_mean_b
##   <fct>       <dbl>       <dbl>
## 1 45           3.15        7.56
## 2 180          3.18        7.50
## 3 450          3.20        7.48

Box-plot dan line chart pengaruh tingkat noise terhadap ARI dan Silhoutte

Box-plot

ggplot(results,
       aes(x = noise,
           y = ARI)) +
  geom_boxplot() +
  labs(
    x = "Tingkat Noise",
    y = "ARI",
    title = "Distribusi ARI Berdasarkan Tingkat Noise"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/5.png", width = 8, height = 6, dpi = 300)

Silhoutte

ggplot(results,
       aes(x = noise,
           y = Mean_Silhouette)) +
  geom_boxplot() +
  labs(
    x = "Tingkat Noise",
    y = expression(bar(Silhouette)),
    title = "Distribusi Mean Silhouette Berdasarkan Tingkat Noise"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/6.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(noise) %>%
  summarise(
    Mean_ARI = mean(ARI)
  ) %>%
  ggplot(
    aes(
      x = noise,
      y = Mean_ARI,
      group = 1
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Tingkat Noise",
    y = expression(bar(ARI)),
    title = "Rata-rata ARI Berdasarkan Tingkat Noise"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/7.png", width = 8, height = 6, dpi = 300)

Silhoutte

results %>%
  group_by(noise) %>%
  summarise(
    Mean_mean_Silhoutte = mean(Mean_Silhouette)
  ) %>%
  ggplot(
    aes(
      x = noise,
      y = Mean_mean_Silhoutte,
      group = 1
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Tingkat Noise",
    y = expression(bar(bar(Silhouette))),
    title = expression(bold(paste(bar(bar(Silhouette))," Berdasarkan Tingkat Noise")))
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5))

ggsave("C:/Users/LENOVO/Documents/Output R/8.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(noise) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b)
  )

## # A tibble: 3 × 3
##   noise Mean_mean_a Mean_mean_b
##   <fct>       <dbl>       <dbl>
## 1 0.5          1.56        6.86
## 2 1.5          3.08        7.18
## 3 3            4.90        8.50

Box-plot dan lince chart pengaruh jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-plot

ggplot(results,
       aes(x = k,
           y = ARI)) +
  geom_boxplot() +
  labs(
    x = "Jumlah Klaster",
    y = "ARI",
    title = "Distribusi ARI Berdasarkan Jumlah Klaster Algoritma K-Means"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/9.png", width = 8, height = 6, dpi = 300)

silhoutte

ggplot(results,
       aes(x = k,
           y = Mean_Silhouette)) +
  geom_boxplot() +
  labs(
    x = "Jumlah Klaster",
    y = expression(bar(Silhouette)),
    title = "Distribusi Mean Silhouette Berdasarkan Jumlah Klaster Algoritma K-means"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/10.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(k) %>%
  summarise(
    Mean_ARI = mean(ARI)
  ) %>%
  ggplot(
    aes(
      x = k,
      y = Mean_ARI,
      group = 1
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Jumlah Klaster",
    y = expression(bar(ARI)),
    title = "Rata-rata ARI Berdasarkan Jumlah Klaster Algoritma K-Means"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/11.png", width = 8, height = 6, dpi = 300)

silhoutte

results %>%
  group_by(k) %>%
  summarise(
    Mean_mean_Silhoutte = mean(Mean_Silhouette)
  ) %>%
  ggplot(
    aes(
      x = k,
      y = Mean_mean_Silhoutte,
      group = 1
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Jumlah Klaster",
    y = expression(bar(bar(Silhouette))),
    title = expression(bold(paste(bar(bar(Silhouette))," Berdasarkan Jumlah Klaster Algoritma K-Means")))
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5))

ggsave("C:/Users/LENOVO/Documents/Output R/12.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(k) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b)
  )

## # A tibble: 3 × 3
##   k     Mean_mean_a Mean_mean_b
##   <fct>       <dbl>       <dbl>
## 1 2            4.35        9.21
## 2 3            2.73        7.50
## 3 4            2.45        5.83

Box-plot dan lince chart pengaruh interaksi antara ukuran sampel dan tingkat noise terhadap ARI dan Silhoutte

Box-plot

ggplot(results,
       aes(x = n,
           y = ARI,
           fill = noise)) +
  geom_boxplot() +
  labs(
    x = "Ukuran Sampel",
    y = "ARI",
    title = "Distribusi ARI Berdasarkan Ukuran Sampel dan Tingkat Noise"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/13.png", width = 8, height = 6, dpi = 300)

Silhoutte

ggplot(results,
       aes(x = n,
           y = Mean_Silhouette,
           fill = noise)) +
  geom_boxplot() +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(Silhouette)),
    title = "Distribusi Mean Silhouette Berdasarkan Ukuran Sampel dan Tingkat Noise"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/14.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(n, noise) %>%
  summarise(
    Mean_ARI = mean(ARI)
  ) %>%
  ggplot(
    aes(
      x = n,
      y = Mean_ARI,
      group = noise,
      colour = noise
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(ARI)),
    title = "Rata-rata ARI Berdasarkan Interaksi Ukuran Sampel dan Tingkat Noise"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/15.png", width = 8, height = 6, dpi = 300)

Silhoutte

results %>%
  group_by(n, noise) %>%
  summarise(
    Mean_mean_Silhoutte = mean(Mean_Silhouette)
  ) %>%
  ggplot(
    aes(
      x = n,
      y = Mean_mean_Silhoutte,
      group = noise,
      colour = noise
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(bar(Silhouette))),
    title = expression(bold(paste(bar(bar(Silhouette))," Interaksi Ukuran Sampel dan Tingkat Noise")))
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5))

ggsave("C:/Users/LENOVO/Documents/Output R/16.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(n, noise) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b),
    .groups = 'drop'
  )

## # A tibble: 9 × 4
##   n     noise Mean_mean_a Mean_mean_b
##   <fct> <fct>       <dbl>       <dbl>
## 1 45    0.5          1.56        6.87
## 2 45    1.5          3.06        7.22
## 3 45    3            4.84        8.58
## 4 180   0.5          1.55        6.85
## 5 180   1.5          3.08        7.16
## 6 180   3            4.92        8.48
## 7 450   0.5          1.55        6.85
## 8 450   1.5          3.09        7.15
## 9 450   3            4.95        8.45

Box-plot dan lince chart pengaruh interaksi antara tingkat noise dan jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-plot

ggplot(results,
       aes(x = noise,
           y = ARI,
           fill = k)) +
  geom_boxplot() +
  labs(
    x = "Tingkat Noise",
    y = "ARI",
    title = "Distribusi ARI Berdasarkan Tingkat Noise dan Jumlah Klaster K-Means"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/17.png", width = 8, height = 6, dpi = 300)

Silhoutte

ggplot(results,
       aes(x = noise,
           y = Mean_Silhouette,
           fill = k)) +
  geom_boxplot() +
  labs(
    x = "Tingkat Noise",
    y = expression(bar(Silhouette)),
    title = "Distribusi Mean Silhoutte Berdasarkan Tingkat Noise dan Jumlah Klaster"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/18.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(noise, k) %>%
  summarise(
    Mean_ARI = mean(ARI)
  ) %>%
  ggplot(
    aes(
      x = noise,
      y = Mean_ARI,
      group = k,
      colour = k
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Tingkat Noise",
    y = expression(bar(ARI)),
    title = "Rata-rata ARI Berdasarkan Interaksi Tingkat Noise dan Jumlah Klaster"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/19.png", width = 8, height = 6, dpi = 300)

Silhoutte

results %>%
  group_by(noise, k) %>%
  summarise(
    Mean_mean_Silhoutte = mean(Mean_Silhouette)
  ) %>%
  ggplot(
    aes(
      x = noise,
      y = Mean_mean_Silhoutte,
      group = k,
      colour = k
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Tingkat Noise",
    y = expression(bar(bar(Silhouette))),
    title = expression(bold(paste(bar(bar(Silhouette))," Interaksi Tingkat Noise dan Jumlah Klaster K-Means")))
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5))

ggsave("C:/Users/LENOVO/Documents/Output R/20.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(noise, k) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b),
    .groups = 'drop'
  )

## # A tibble: 9 × 4
##   noise k     Mean_mean_a Mean_mean_b
##   <fct> <fct>       <dbl>       <dbl>
## 1 0.5   2           2.97         8.60
## 2 0.5   3           0.886        7.01
## 3 0.5   4           0.811        4.96
## 4 1.5   2           4.20         8.85
## 5 1.5   3           2.64         7.14
## 6 1.5   4           2.40         5.54
## 7 3     2           5.88        10.2 
## 8 3     3           4.67         8.35
## 9 3     4           4.15         6.98

Box-plot dan lince chart pengaruh interaksi antara ukuran sampel dan jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-Plot

ggplot(results,
       aes(x = n,
           y = ARI,
           fill = k)) +
  geom_boxplot() +
  labs(
    x = "Ukuran Sampel",
    y = "ARI",
    title = "Distribusi ARI Berdasarkan Ukuran Sampel dan Jumlah Klaster K-Means"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/21.png", width = 8, height = 6, dpi = 300)

Silhoutte

ggplot(results,
       aes(x = n,
           y = Mean_Silhouette,
           fill = k)) +
  geom_boxplot() +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(Silhouette)),
    title = "Distribusi Mean Silhouette Berdasarkan Ukuran Sampel dan Jumlah Klaster"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/22.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(n, k) %>%
  summarise(
    Mean_ARI = mean(ARI)
  ) %>%
  ggplot(
    aes(
      x = n,
      y = Mean_ARI,
      group = k,
      colour = k
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(ARI)),
    title = "Rata-rata ARI Berdasarkan Interaksi Ukuran Sampel dan Jumlah Klaster"
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5, face = 'bold'))

ggsave("C:/Users/LENOVO/Documents/Output R/23.png", width = 8, height = 6, dpi = 300)

Silhoutte

results %>%
  group_by(n, k) %>%
  summarise(
    Mean_mean_Silhoutte = mean(Mean_Silhouette)
  ) %>%
  ggplot(
    aes(
      x = n,
      y = Mean_mean_Silhoutte,
      group = k,
      colour = k
    )
  ) +
  geom_line() +
  geom_point(size = 3) +
  labs(
    x = "Ukuran Sampel",
    y = expression(bar(bar(Silhouette))),
    title = expression(bold(paste(bar(bar(Silhouette))," Interaksi Ukuran Sampel dan Jumlah Klaster K-Means")))
  ) +
  theme_classic() +
  theme(plot.title = element_text(hjust = 0.5))

ggsave("C:/Users/LENOVO/Documents/Output R/24.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(n, k) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b),
    .groups = 'drop'
  )

## # A tibble: 9 × 4
##   n     k     Mean_mean_a Mean_mean_b
##   <fct> <fct>       <dbl>       <dbl>
## 1 45    2            4.34        9.28
## 2 45    3            2.72        7.52
## 3 45    4            2.40        5.87
## 4 180   2            4.35        9.19
## 5 180   3            2.74        7.49
## 6 180   4            2.47        5.81
## 7 450   2            4.35        9.16
## 8 450   3            2.75        7.49
## 9 450   4            2.50        5.79

Box-plot dan lince chart pengaruh interaksi antara ukuran sampel, noise, dan jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-Plot

ggplot(results,
       aes(x = n, 
           y = ARI, 
           fill = k)) +      
  geom_boxplot(outlier.size = 1, alpha = 0.8) +
  # Memisahkan panel berdasarkan tingkat Noise
  facet_wrap(~ noise, labeller = label_both) + 
  labs(
    x = "Ukuran Sampel (n)",
    y = "ARI",
    fill = "Jumlah Klaster (k)",
    title = "Distribusi ARI berdasarkan Ukuran Sampel, Tingkat Noise, dan Jumlah Klaster"
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = 0.5, face = 'bold', size = 12),
    strip.text = element_text(face = 'bold', size = 10), 
    legend.position = "bottom" 
  )

ggsave("C:/Users/LENOVO/Documents/Output R/25.png", width = 8, height = 6, dpi = 300)

Silhoutte

ggplot(results,
       aes(x = n, 
           y = Mean_Silhouette, 
           fill = k)) +      
  geom_boxplot(outlier.size = 1, alpha = 0.8) +
  # Memisahkan panel berdasarkan tingkat Noise
  facet_wrap(~ noise, labeller = label_both) + 
  labs(
    x = "Ukuran Sampel (n)",
    y = expression(bar(bar(Silhouette))),
    fill = "Jumlah Klaster (k)",
    title = expression(bold(paste("Distribusi ", bar(bar(Silhouette)), " berdasarkan Ukuran Sampel, Tingkat Noise, dan Jumlah Klaster")))
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = 0.5, face = 'bold', size = 12),
    strip.text = element_text(face = 'bold', size = 10), 
    legend.position = "bottom" 
  )

ggsave("C:/Users/LENOVO/Documents/Output R/26.png", width = 8, height = 6, dpi = 300)

Line Chart

results %>%
  group_by(n, noise, k) %>%
  summarise(
    Mean_ARI = mean(ARI),
    .groups = "drop"
  ) %>%

  ggplot(
    aes(
      x = n,
      y = Mean_ARI,
      group = k,
      color = k
    )
  ) +
  geom_line(linewidth = 1) +
  geom_point(size = 3) +
  # Memisahkan grafik berdasarkan tingkat Noise
  facet_wrap(~ noise, labeller = label_both) + 
  labs(
    x = "Ukuran Sampel (n)",
    y = expression(bar(ARI)),
    color = "Jumlah Klaster (k)",
    title = expression(bold(paste("Interaksi n, Noise, dan Jumlah Klaster terhadap ", bar(ARI))))
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = 0.5, face = 'bold', size = 12),
    strip.text = element_text(face = 'bold', size = 10) # Menebalkan judul panel noise
  )

ggsave("C:/Users/LENOVO/Documents/Output R/27.png", width = 8, height = 6, dpi = 300)

Silhoutte

results %>%
  group_by(n, noise, k) %>%
  summarise(
    Mean_Sil = mean(Mean_Silhouette),
    .groups = "drop"
  ) %>%

  ggplot(
    aes(
      x = n,
      y = Mean_Sil,
      group = k,
      color = k
    )
  ) +
  geom_line(linewidth = 1) +
  geom_point(size = 3) +
  # Memisahkan grafik berdasarkan tingkat Noise
  facet_wrap(~ noise, labeller = label_both) + 
  labs(
    x = "Ukuran Sampel (n)",
    y = expression(bar(bar(Silhouette))),
    color = "Jumlah Klaster (k)",
    title = expression(bold(paste("Interaksi n, Noise, dan Jumlah Klaster terhadap ", bar(bar(Silhouette)))))
  ) +
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = 0.5, face = 'bold', size = 12),
    strip.text = element_text(face = 'bold', size = 10) # Menebalkan judul panel noise
  )

ggsave("C:/Users/LENOVO/Documents/Output R/28.png", width = 8, height = 6, dpi = 300)

# Tabel Ringkasan
results %>%
  group_by(n, noise, k) %>%
  summarise(
    Mean_mean_a = mean(Mean_a),
    Mean_mean_b = mean(Mean_b),
    .groups = 'drop'
  )

## # A tibble: 27 × 5
##    n     noise k     Mean_mean_a Mean_mean_b
##    <fct> <fct> <fct>       <dbl>       <dbl>
##  1 45    0.5   2           2.99         8.62
##  2 45    0.5   3           0.886        7.01
##  3 45    0.5   4           0.797        4.97
##  4 45    1.5   2           4.18         8.91
##  5 45    1.5   3           2.64         7.15
##  6 45    1.5   4           2.36         5.59
##  7 45    3     2           5.84        10.3 
##  8 45    3     3           4.63         8.39
##  9 45    3     4           4.04         7.06
## 10 180   0.5   2           2.96         8.59
## # ℹ 17 more rows

Pengaruh Kualitas Data Terhadap Kualitas Clustering

Tsalis Ainur Rofi

2026-06-04

Package yang diperlukan

Fungsi Pembangkit Data

Fungsi menghitung parameter alpha dan beta Silhoutte

Fungsi Setiap Replikasi Dalam Kombinasi Simulasi Tertentu

Desain Simulasi

Simulasi Monte Carlo

Data Hasil Simulasi

Data Ringkasan Kombinasi

ANOVA dan Asumsinya

1. ANOVA ARI

Uji Asumsi ANOVA ARI

2. Silhoutte

Uji Asumsi ANOVA Silhoutte

Plot

Box-plot dan lince chart pengaruh ukuran sampel terhadap ARI dan Silhoutte

Boxplot

Line Chart

Box-plot dan line chart pengaruh tingkat noise terhadap ARI dan Silhoutte

Box-plot

Line Chart

Box-plot dan lince chart pengaruh jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-plot

Line Chart

Box-plot dan lince chart pengaruh interaksi antara ukuran sampel dan tingkat noise terhadap ARI dan Silhoutte

Box-plot

Line Chart

Box-plot dan lince chart pengaruh interaksi antara tingkat noise dan jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-plot

Line Chart

Box-plot dan lince chart pengaruh interaksi antara ukuran sampel dan jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-Plot

Line Chart

Box-plot dan lince chart pengaruh interaksi antara ukuran sampel, noise, dan jumlah klaster pada algoritma K-Means terhadap ARI dan Silhoutte

Box-Plot

Line Chart